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# Sample Problems:

## Chapter 1

Taken from Atkins, page 26.

1. For an ideal gas, find the volume occupied by one mole of gas at 1 atm pressure and temperature of 25 C.

2. For an ideal gas, find the temperature at which one mole of gas at 1 atm pressure occupies 10 L.

3. For an ideal gas, find the pressure at which three moles of gas occupy 17.3 L at a temperature of 100 C.

4. A sample of air occupies 1.0 L at 25 oC and 1.00 atm. What pressure is needed to compress it to 100 cm³ at this temperature?

5. (a) Could 1.31 g of xenon gas in a vessel of volume 1.0 L exert a pressure of 20 atm at 25 oC if it behaved as a perfect gas? (b) What pressure would it exert if it behaved as a van der Waals gas?

6. A perfect gas undergoes isothermal compression, which reduces its volume by 2.20 L. The final pressure and volume of the gas are 1.48 × 10³ Torr and 4.665 L, respectively. Calculate the original pressure of the gas in Torr, and bar.

7. To what temperature must a sample of perfect gas of volume 500 mL be cooled from 35 oC in order to reduce its volume to 150 cm³?

8. A car tire was inflated to a pressure of 24 lb in-2 (1.00 atm = 14.7 lb -2) on a winter's day when the temperature was -5oC. What pressure will be found, assuming no leaks and constant volume, on a summer's day when the temperature is 35 oC?

9. 255 mg of neon occupies 3.00 L at 122 K. Use the perfect gas law to calculate the gas pressure.

10. In an attempt to determine an accurate value of the gas constant R, a student heated a 20.000 L container filled with 0.25132 g of helium gas to 500 oC and measured the pressure as 206.402 cm of water in a manometer at 25 oC. Calculate the value of R from these data. The density of water is 0.99797 g cm -3 at 25 oC.

11. At 500 oC and 699 Torr, the mass density of sulfur is 3.71 g L -1. What is the molecular formula of sulfur under these conditions?

## Chapter 2

Taken from Atkins.

2.4 (a) Calculate the work done to raise a mass of 1.0 kg through 10 m on the surface of the (1)earth (g = 9.81 m s-1) and (b) the moon (g=1.60 m s-1).

2.5 (a) Calculate the work needed for a 65 kg person to climb through 4.0 m on the surface of the earth.

2.6 (a) A chemical reaction takes place in a container of cross-sectional area 50.0 cm2. As a result of the reaction, a piston is pushed out through 10 cm against an external pressure of 1.0 atm. Calculate the work done by the reaction.

2.7 (a) A sample consisting of 1.00 mol Ar is expanded isothermally at 0 oC from 22.4 L to 44.8 L (a) reversibly, (b) against a constant external pressure equal to the final pressure of the gas, and (c) freely (against zero external pressure). For the three processes calculate q, w, Δ U, and Δ H.

2.8 (a) A sample consisting of 1.00 mol of monoatomic gas perfect gas, for which C V,M = 3R/2, initially at p1 = 1.00 atm and T1 = 300 K, is heated reversibly to 400 K at constant volume. Calculate the final pressure, ΔU, q, and w.

2.9 (a) A sample of 4.50 g of methane occupies 12.7 L at 310 K. (a) Calculate the work done when the gas expands isothermally against a constant external pressure of 200 Torr until its volume has increased by 3.3 L. (b) Calculate the work that would be done if the same expansion were done reversibly.

2.10 (a) In the isothermal reversible compression of 52.0 mmol of a perfect gas at 260 K, the volume of the gas is reduced to one-third its initial value. Calculate w for the process.

2.11 (a) A sample of 1.00 mol H2O (g) is condensed isothermally and reversibly to liquid water at 100 oC. The standard enthalpy of vaporization of water is 40.656 kJ mol-1. Find w, q, ΔU, and ΔH.

2.12 (a) A strip of magnesium of mass 15 g is dropped into a beaker of dilute hydrochloric acid. Calculate the work done by the system as a result of the reaction. The atmospheric pressure is 1.0 atm and the temperature is 25 oC.

2.13 (a) Calculate the heat required to melt 750 kg of sodium metal at 371 K. The enthalpy of fusion of sodium is 2.601 kJ mol-1.

## Chapter 3

Taken from Atkins, page 87.

3.4 (a) Show that the following functions have exact differentials: (a) x2y + 3y2, (b) x cos xy

3.5 (a) Let z = ax2y3. Find dz.

3.6 (a) What is the total differential of z= x2 + 2y2 -2xy -4y -8?

3.7 (a) Let z = xy - y + ln x +2. Find dz and show it is exact.

3.8 (a) Express (∂CV/∂V)T, as a second derivative and find its relation to (∂U/∂V)T. From this relation show that (∂CV/∂V)p = 0 for a perfect gas.

3.9 (a) By direct differentiation of H = U + pV, obtain a relation between (∂H/∂U)p and (∂U/∂V)p.

3.10 (a) Write an expression for dV given that V is a function of p and T. Deduce an expression for d ln V in terms of the expansion coefficient and the isothermal compressibility.

3.11 (a) The internal energy of a perfect monoatomic gas relative to its value at T = 0 is 3nRT/2. Calculate (∂U/∂V)p and (∂H/∂V)T for the gas.

3.12 (a) Starting from the expression for the total differential dV in terms of T and p, show that (∂p/∂T)V = α/kT.

3.13 (a) When a certain freon used in refrigeration was expanded adiabatically from an initial pressure of 32 atm and 0 oC to a final pressure of 1.00 atm, the temperature fell by 22 K. Calculate the Joule-Thomson coefficient, μ, at 0 oC, assuming it remains constant over this temperature range.

## Chapter 4

Taken from Atkins, page 116.

4.4 (a) Calculate the change in entropy when 25 kJ of energy is transferred reversibly and isothermally as heat to a large block of iron at (a) 0 oC; (b) 100 oC.

4.5 (a) Calculate the molar entropy of a constant-volume sample of neon at 500 K given that it is 146.22 J K -1 mol -1 at 298 K.

4.6 (a) A sample consisting of 1.00 mol of a monatomic perfect gas with CV,m = 3R/2 is heated from 100 oC to 300 oC at constant Pressure. Calculate ΔS (for the system).

4.7 (a) Calculate ΔS (for the system) when the state of 3.00 mol of monoatomic perfect gas, for which Cp,m = 5R/2 is changed from 25 oC and 1.00 atm to 125 oC and 5.00 atm. How do you rationalize the sign of ΔS?

4.8 (a) A sample consisting of 3.00 mol of of a diatomic perfect gas at 200 K is compressed reversibly and adiabatically until its temperature reaches 250 K. Given that CV, m = 27.5 J K -1 mol -1, calculate q, w, ΔU, ΔH, and ΔS.

4.9 (a) Calculate the increase in entropy when 1.00 mol of monoatomic perfect gas with Cp,m = 5R/2 is heated from 300 K to 600 K and simultaneously expanded from 30.0 to 50.0 L.

4.10 (a) A system undergoes a process in which the entropy change is +5.51 J K -1. During the process, 1.00 kJ of heat is added to the system at 350 K. Is the process thermodynamically reversible? Explain your reasoning.

4.11 (a) A sample of aluminum of mass 1.75 kg is cooled at constant pressure from 300 K to 265 K. Calculate (a) the energy that must be removed as heat and (b) the change in entropy of the sample.

4.12 (a) A sample of methane gas of mass 25 g at 250 K and 18.5 atm expands isothermally until its pressure is 2.5 atm. Calculate the change in entropy of the gas.

4.13 (a) A sample of perfect gas that initially occupies 15.0 L at 250 K and 1.00 atm is compress isothermally. To what volume must the gas be compressed to reduce its entropy by 5.0 J K -1?