The mass defect of the oxygen nucleus is 16 8o 816o. the mass of neutral 16 8o 816o is equal to 15.994914 atomic mass units
8(1.008665)+8(1.007825)
=16.13192
16.13192-15.994914
=.13701 amu
The atomic nucleus is a small, dense region made up of protons and neutrons at the center of an atom, discovered by Ernest Rutherford in 1911, based on Geiger-Marsden's gold leaf experiment in 1909. After the discovery of the neutron in 1932, models of the nucleus composed of protons and neutrons were rapidly developed by Dmitri Ivanenko[1] and Werner Heisenberg. I was.
The cell nucleus carries genes, structures that control and regulate cell activity (such as growth and metabolism) and contain genetic information. Nucleoli are small bodies commonly found within the nucleus. The nucleoplasm is the gel-like matrix in which the core components are suspended.
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How many oxygen (O) atoms would a carbon (C) atom need to bond with to form a stable compound?
A.3
B.4
C.1
D.2
Beryllium hydrogen carbonate is more than 3% hydrogen by mass.
True
False
which reactant (fe3 and scn-) is in excess and which is limiting? what is the purpose of making one reactant in excess? (connect to le chatelier's principle ) how will you know the concentration of fe(scn)2
Making both reactants in excess and the concentration of Fe(SCN)* can be determined, Making FeSt in excess and SCN as the limiting reactant and the concentration of Fe(SCN)* will be equal to the concenation of SCN.
A reagent, sometimes known as an analytical reagent, in chemistry is a substance or compound supplied to a system to either initiate a chemical reaction or test whether one happens. Although the terms "reactant" and "reagent" are not frequently used interchangeably, "reactant" refers to a material that is consumed during a chemical reaction. The anion [SCN] is thiocyanate. Thiocyanic acid's conjugate base is it. The colorless compounds potassium thiocyanate and sodium thiocyanate are examples of common derivatives. In the past, pyrotechnics employed mercury(II) thiocyanate. Thiocyanic acid is a hydracid, which is cyanic acid in which the oxygen is substituted by a sulfur atom. SCN is a tiny, very acidic [1] pseudohalide thiolate.
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(b) Explain using physical properties of the gas why ammonia is not collected by downward delivery
Explanation:
★ ᴇxᴘʟᴀɪɴ ᴜꜱɪɴɢ ᴘʜʏꜱɪᴄᴀʟ ᴘʀᴏᴘᴇʀᴛɪᴇꜱ ᴏꜰ ᴛʜᴇ ɢᴀꜱ ᴡʜʏ ᴀᴍᴍᴏɴɪᴀ ɪꜱ ɴᴏᴛ ᴄᴏʟʟᴇᴄᴛᴇᴅ ʙʏ ᴅᴏᴡɴᴡᴀʀᴅ ᴅᴇʟɪᴠᴇʀʏ ★
ΛЛらƜƐ尺 :-
=》ꜱɪɴᴄᴇ ᴀᴍᴍᴏɴɪᴀ ɢᴀꜱ ɪꜱ ʟɪɢʜᴛᴇʀ ᴛʜᴀɴ ᴀɪʀ ᴛʜᴇʀᴇꜰᴏʀᴇ ɪᴛ ɪꜱ ᴄᴏʟʟᴇᴄᴛᴇᴅ ʙʏ ᴅᴏᴡɴᴡᴀʀᴅ ᴅɪꜱᴘʟᴀᴄᴇᴍᴇɴᴛ ᴏꜰ ᴀɪʀ. ᴀᴍᴍᴏɴɪᴀ ɪꜱ ꜱᴏʟᴜʙʟᴇ ɪɴ ᴡᴀᴛᴇʀ ᴛʜᴇʀᴇꜰᴏʀᴇ ᴄᴀɴɴᴏᴛ ʙᴇ ᴄᴏʟʟᴇᴄᴛᴇᴅ ᴏᴠᴇʀ ɪᴛ
a component of John Dalton's atomic
theory?
O. The ratio of atoms in a compound is fixed.
• The atoms of different elements are the same.
O An atom Is a small particle of matter that can be broken down.
• A reaction can create or
destroy atoms as well as
rearrange them
A component of John Dalton's atomic theory is The ratio of atoms in a compound is fixed . Atoms combine in a ratio of small whole numbers to form compounds.
What is Dalton's atomic theory?According to Daltons atomic theory ,all matter, an element, a compound or a mixture is composed of small particles called atoms.
The postulates of this theory are as follows:
(i) All matter is made of tiny particles called atoms.
(ii) Atoms are indivisible particles which cant be created or destroyed in a chemical reaction.
(iii) Atoms of a given element are identical in mass and chemical properties.
(iv) Atoms of different elements have different masses and chemical properties.
(v) Atoms combine in ratio of small whole numbers to form compounds.
(vi) Atoms can neither be created nor be destroyed
Only statement 1 is correct from the given options.
Statement 2 , 3 and 4 in the given options are wrong.
Atoms of different elements are different, and not sameAtoms are indivisible and cannot be broken downAtoms cannot be created or destroyedLearn more about Dalton's atomic theory at
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The percent composition of a compound was found to be 63.5% silver, 8.2 %
nitrogen, and 28.3 % oxygen. Determine the compound's empirical formula.
Considering the definition of empirical formula, the empirical formula is Ag₁N₁O₃= AgNO₃.
Definition of empirical formulaThe empirical formula is the simplest expression to represent a chemical compound, which indicates the elements that are present and the minimum proportion in whole numbers that exist between its atoms, that is, the subscripts of chemical formulas are reduced to the most integers. small as possible.
Empirical formula in this caseAssuming a 100 grams sample, the percentages match the grams in the sample. So you have 63.5 grams of silver, 8.2 grams of nitrogen and 28.3 grams of oxygen.
Then it is possible to calculate the number of moles of each atom in the molecule, taking into account the corresponding molar mass:
Silver: \(\frac{63.5 g}{107.87 \frac{g}{mole} } =\)0.588 moles
Nitrogen: \(\frac{8.2 g}{14 \frac{g}{mole} } =\) 0.586 moles
Oxygen: \(\frac{28.3 g}{16 \frac{g}{mole} } =\)1.77 moles
The empirical formula must be expressed using whole number relationships, for this the numbers of moles are divided by the smallest result of those obtained. In this case:
Silver: \(\frac{0.588 moles}{0.586 moles}\)≅ 1
Nitrogen: \(\frac{0.586 moles}{0.586 moles}\)= 1
Oxygen: \(\frac{1.77 moles}{0.586 moles}\)≅ 3
Therefore the Ag: N: O mole ratio is 1: 1: 3
Finally, the empirical formula is Ag₁N₁O₃= AgNO₃.
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How many feet are in i yard
Answer:
3 feet is in one yard, which is 36 inches.
CsH16 +12028CO2 +8H₂O
What is the ratio of octene (C8H16) to
oxygen in the reaction?
The ratio of octene to oxygen is 1:12.
To determine the ratio of octene (C8H16) to oxygen (O2) in the given reaction, we need to examine the balanced chemical equation. However, the equation you provided does not seem to be balanced. The coefficients for each compound must be determined to achieve a balanced equation before we can calculate the desired ratio.
Assuming you meant the combustion reaction of octene, a balanced equation would be:
C8H16 + 12O2 → 8CO2 + 8H2O
From the balanced equation, we can see that for every 1 mole of octene (C8H16), we require 12 moles of oxygen (O2) to completely react.
This means that for every 1 mole of octene, we need 12 moles of oxygen to fully combust the octene and produce the corresponding amounts of carbon dioxide (CO2) and water (H2O) as shown in the balanced equation.
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on what bases are the elements of periodic table classified?
The elements can also be classified into the main-group elements (or representative elements) in the columns labeled 1, 2, and 13–18; the transition metals in the columns labeled 3–12; and inner transition metals in the two rows at the bottom of the table (the top-row elements are called lanthanides and the bottom-row ...
Hello,
What are Elements?Elements are a group of the Periodic Table that shares common valence electron structures. They are arranged in order of increasing Atomic Number.
Now back to the question:-In modern periodic table they are classified into three parts- metals, non-metals and metalloids.
In detail:-
• Metals- Metals are those elements which donate electrons. Ex- Na, K, Rb, Mg, Ca, etc.
• Non-metals- Non-metals are those elements which accept electrons. Ex- N, O, F, Cl, etc .
• Metalloids- Metalloids are those elements which show property of both metals and non-metals. Ex- B, Si, Ge, etc.
Hope it helps...
(by Benjemin)
a sealed flask initially contains pure nitrogen dioxide gas (no2). over time, the nitrogen dioxide forms dinitrogen tetroxide gas (n2o4). the graph below shows the relative amounts of (no2) and (n2o4) over time. what is true about the time indicated by the blue arrow? a. no2 molecules are no longer reacting to form n2o4 molecules. b. the reactant has been used up so the reaction can no longer proceed. c. the rate of the forward reaction (n2o4 formation) is equal to the rate of the reverse reaction (no2 formation). d. the activation energy required for the reaction to occur has been used up.
Based on the given information, the true statement about the time indicated by the blue arrow is: (c) The rate of the forward reaction (N₂O₄ formation) is equal to the rate of the reverse reaction (NO₂ formation).
The graph shows the relative amounts of NO₂ and N₂O₄ over time, and the point indicated by the blue arrow represents a state of equilibrium. In an equilibrium state, the forward and reverse reactions occur at equal rates.
The concentrations of NO₂ and N₂O₄ reach a constant value, indicating that the conversion of NO₂ to N₂O₄ and the conversion of N₂O₄ to NO₂ are occurring at the same rate.
Option a suggests that NO₂ molecules are no longer reacting, which is incorrect as the reaction is still ongoing at equilibrium. Option b suggests that the reactant has been completely used up, which is not the case in an equilibrium state. Option d refers to the activation energy, which is unrelated to the equilibrium state. Therefore, option c is the correct choice.
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a 0.478 g sample of a compound containing only c and h was burned in an attempt to determine its simplest formula. 1.50 g of co2 and 0.615 g of h2o were collected. find the simplest formula for the compound.
The simplest formula for the compound is \(CO_{2}\) if a 0.478g sample of the compound was burned.
The simplest formula can be termed as the imperial formula which can be determined by using the molar mass to convert the mass of each element to moles. Then each mole value is divided by the smallest calculated number of moles.
First, we find the number of moles of carbon, hydrogen, and oxygen as follows;
Mass of carbon = 1.50 × (12/44) = 0.41 g
Number of moles of carbon = 0.41 / 12 = 0.034 moles
Mass of hydrogen = 0.615 × (2/18) = 0.068 g
Number of moles of hydrogen = 0.068 / 1 = 0.068 moles
Mass of oxygen = 0.478 - (0.41g + 0.068g) = 0 g
Number of moles of oxygen = 0 moles
Now we divide the calculated number of moles of carbon and hydrogen by the smallest calculated number of moles which in this case is of carbon.
Carbon: 0.034 ÷ 0.034 = 1
Oxygen: 0.068 ÷ 0.034 = 2
Therefore, the simplest formula for the compound is determined to be \(CO_{2}\)
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ignoring activity effects, find the concentration of nh3(aq) if the ph is fixed at 9.25
To find the concentration of nh3(aq) if the pH is fixed at 9.25, we need to use the equilibrium constant expression for the reaction of NH3 with water:
NH3 + H2O ⇌ NH4+ + OH-
The equilibrium constant expression for this reaction is:
Kw/Kb = [NH4+][OH-]/[NH3]
Where Kw is the ion product constant of water (1.0 x 10^-14) and Kb is the base dissociation constant of NH3. At a pH of 9.25, the pOH is 4.75 and the Kb for NH3 is 1.8 x 10^-5.
Using the equation above and substituting the values, we get:
1.0 x 10^-14/1.8 x 10^-5 = [NH4+][OH-]/[NH3]
Solving for [NH3], we get:
[NH3] = [NH4+][OH-]/(1.0 x 10^-14/1.8 x 10^-5)
At a pH of 9.25, the [NH4+] concentration can be calculated using the equation:
pH = pKa + log([NH4+]/[NH3])
The pKa of NH4+ is 9.24.
Substituting the values and solving for [NH4+], we get:
9.25 = 9.24 + log([NH4+]/[NH3])
log([NH4+]/[NH3]) = 0.01
[NH4+]/[NH3] = 1.02
Substituting this value in the expression for [NH3], we get:
[NH3] = (1.02)(1.0 x 10^-14/1.8 x 10^-5)
[NH3] = 5.67 x 10^-10 M
Therefore, the concentration of NH3 in the solution is 5.67 x 10^-10 M if the pH is fixed at 9.25.
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The equation shows reactants to a neutralization reaction.
ca2 + oh– arrow h+ no-
which describes what will happen to the h when these reactants form products?
a. h binds with no to make a salt.
b. h binds with ca2 to make an acid.
c. h binds with oh– to make water.
d. h binds with ca2 to make a base.
The equation shows reactants to a neutralization reaction.
Ca²⁺ + OH⁻ → H⁺ + NO⁻. Here H binds with OH⁻ to make water. So the option c is correct.
As the answer to the question is cleared from these reactions. Firstly calcium hydroxide combines with nitric acid to form the products as follows;
Ca(OH)₂ + 2HNO₃ → Ca(NO₃)₂ + 2H₂O
Now the reaction between ionic species will be as follows
Ca²⁺ + 2OH⁻ + 2H⁺ + 2NO₃⁻ → Ca²⁺ + 2NO₃⁻ + 2H₂O
Hence OH⁻ combines with H⁺ to make H₂O(water)
OH⁻ + H⁺ → H₂O
H⁺ binds with OH⁻ to make water
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a compound was analyzed and found to contain 13.5 grams calcium, 10.8 grams oxygen, and 0.675 grams of hydrogen. what is the empirical formula for the compound?
The empirical formula for the compound is Ca(OH)₂.
To determine the empirical formula of the compound, we need to find the simplest whole-number ratio of the elements present. We can do this by calculating the number of moles of each element and then finding the ratio between them.
Mass of calcium (Ca) = 13.5 grams
Mass of oxygen (O) = 10.8 grams
Mass of hydrogen (H) = 0.675 grams
First, we need to convert the masses of each element to moles using their respective atomic masses.
Atomic mass of Ca = 40.08 g/mol
Atomic mass of O = 16.00 g/mol
Atomic mass of H = 1.01 g/mol
Number of moles of Ca = 13.5 g / 40.08 g/mol = 0.3367 mol
Number of moles of O = 10.8 g / 16.00 g/mol = 0.675 mol
Number of moles of H = 0.675 g / 1.01 g/mol = 0.6693 mol
Next, we need to find the simplest whole-number ratio by dividing the number of moles of each element by the smallest number of moles obtained.
Dividing by 0.3367 (smallest value):
Number of moles of Ca = 0.3367 mol / 0.3367 mol = 1
Number of moles of O = 0.675 mol / 0.3367 mol = 2.005
Number of moles of H = 0.6693 mol / 0.3367 mol = 1.988
Rounding these values to the nearest whole number, we have:
Number of moles of Ca = 1
Number of moles of O = 2
Number of moles of H = 2
Thus, the empirical formula of the compound is Ca(OH)₂.
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What is the largest limiting factor that keeps us
from traveling far away from Earth in space?
Which of the structures shown are examples of the monobrominated compounds (including stereoisomers) produced when 2-propyl-1-pentene is treated with nbs and uv light irradiation?.
The monobrominated compounds produced when 2-propyl-1-pentene is treated with NBS and UV light irradiation are the compounds that contain a bromine atom bonded to a single carbon atom within the 2-propyl-1-pentene molecule.
When 2-propyl-1-pentene undergoes bromination using NBS (N-bromosuccinimide) and UV light, the reaction occurs via a radical mechanism. This leads to the substitution of a hydrogen atom with a bromine atom, resulting in the formation of monobrominated compounds.
To determine the specific monobrominated compounds and their stereoisomers, it is necessary to analyze the structure of 2-propyl-1-pentene and consider the possible sites of bromination. 2-propyl-1-pentene has multiple carbon atoms that could potentially undergo bromination, leading to different structural isomers.
By introducing a bromine atom at various positions within the 2-propyl-1-pentene molecule, different monobrominated compounds can be formed. These compounds may exhibit stereoisomerism if there are chiral centers present in the original molecule.
To provide a comprehensive answer, the specific structures of the monobrominated compounds and their stereoisomers resulting from the reaction would need to be analyzed and described.
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In the compound NH3, how are the atoms likely bonded to one another?
(1 point)
O Nitrogen shares one electron with each hydrogen.
O Each hydrogen shares two electrons with nitrogen.
O Each hydrogen donates its one electron to nitrogen.
O Nitrogen donates one electron to each hydrogen.
Answer
b
Explanation:
because I took the test
Each hydrogen shares two electrons with nitrogen.
NH3 is a molecular compound. In molecular compounds, electrons are shared between the bonding atoms in a covalent bond. The number of electrons shared between atoms depends on the respective valencies of the combining atoms.
Nitrogen has a valency of three and hydrogen has a valency of one. Therefore, in NH3, each hydrogen shares two electrons with nitrogen.
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Draw the Lewis dot structure for the compound gallium oxide with the chemical formula Ga2O3
Answer:
Refer to your periodic table. Lewis dot structures are based off the number of valence electrons an atom has.
Looking at the compounds, we can see that Gallium has three valence electrons in its outer shell and oxygen has six. Oxygen and Gallium are going to share electrons with one another, making a V shape in their diagram.
One Oxygen would make a double bond with a Gallium, leaving one valence electron to another oxygen. That oxygen takes that Final electron. It now has 7 in its outer shell. The remaining Gallium and Oxygen do the same double bond as the one before, leaving the 7 valence electron oxygen with one more electron.
The Lewis dot structure of Ga₂O₃ is shown below.
In molecular structure, Lewis structures describe the relationship between molecules' atoms and their lone pairs of electrons. Lewis structures are also used to predict molecular geometry in conjunctions with hybrid orbitals.
Ga₂O₃ is the inorganic compound of gallium (III) oxide. It is a semiconductor with a very wide bandgap. It is widely used in power electronics. It is also used in phosphors and gas sensing.
There are several polymorphs of gallium oxide. The most stable polymorph of gallium oxide is the polymorph of gallium(III)(monoclinic).
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The image for the Lewis dot structure is shown below.
which of the following questions can be answered by science?
Answer:Is Fruit ripening dependent on the type of light exposed to?
Explanation: Because you can test this theory
2. To make the correct volume of stock solution, which should you add first to a volumetric flask, the solid or water? Why?
Answer:
A stock or standard solution is a solution in which you accurately know its concentration. You can make stock solutions in the chemistry laboratory or buy from chemical manufacturers. Once you have a stock solution, you can prepare solutions of lower concentration by diluting the concentrated stock solution.
Explanation:
To make the correct volume of stock solution, we should add first solid to a volumetric flask.
What is stock solution?Stock solution is a standard solution in which exact concentration of solute is present in particular volume. It is mainly used in analytical chemistry during the titration process.
During the preparation of stock solution, we should first add solid in the volumetric flask and then little amount of water to dissolve the solid and then finally add water to the required volume. If we first add total volume and then add solid then dissolution of solid may increase volume.
Hence, first we add solid in the volumetric flask.
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draw the enantiomer of (s)-2-bromo-2-chlorobutane shown below. it may help to use molecular models.
Enantiomers are pairs of compounds with exactly the same connectivity but opposite three-dimensional shapes.
What is a enantiomer?
In chemistry, an enantiomer (also called an optical isomer, enantiomer, or optical antipode) is one of two stereoisomers that are not superimposable on their own mirror image. Enantiomers are similar to the right and left hands and cannot be superimposed when looking at the same face. No amount of reorientation will align the four unique groups (see Chirality (Chemistry)) on the chiral carbons exactly. The number of stereoisomers a molecule has can be determined by the number of chiral carbons it has. Stereoisomers include both enantiomers and diastereomers.
Like enantiomers, diastereomers have the same molecular formula and are not superimposable, but they are not mirror images of each other.
Therefore, Enantiomers are pairs of compounds with exactly the same connectivity but opposite three-dimensional shapes.
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What element blackens when exposed to oxygen?
Answer:
i believe lithium
Explanation: i hope this is right.
24 dm3 of gas is produced when one mole of a Group 2 carbonate is heated.
Determine the relative formula mass of the Group 2 carbonate W.
Use the graph above.
The relative formula mass of the group 2 carbonate W is 41 g/mol.
How to determine relative formula mass?Assuming that the gas produced is measured at standard temperature and pressure (STP), which is 0°C and 1 atmosphere pressure, the volume of one mole of gas is 22.4 dm³.
So if 1 mole of Group 2 carbonate W produces 24 dm³ of gas at STP, then the molar volume of the gas produced is:
24 dm³ / 22.4 dm³/mol = 1.07 mol
This means that one mole of Group 2 carbonate W produces 1.07 moles of gas. Since the gas is most likely carbon dioxide (CO₂) which has a formula mass of 44 g/mol, the relative formula mass of Group 2 carbonate W can be calculated as:
Relative formula mass = Mass of 1 mole of CO₂ / 1.07
Relative formula mass = 44 g/mol / 1.07
Relative formula mass ≈ 41 g/mol
Therefore, the relative formula mass of the Group 2 carbonate W is approximately 41 g/mol.
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The complete question is:
24 dm3 of gas is produced when one mole of a Group 2 carbonate is heated.
Determine the relative formula mass of the Group 2 carbonate W.
Use the graph above.
Calculate the amount of heat that must be absorbed by 10. 0 g of ice at –20°c to convert it to liquid water at 60. 0°c. Given: specific heat (ice) = 2. 1 j/g·°c; specific heat (water) = 4. 18 j/g·°c; δhfus = 6. 0 kj/mol.
The amount of heat to absorb is 6261 J
The heat capacity is the amount of heat expressed usually in Joules or calories needed to change the system by 1 degree Celsius
Here the calculation for heat is
Heat required to raise the temprature of ice form -20°C to 0°C
Then the formula for specific heat is used to calculate the amount of heat
Q = c×m×ΔT
Where Q = heat exchanged by a body
m = mass of the body
c = specific heat
ΔT = change in temprature
Then the given data is
m = 10g
Specific heat of the ice = 2.1
ΔT = 0°C - (-20°C) = 20°C
Then substituting the value
Q = 10g× 2.1× 20°C
Q = 420 J
Heat required to convert 0°C ice to 0°C water
The heat Q necessary to melt a substances depend on its mass m and this called latent heat of fusion of each substances
Q = m×ΔH fusion
Heat required to raise the temprature of water from 0°C to 60°C
m = 10g
Specific heat of water = 4.18
ΔT = 60°C -(- 0°C) = 60°C
Then substituting
Q = 10g×4.18×60°C
Q = 2508 J
Then Q total = 420J+3333J+2508J
Q total = 6261 J
The amount of heat to absorb is 6261 J
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An atom of Bismuth (Bi) having an atomic mass of 209 amu has an atomic numbr of 83. How many neutrons are present in this atom of Bismuth? (show the calculations)
Answer:
There are 126 neutrons in the bismuth atom.
Explanation:
Pre-SolvingWe are given that a Bi atom has an atomic mass of 209 amu and an atomic number of 83.
We want to find how many neutrons the bismuth atom has.
SolvingThe atomic mass of an atom is equal to the mass of the protons + mass of neutrons (n.b. the electrons are part of the mass too, however they are very, very small. Therefore, we tend to count the mass of the electrons as 0 when calculating the atomic mass).
Recall that protons and neutrons both have a mass of about 1 amu.
Also recall that the proton number is also the atomic number. Because of this, the bismuth atom has 83 protons. And since that protons have a mass of about 1 amu, the atomic mass of the protons will be:
83 protons × \(\frac{1 amu}{1 proton}\) = 83 amu
That means that if the atomic mass is 209 amu, it is equal to the proton mass (83 amu) + an unknown mass of neutrons (let's say it is x amu).
As an equation, it will be:
83 + x = 209
Subtract 83 from both sides.
x = 126
This means that the neutrons will weigh 126 amu.
Since every neutron is about 1 amu, the amount of neutrons will be:
126 amu × \(\frac{1 neutron}{1 amu}\) = 126 neutrons
Answer:
126
Explanation:
To calculate for neutron #, subtract atomic # from atomic mass.
t hus 09- 83= 126
true/false: plasticizers are liquids of low volatility which can be lost by diffusion or evaporation as a plastic material ages.
True. Plasticizers are indeed liquids of low volatility that can be lost through diffusion or evaporation as a plastic material ages.
Plasticizers are substances added to plastics to enhance their flexibility, durability, and workability. They are typically low-molecular-weight compounds with a liquid form and have a relatively low boiling point, which makes them volatile. Over time, as plastic materials age and are exposed to various environmental factors such as heat, light, and mechanical stress, the plasticizers can migrate or evaporate out of the plastic matrix.
Diffusion refers to the process of plasticizers gradually moving from areas of high concentration within the plastic to areas of lower concentration. This diffusion can occur both within the plastic material itself and between the plastic and its surrounding environment. Evaporation, on the other hand, involves the direct conversion of the liquid plasticizers into vapor, which can escape into the air.
The loss of plasticizers can have significant effects on the properties of the plastic material. As plasticizers are responsible for increasing flexibility and reducing brittleness, their loss can lead to increased stiffness, decreased elongation, and potential cracking or degradation of the plastic. Therefore, proper selection and monitoring of plasticizers are crucial in ensuring the long-term performance and integrity of plastic materials.
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Drag each characteristic to the correct category. Viruses do not possess all the characteristics of life. Identify those characteristics that viruses display and those they don't display.
Answer:
Virus is living due to reproduction and non-living due to crystal appearance.
Explanation:
Characteristics that viruses display is the ability of reproduction in which they increase in population which is a living character and have DNA or RNA which help them to make exact copies of itself. Virus is parasitic in nature because it causes harm to the living host such as humans, animals and plants. Some characteristics that viruses don't display are that they are not like living cells, have no membrane around them, no organelles such as mitochondria, golgi bodies, endoplasmic reticulum and lysosomes etc. Viruses are present in crystal form outside the cell.
A large fish tank is initially filled with 30 litres of fresh water. You begin to fill the tank by slowly pouring in water with salt concentration of 35 grams per litre (approximate salinity of sea water) at a rate of 2 litres per minute. At the same time, the (perfectly mixed) fluid in the tank is drained from the bottom at a rate of 1 litre per minute. 1. Determine the volume of water in the tank at time t. [1 mark] 2. Let S(t) denote the amount of salt in the fish tank at time t in grams. Show that S(t) satisfies the ODE S
′
(t)=70−
t+30
S
. Write down the appropriate initial condition for the ODE as well. [2 marks] 3. What order is this ODE? Is it linear? Is it separable? [1 mark] 4. Solve the initial value problem to find S(t) using the method of integrating factors. [3 marks] 5. What is the salt concentration in the tank as t→[infinity] ? [1 mark] Part B: Double tanks Next you hook up two fish tanks in a loop so that there is a pipe from tank A to tank B, and also a pipe from tank B back to tank A. Two pumps are added so that you can control the flow rate in each pipe. Initially tank A contains 80 litre of fresh water and tank B 60 litres of fresh water. You begin to pour salt water with concentration 35 grams per litre into tank A at a rate of 2 litres per minute. To keep the tanks from overflowing, you set your pumps so that water is flowing at a constant rate of 4 litres per minute from tank A to tank B, and 2 litre per minute from tank B to tank A. You also put a drain in tank B so that fluid is draining at a rate of 2 litres per minute. 1. Sketch a diagram of the tank setup with arrows for flows entering and leaving each tank. [
1 mark]
2. Let P(t) and Q(t) denote the amount of salt in tank A and tank B respectively. Show that P and Q satisfy a system of ODE's in the form of
P
′
(t)
Q
′
(t)
=c
1
P(t)+c
2
Q(t)+c
3
=c
4
P(t)+c
5
Q(t)
where c
1
,c
2
,c
3
,c
4
and c
5
are constants. Determine the constant c
1
,c
2
,c
3
,c
4
,c
5
and write down appropriate initial conditions. [2 marks] 3. Show that the system of ODE's can be converted into the following second order ODE for P(t) P
′′
(t)=−
60
7
P
′
(t)−
600
1
P(t)+
3
14
State the initial conditions for this ODE. [2 marks] 4. Solve this second order ODE to find P(t), and hence Q(t) as well.
1. The volume of water in the tank at time t is given by the equation
Volume(t) = 30 + t.
2.The appropriate initial condition for the ODE is S(0) = 0, as there is no salt initially in the tank.
3. It is not separable because the variables S(t) and t are not separable on opposite sides of the equation.
4. The solution can be expressed in terms of the integral as:
\(S(t) = (70 * \int e^{(t^{2/2} + 30t)} dt) / e^{(t^{2/2} + 30t)})\)
5. the salt concentration in the tank as t→infinity is zero.
1. To determine the volume of water in the tank at time t, we need to consider the rate at which water is being added and drained. The tank is being filled at a rate of 2 liters per minute and drained at a rate of 1 liter per minute.
Since the tank starts with an initial volume of 30 liters, the volume of water in the tank at time t can be calculated using the equation:
Volume(t) = Initial volume + (Rate of filling - Rate of draining) * t
Volume(t) = 30 + (2 - 1) * t
So, the volume of water in the tank at time t is given by the equation
Volume(t) = 30 + t.
2. Let S(t) denote the amount of salt in the fish tank at time t in grams.
To show that S(t) satisfies the ODE S'(t) = 70 - (t+30)S(t),
we need to take the derivative of S(t) with respect to t and substitute it into the given ODE.
Taking the derivative of S(t), we have:
S'(t) = 0 - (1+0)S(t) + 0
S'(t) = -S(t)
Substituting this into the given ODE, we get:
-S(t) = 70 - (t+30)S(t)
Simplifying the equation, we have:
S'(t) = 70 - (t+30)S(t)
Therefore, S(t) satisfies the ODE S'(t) = 70 - (t+30)S(t).
The appropriate initial condition for the ODE is S(0) = 0,
as there is no salt initially in the tank.
3. This ODE is a first-order linear ordinary differential equation. It is not separable because the variables S(t) and t are not separable on opposite sides of the equation.
4. To solve the initial value problem for S(t) using the method of integrating factors, we first rewrite the ODE in standard form:
S'(t) + (t+30)S(t) = 70
The integrating factor is given by:
\(\mu(t) = e^{(\int (t+30) dt)} = e^{(t^2/2 + 30t)\)
Multiplying both sides of the equation by μ(t), we have:
\(e^{(t^2/2 + 30t)} * S'(t) + e^{(t^2/2 + 30t)} * (t+30)S(t) = 70 * e^{(t^2/2 + 30t)\)
Applying the product rule to the left side of the equation, we get:
\((e^{(t^{2/2} + 30t) * S(t))' = 70 * e^{(t^{2/2} + 30t)})\)
Integrating both sides of the equation with respect to t, we have:
\(\int (e^{(t^2/2 + 30t)} * S(t))' dt = \int (70 * e^{(t^2/2 + 30t))} dt\)
Using the fundamental theorem of calculus, the left side becomes:
\(e^{(t^2/2 + 30t)} * S(t) = \int (70 * e^{(t^2/2 + 30t))} dt\)
Simplifying the right side by integrating, we get:
\(e^{(t^2/2 + 30t)} * S(t) = 70 * \int e^{(t^2/2 + 30t)} dt\)
At this point, the integration of \(e^{(t^2/2 + 30t)\) becomes difficult to express in terms of elementary functions.
Hence, the solution can be expressed in terms of the integral as:
\(S(t) = (70 * \int e^{(t^2/2 + 30t)} dt) / e^{(t^2/2 + 30t)\)
5. As t approaches infinity, the exponential term \(e^{(t^2/2 + 30t)\) becomes very large, causing the salt concentration S(t) to approach zero. Therefore, the salt concentration in the tank as t→infinity is zero.
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The salt concentration in the tank as t approaches infinity is 70/3.
1. To determine the volume of water in the tank at time t, we need to consider the rate at which water is being poured into the tank and the rate at which water is being drained from the bottom.
At a rate of 2 litres per minute, water is being poured into the tank. So after t minutes, the amount of water poured into the tank is 2t litres.
At a rate of 1 litre per minute, water is being drained from the tank. So after t minutes, the amount of water drained from the tank is t litres.
Since the tank was initially filled with 30 litres of fresh water, the volume of water in the tank at time t is given by:
Volume(t) = 30 + 2t - t
Volume(t) = 30 + t
2. Let S(t) denote the amount of salt in the fish tank at time t. To determine the ODE for S(t), we need to consider the salt being poured into the tank and the salt being drained from the tank.
The salt concentration in the water being poured into the tank is 35 grams per litre. So the amount of salt being poured into the tank per minute is 35 * 2 = 70 grams.
The amount of salt being drained from the tank per minute is S(t)/Volume(t) * 1.
Therefore, the ODE for S(t) is:
S'(t) = 70 - S(t)/Volume(t)
The initial condition for this ODE is S(0) = 0, since there was no salt in the tank initially.
3. The ODE S'(t) = 70 - S(t)/Volume(t) is a first-order linear ODE. It is not separable since the variables S(t) and Volume(t) are mixed together.
4. To solve the initial value problem for S(t), we can rewrite the ODE as:
Volume(t) * S'(t) + S(t) = 70 * Volume(t)
This is a linear ODE of the form y'(t) + p(t)y(t) = g(t), where p(t) = 1/Volume(t) and g(t) = 70 * Volume(t).
To solve this type of ODE, we can multiply both sides by an integrating factor, which is the exponential of the integral of p(t).
The integrating factor is exp(integral of 1/Volume(t) dt) = exp(ln(Volume(t))) = Volume(t).
Multiplying both sides of the ODE by the integrating factor, we get:
Volume(t) * S'(t) + S(t) = 70 * Volume(t)
Volume(t) * S'(t) + Volume(t) * S(t) = 70 * Volume(t)^2
( Volume(t) * S(t) )' = 70 * Volume(t)^2
Integrating both sides with respect to t, we get:
Volume(t) * S(t) = 70/3 * Volume(t)^3 + C
S(t) = 70/3 * Volume(t)^2 + C/Volume(t)
Using the initial condition S(0) = 0, we can solve for C:
0 = 70/3 * 30^2 + C/30
C = -70000
Therefore, the solution for S(t) is:
S(t) = 70/3 * Volume(t)^2 - 70000/Volume(t)
5. As t approaches infinity, the volume of water in the tank becomes very large. In this case, we can approximate the volume of the tank as t, since the rate at which water is being poured in is 2 litres per minute. So the salt concentration in the tank as t approaches infinity is given by:
S(t)/Volume(t) = (70/3 * t^2 - 70000/t) / t
As t approaches infinity, the second term (-70000/t) approaches 0, so the salt concentration in the tank as t approaches infinity is:
S(t)/Volume(t) = 70/3 * t^2 / t = 70/3 * t
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5. Simplify 17.9g +4-10 - 21.4g, if possible.
Answer:
-3.5g−6
Explanation:
-3.5g−6
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