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Midterm Exam ICHM 3410, Dr. Mebel, Fall 2013

1. (20 pts.) Consider the system at T = 298 K, shown in the figure below:

He2.00 L

1.50 bar

Ne3.00 L

2.50 bar

Xe1.00 L

1.00 bar

Initially, the gases are placed in individual compartments separated by walls (barriers).Assuming ideal gas behavior, calculate the total pressure and the partial pressure of eachcomponent if the barriers separating the compartments are removed.

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2. (20 pts.) Two ideal gas systems undergo reversible expansion under differentconditions starting from the same p and V. At the end of the expansion, the two systemshave the same volume. The first system has undergone adiabatic expansion and thesecond has undergone isothermal expansion. Which system will have the lower pressure?Explain your answer both with and without using equations.

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3. (20 pts) Assume the hypothetical reaction for fixing nitrogen biologically isN2(g) + 3 H2O(l) → 2 NH3(aq) + 3/2 O2(g)

a. Calculate the standard reaction enthalpy and standard reaction internal energy changefor such biosynthetic fixation of nitrogen at T = 298 K. For NH3(aq), ammonia dissolvedin aqueous solution, use ΔfH∅ = -80.3 kJ mol-1.

b. In some bacteria, glycine is produced from ammonia by the reactionNH3(g) + 2 CH4(g) + 5/2 O2(g) → NH2CH2COOH(s) + 3 H2O(l)

Calculate the standard reaction enthalpy and standard reaction internal energy change forthe synthesis of glycine from ammonia at T = 298 K. For glycine, ΔfH∅ = -537.2 kJ mol-1.

c. Calculate the standard reaction enthalpy for the synthesis of glycine from nitrogen,water, oxygen, and methane at = 298 K and 348 K. Use Cp,m(glycine,s) = 99.14 J K-1 mol-1.

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4. (20 pts.) 1.75 moles of an ideal monoatomic gas are transformed from an initial state T =750 K and p = 1.75 bar to a final state T = 350 K and p = 5.25 bar. Calculate ΔU, ΔH, andΔS for this process.

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5. (20 pts) Derive expressions for the internal pressure,

€

πT , of (a) an ideal gas and (b) van

der Waals gas using the fact that

€

πT is related to p, V, and T by the following formula:

€

πT = T ∂p∂T

V− p

Show that your result for van der Waals gas will tend to the result for the ideal gas as thevolume increases and the attractive interaction between molecules decreases.

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Midterm Exam I

CHM 3410, Dr. Mebel, Fall 2014

1. (20 pts.) A student is told that a closed vessel holds a pure noble gas. He measures the

density of the gas in the vessel at 298 K and 1 atm pressure and finds it to be 0.8252

g L-1

.

(a) What gas does the student think is in the vessel?

(b) After turning in his report, he is told that the vessel actually contains a mixture of

He and Ar. What is the mole fraction of He in the mixture?

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2. (20 pts.) One mole of a perfect gas at a temperature of T1 = 500 K and a pressure of p1

= 6 atm is subjected to the following changes (in a Carnot cycle):

Step 1. The gas is expanded isothermally and reversibly to a final pressure of 5 atm.

Step 2. After completion of Step 1, the gas is expanded adiabatically and reversibly until

the pressure reaches 4 atm.

Step 3. After Step 2 is completed, the gas is compressed isothermally and reversibly to a

pressure of 4.8 atm.

Step 4. After Step 3, the gas is compressed adiabatically and reversibly to a pressure of 6

atm, at which point the temperature is found to be 500 K.

The molar heat capacity of the gas at constant volume is CV,m = 3/2 R.

a) Find the initial volume of the gas V1 and temperature and volume of the gas after

each step.

b) Find w, q, U, H, and S for each step and overall, after the Carnot cycle is

completed.

c) Why this cycle can be used as an engine? Does it produce work and where the

energy comes from if the work is produced? What is the efficiency of the engine

working on this Carnot cycle?

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3. (20 pts) 50 g of hexadecane (C16H34(s), the standard enthalpy of formation is –447.97 kJ

mol-1

) are burned with insufficient oxygen for complete combustion to CO2(g). As a result

some of the reactant forms CO(g) and H2O(l) via the reaction

C16H34(s) + 16.5 O2(g) 16 CO(g) +17 H2O(l)

and some of the reactant forms CO2(g) and H2O(l) via the reaction

C16H34(s) + 24.5 O2(g) 16 CO2(g) +17 H2O(l)

At constant pressure of 1 bar and 298.15 K, the heat change in the process is found to be –

1,945.2 kJ.

a) Compute the percent of hexadecane that reacted to form CO(g) in the process.

b) If the process had been carried out in a constant volume calorimeter, how much heat

would have been released? Assume that the percent of reactant forming CO(g)

would be the same as that computed in part a) of the problem.

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4. (20 pts.) Give several different formulations of the Second Law of thermodynamics and

explain the relationships between them.

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5. (20 pts) Use the relation

Cp CV TV

T

p

p

T

V

,

the cyclic rule and the van der Waals equation of state,

p nRT

V nb an2

V 2

to derive an equation for

Cp CV in terms of V, T, and the gas constants R, a, and b.

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Midterm Exam I

CHM 3410, Dr. Mebel, Fall 2017

1. (20 pts.) A mixture of H2 and NH3 has a volume of 153.2 cm3 at 0.0C and p = 1 atm.

The mixture is cooled to the temperature of liquid nitrogen at which ammonia freezes out

and the remaining gas is removed from the vessel. Upon warming the vessel back to

0.0C and p = 1 atm, the volume is 98.7 cm3. Calculate the mole fractions of NH3 and H2

in the original mixture.

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2. (20 pts.) Two moles of a perfect gas at a temperature of T = 300 K and a pressure of p1

= 10 atm is subjected to the following changes:

Step 1. The gas is expanded isothermally against a constant pressure of 5 atm to a final

pressure p2 = 7 atm.

Step 2. After completion of Step 1, the external pressure is reduced to zero and the gas is

further expanded into a vacuum until an internal pressure of p3 = 1 atm is reached with T

= 300 K remaning unchanged.

Step 3. After Step 2 is completed, the gas is compressed isothermally and reversibly back

to its initial state T = 300 K and p1 = 10 atm.

a) Find the initial volume of the gas V1 and volume of the gas after each step.

b) Find w, q, U, H, and S for each step and overall, after the cycle is completed.

c) After the entire process is finished has heat been gained or lost by the system?

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3. (20 pts) At 298.15 K, the standard molar enthalpy of combustion of dipropyl ketone,

H7C3-CO-C3H7, is -4395.3 kJ mol-1

.

a) Calculate the standard molar enthalpy of formation of dipropyl ketone.

b) How much heat is released if 10 g of dipropyl ketone are burned in excess of

oxygen in a constant volume calorimeter?

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4. (20 pts.) Give several different formulations of the Second Law of thermodynamics and

explain the relationships between them.

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5. (20 pts) Consider a gas whose equation of state over a certain temperature range can be

represented as

2naTnRTpV

Derive expressions for the expansion coefficient (in terms of T and constants) and the

isothermal compressibility T (in terms of p) for such a gas and demonstrate that its

isothermal compressibility is the same as for the perfect gas.