NEET Thermodynamics — Set 17

Question 1

For a reaction with $\Delta G^\circ = -20 \, \text{kJ/mol}$ at 298 K, what is the equilibrium constant $K$? ($R = 8.314 \, \text{J/mol·K}$)

Accepted Answer

$\Delta G^\circ = -RT \ln K$, $-20 \times 10^3 = -8.314 \times 298 \times \ln K$, $\ln K = 8.07$, $K = e^{8.07} \approx 3160$.

Question 2

For the reaction $ CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) $, $ \Delta H = -890.00 \, \text{kJ/mol} $ at 298 K. What is $ \Delta U $? ($ R = 8.314 \, \text{J/mol·K} $)

Accepted Answer

For $ \Delta n_g = 1 - 3 = -2 $, $ RT = 8.314 \times 298 \times 10^{-3} = 2.4776 \, \text{kJ} $. Using $ \Delta H = \Delta U + \Delta n_g RT $, $ \Delta U = -890.00 - (-2 \times 2.4776) = -890.00 + 4.9552 = -885.04 \approx -885.0 \, \text{kJ/mol} $.

Question 3

For an ideal gas, the relationship between molar heat capacities at constant pressure ($C_p$) and constant volume ($C_v$) is:

Accepted Answer

For an ideal gas, $C_p - C_v = R$, where $R$ is the gas constant.

NEET Chemistry: Thermodynamics — Practice Set 17

Q1. For a reaction with \(\Delta G^\circ = -20 \, \text{kJ/mol}\) at 298 K, what is the equilibrium constant \(K\)? (\(R = 8.314 \, \text{J/mol·K}\))

Q2. For the reaction \( CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) \), \( \Delta H = -890.00 \, \text{kJ/mol} \) at 298 K. What is \( \Delta U \)? (\( R = 8.314 \, \text{J/mol·K} \))

Q3. For an ideal gas, the relationship between molar heat capacities at constant pressure (\(C_p\)) and constant volume (\(C_v\)) is:

Q4. Calculate the work done when 2 mol of an ideal gas expands isothermally and reversibly from 8 L to 24 L at 400 K. (\(R = 8.314 \, \text{J/mol·K}\))

Q5. For \( CH_3OH(l) \rightarrow CO(g) + 2H_2(g) \), \( \Delta H = 128.10 \, \text{kJ/mol} \) at 298 K, what is \( \Delta U \)? (\( R = 8.314 \, \text{J/mol·K} \))

Q6. What is the entropy change of the system (\( \Delta S_{sys} \)) when 1 mol of an ideal gas expands isothermally from 2 L to 4 L? (\( R = 8.314 \, \text{J/mol·K} \))

Q7. Calculate the work done when 1 mol of an ideal gas expands reversibly and isothermally from 10 atm to 2 atm at 300 K. (\( R = 8.314 \, \text{J/mol·K} \))

Q8. For an ideal gas compressed reversibly and isothermally from 15 L to 3 L at 350 K, calculate the work done. (\( R = 8.314 \, \text{J/mol·K} \), 1 mol gas)

Q9. In an adiabatic irreversible expansion of an ideal gas against a constant external pressure, the work done is:

Q10. For a spontaneous process in an isolated system, which is true?