2 questions, one for each idea where we can. Answer them, then see which ideas to fix.
Question 1 of 2
The diagram represents the particles in a sealed, rigid container, held at constant temperature, before and after a reaction; the reactants and the product are all gases. Which statement correctly describes what the diagram shows and the resulting entropy change of the system?
Answer and reasoning
AAtoms per molecule increase from 2 to 3, and the entropy of the system increases A student who decides the sign of ΔS from the size of the molecules picks this. Each product molecule does contain 3 atoms, but 6 gas molecules have become 4, and for a reaction between gases the decrease in the number of gas particles is what generally fixes the sign: the entropy decreases.
BGas molecules decrease from 6 to 4, and the entropy of the system decreasesCorrect The box before the reaction holds 6 gas molecules (four XY and two Y₂); the box after it holds 4 gas molecules (four XY₂). With fewer gas particles moving independently in the same volume, the matter is less dispersed, so the entropy of the system decreases.
CAtoms in the container stay at 12, and the entropy of the system stays constant A student who counts atoms instead of molecules picks this. The 12 atoms are conserved, as in every reaction, but they are bonded into 4 gas molecules instead of 6, so the matter is less dispersed and the entropy of the system decreases.
DTemperature in the container stays fixed, and the entropy of the system stays constant A student who thinks entropy changes only when the temperature changes picks this. The temperature is fixed, but the entropy also changes when the dispersal of matter changes: here 6 gas molecules become 4 in the same volume, so the entropy decreases.
A sample of neon gas in a sealed, rigid container is heated from 300 K to 600 K. According to kinetic molecular theory, which change in the neon atoms accounts for the increase in the entropy of the gas?
Answer and reasoning
AThe kinetic energies of the atoms are spread over a wider range of valuesCorrect According to kinetic molecular theory, the distribution of kinetic energy among the particles of a gas broadens as the temperature increases. The energy of the sample is then dispersed over a wider range of values, so the entropy of the neon is greater at 600 K.
BThe atoms expand and take up a larger share of the container's volume A student who thinks particles expand when a substance is heated picks this. The atoms stay the same size, and in a rigid container the gas occupies the same volume; heating changes the kinetic energies of the atoms, not the atoms themselves.
CThe kinetic energies of the atoms all rise to the same, higher value A student who thinks every particle at one temperature has the same kinetic energy picks this. At each temperature the atoms have a range of kinetic energies; heating raises the average and widens the range, and it is this wider distribution that corresponds to greater entropy.
DThe number of atoms with the most probable kinetic energy grows larger A student who expects the peak of the distribution to rise on heating picks this. For a fixed number of atoms the distribution flattens as it broadens, so a smaller fraction of the atoms has kinetic energy near the most probable value at 600 K.
In preparation: 0 of 2 sections compiled and reviewed. The rest show key terms and common mistakes from our question bank until they are.
9.1.A.1 Entropy, S Fix
Entropy, S
A property of a system that increases when its matter becomes more dispersed or when its energy becomes more dispersed among its particles. In AP Chemistry the entropy change of a process is judged qualitatively from the dispersal of matter and of energy.
Entropy change of a system, ΔS
The entropy of the system after a process minus its entropy before the process. ΔS is positive when the matter or the energy of the system becomes more dispersed, and negative when it becomes less dispersed.
Dispersal of matter in a phase change
When a solid melts or a liquid vaporizes, the particles become freer to move and generally occupy a larger volume, so the entropy of the substance increases; freezing and condensation decrease it. Because a gas occupies a far larger volume than the same amount of liquid, vaporization typically gives a much larger entropy increase than melting does.
Entropy and the volume of a gas
At constant temperature, the entropy of a gas increases when its volume increases, because the same particles are able to move within a larger space.
Entropy and moles of gas in a reaction
For a reaction with gas-phase reactants or products, the entropy generally increases when the total number of moles of gas-phase products is greater than the total number of moles of gas-phase reactants, and generally decreases when it is smaller. The physical state of every species must be known before the comparison is made.
Students often think Larger molecules, with more atoms or a greater molar mass, have more entropy, so a reaction that makes larger molecules from smaller ones has a positive ΔS. In fact No. For reactions involving gases, the change in the total number of moles of gas is generally the deciding factor: when fewer moles of gas are present after the reaction, the matter is less dispersed and the entropy generally decreases, even if each product molecule has more atoms or a greater molar mass than the reactant molecules.
Students often think The same atoms are present before and after a reaction, so the matter is no more and no less dispersed, and the entropy of the system does not change. In fact No. Atoms are conserved in every chemical reaction, yet the entropy can change, because entropy depends on how dispersed the matter is. When the same atoms are bonded into fewer gas molecules, there are fewer independently moving particles and the entropy of the system generally decreases.
9.1.A.2 Dispersal of energy and temperature Fix
Dispersal of energy and temperature
According to kinetic molecular theory, the particles of a gas at a given temperature have a range of kinetic energies. As the temperature increases, this distribution of kinetic energy broadens, the energy is dispersed over a wider range of values, and the entropy of the system increases.
Students often think The particles of a substance expand when it is heated, so the atoms of a hot gas are larger and take up more of the container than the atoms of a cold gas. In fact No. Heating a gas increases the average kinetic energy of its particles; the particles themselves stay the same size. In a rigid container the gas occupies the same volume before and after heating.
Students often think All the particles of a gas at one temperature have the same kinetic energy, so heating a gas moves every particle to the same, higher kinetic energy. In fact No. Temperature is a measure of the average kinetic energy. At any temperature the particles of a gas have a range of kinetic energies, described by a distribution, and that distribution broadens as the temperature increases.
3 more questions. Every wrong answer here is a real mistake students make, and you see why it is wrong as soon as you answer.
Question 1 of 3
The diagram represents a sample of helium gas in two connected rigid bulbs before and after the valve between the bulbs is opened. The temperature of the helium is the same before and after. Which claim about the entropy of the helium is supported by the diagram?
Answer and reasoning
AIt decreases, because the atoms are less crowded and collide less often A student who equates entropy with how chaotic and crowded a system looks picks this. The atoms are less crowded after the valve is opened, but being able to move within a larger space makes the matter more dispersed, so the entropy increases.
BIt stays the same, because the average kinetic energy is unchanged A student who thinks entropy changes only when the temperature changes picks this. The average kinetic energy of the atoms is unchanged at constant temperature, but the atoms occupy twice the volume, and this dispersal of matter increases the entropy.
CIt stays the same, because the number of gas atoms is unchanged A student who applies the moles-of-gas rule for reactions to every process picks this. Eight atoms are present before and after, but that rule is for reactions; a fixed amount of gas gains entropy when its volume increases at constant temperature.
DIt increases, because the same atoms move within twice the volumeCorrect The diagram shows the same eight atoms, first confined to one bulb and then spread through two bulbs of equal size. At constant temperature, a gas whose particles are able to move within a larger space has its matter more dispersed, so the entropy of the helium increases.
A student is given the balanced equation 2 A + B → 2 C, written without the physical states of A, B and C. Which additional information does the student need in order to predict the sign of the entropy change, ΔS, of the reaction?
Answer and reasoning
AThe molar masses of the reactants A and B and of the product C A student who decides the sign of ΔS from the size of the molecules picks this. Molar masses do not show whether the matter becomes more or less dispersed; the comparison that matters is the number of moles of gas before and after, which requires the physical states.
BThe enthalpy change of the reaction for the equation as written A student who thinks a reaction that releases energy must gain entropy picks this. The sign of ΔH does not fix the sign of ΔS for the reacting substances; ΔS depends on how dispersed the matter is, which is judged from the physical states and the moles of gas.
CThe physical states of the reactants A and B and of the product CCorrect The sign of ΔS for a reaction is predicted by comparing the total moles of gas-phase products with the total moles of gas-phase reactants. The coefficients are given, so the missing information is which of A, B and C are gases: if all three are gases, 3 mol of gas forms 2 mol and ΔS is negative.
DThe temperature of the surroundings in which the reaction takes place A student who takes entropy to be a measure of temperature alone picks this. The temperature at which a reaction is run does not show whether its products are more dispersed than its reactants; the physical states and the moles of gas do.
Working No calculation. The sign of ΔS is predicted from the change in the number of moles of gas: Δn(gas) = (moles of gas-phase products) − (moles of gas-phase reactants). The coefficients 2, 1 and 2 are known; the quantity that cannot be found is Δn(gas), because the physical states are missing. Example: if A, B and C are all gases, Δn(gas) = 2 − 3 = −1, so ΔS < 0.
A 1.0 mol sample of H₂O undergoes each of the following changes at a constant pressure of 1.0 atm. Which change gives the greatest increase in the entropy of the H₂O?
Answer and reasoning
ALiquid water warming from 0°C to 100°C A student who thinks entropy changes only when the temperature changes picks this, as the only change listed with a temperature rise. Warming the liquid does increase its entropy, but far less than vaporization, in which the molecules become dispersed through a volume more than a thousand times larger.
BIce melting to form liquid water at 0°C A student who equates entropy with visible disorder picks this, because the ordered arrangement of the solid is lost. The molecules of the liquid remain close together, so the entropy increase on melting, about 22 J/(mol·K), is much smaller than that on vaporization, about 109 J/(mol·K).
CSteam condensing to form liquid water at 100°C A student who thinks a process that releases energy increases the entropy of the substance picks this. Condensation releases energy to the surroundings, but the H₂O molecules become far less dispersed, so the entropy of the H₂O decreases.
DLiquid water vaporizing to steam at 100°CCorrect Vaporization disperses the molecules from a liquid into a gas that occupies a far larger volume, so it produces the greatest dispersal of matter: about 109 J/(mol·K) for H₂O, compared with about 22 J/(mol·K) for melting and about 23 J/(mol·K) for warming the liquid from 0°C to 100°C. Condensation decreases the entropy of the H₂O.
Compiled from the AP Chemistry Course and Exam Description (effective Fall 2024) and our question bank · Specialist review in progress. How these pages are made · Free, no account
