Practice Questions

Calculate the amount of heat required to raise the temperature of 100 g of copper from $25^\circ\text{C}$ to $125^\circ\text{C}$. The specific heat capacity of copper is $0.385 \text{ J g}^{-1} \text{ K}^{-1}$.

Calculate the work done when 2 moles of an ideal gas expand from a volume of 5 L to 15 L against a constant external pressure of 2 atm. (1 L atm = 101.3 J)

Define an isolated system.

State the first law of thermodynamics.

Define entropy (S).

A system absorbs 500 J of heat and does 200 J of work on the surroundings. Calculate the change in internal energy of the system.

What is an intensive property? Give one example.

What is the value of the standard enthalpy of formation for an element in its reference state?

Explain the difference between a system and its surroundings in thermodynamics, using an example.

For the reaction $2SO_2(g) + O_2(g) \rightarrow 2SO_3(g)$, analyze whether $\Delta H$ is greater than, less than, or equal to $\Delta U$.

Propose a reason why the standard enthalpy of formation of C(diamond) is not zero, while that of C(graphite) is zero.

Explain the sign conventions for heat (q) and work (w) in chemical thermodynamics as per IUPAC.

Differentiate between open, closed, and isolated systems. Provide one example for each type.

State Hess's Law of Constant Heat Summation and explain its importance.

(a) Define standard enthalpy of formation ($\Delta_f H^{\ominus}$). (b) Explain what a thermochemical equation is, providing a complete example.

Explain the following thermodynamic terms: (a) Adiabatic process (b) Extensive properties (c) Reversible process (d) Spontaneous process

Examine the following scenarios and classify each system as open, closed, or isolated: (a) Coffee in a perfect thermos flask. (b) A human being.

For the reaction $N_2O_4(g) \rightleftharpoons 2NO_2(g)$, the standard Gibbs energy change $\Delta_r G^\ominus$ is $+4.85 \text{ kJ mol}^{-1}$ at $298 \text{ K}$. (a) Calculate the equilibrium constant, $K_p$. (b) Analyze whether the formation of $NO_2$ is favored under standard conditions. ($R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}$)

Formulate the general relationship between molar heat capacity at constant pressure ($C_p$) and molar heat capacity at constant volume ($C_v$) for an ideal gas. Starting from the fundamental definitions of enthalpy and heat capacity, derive the expression $C_p - C_v = R$. Justify each mathematical step in your derivation.

Define the terms: (a) Internal Energy (U), (b) Enthalpy (H), and (c) State Function.

What is meant by the standard enthalpy of vaporization? Explain why the enthalpy of vaporization for water is higher than that for acetone.

2 moles of an ideal gas expand isothermally and reversibly from 1 L to 10 L at $27^\circ\text{C}$. Calculate the work done by the gas. ($R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}$)

For a reaction, $\Delta H = -28.0 \text{ kJ mol}^{-1}$ and $\Delta S = -60.0 \text{ J K}^{-1} \text{ mol}^{-1}$. At what temperature will the reaction become spontaneous? Analyze the conditions for spontaneity.

Compare the magnitude of work done by the system during the expansion of a gas from $V_1$ to $V_2$ under (a) isothermal reversible conditions and (b) isothermal irreversible conditions (against a constant external pressure, $p_{ex}$). Demonstrate which process yields more work.

Calculate the change in internal energy ($\Delta U$) when 1 mole of liquid water vaporizes at $100^\circ\text{C}$ and 1 atm pressure. The enthalpy of vaporization ($\Delta_{vap}H$) is $40.79 \text{ kJ mol}^{-1}$. Assume the water vapor behaves as an ideal gas. ($R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}$)

The combustion of 1.2 g of benzoic acid ($C_7H_6O_2$) in a bomb calorimeter caused a temperature rise of $2.15 \text{ K}$. The heat capacity of the calorimeter is $14.8 \text{ kJ K}^{-1}$. Calculate the molar enthalpy of combustion ($\Delta_c H^\ominus$) of benzoic acid at $298 \text{ K}$.

Justify why the enthalpy of neutralization for a strong acid reacting with a strong base is a constant value, whereas it varies when a weak acid or weak base is involved.

A student claims that for the reaction $2\text{SO}_2(\text{g}) + \text{O}_2(\text{g}) \rightarrow 2\text{SO}_3(\text{g})$, the values of $\Delta H$ and $\Delta U$ are nearly identical. Critique this reasoning. Then, assuming the reaction occurs at 298 K and has $\Delta_r H^\ominus = -198.0 \text{ kJ mol}^{-1}$, calculate the value of $\Delta_r U^\ominus$ and justify whether the student's claim is valid.

Critique the statement: "All exothermic reactions are spontaneous." Use thermodynamic principles to justify your conclusion.

Justify, using the concept of pressure-volume work, why the magnitude of work done in a reversible isothermal expansion of an ideal gas is greater than that in an irreversible isothermal expansion between the same initial and final volumes.

Evaluate the spontaneity of the vaporization of a liquid at its normal boiling point. Justify your conclusion by analyzing the signs of $\Delta H$, $\Delta S$, and the resulting value of $\Delta G$.

Formulate a Born-Haber cycle for the formation of solid magnesium oxide (MgO). From this cycle, create a single algebraic expression to represent the lattice enthalpy ($\Delta_{\text{lattice}}H^\ominus$) of MgO using the following defined thermodynamic terms:

• Enthalpy of formation of MgO(s): $\Delta_f H^\ominus$
• Enthalpy of sublimation of Mg(s): $\Delta_{\text{sub}}H^\ominus$
• First and second ionization enthalpies of Mg(g): $IE_1$ and $IE_2$
• Bond dissociation enthalpy of O₂(g): $\Delta_{\text{bond}}H^\ominus$
• First and second electron gain enthalpies of O(g): $\Delta_{eg}H_1^\ominus$ and $\Delta_{eg}H_2^\ominus$

Propose a complete experimental and computational procedure to determine the standard enthalpy of formation of liquid benzene ($\text{C}_6\text{H}_6(\text{l})$) using only data obtainable from bomb calorimetry. You are provided with pure samples of benzene, high-purity graphite, and hydrogen gas. You do not need to provide numerical values, but you must formulate the specific thermochemical equations and the final Hess's Law calculation.

The enthalpy of fusion for ice is $6.01 \text{ kJ mol}^{-1}$. Calculate the heat required to melt 9 g of ice.

Using the following thermochemical equations, calculate the standard enthalpy of formation ($\Delta_f H^\ominus$) for acetylene, $C_2H_2(g)$.

1. $C(\text{graphite}) + O_2(g) \rightarrow CO_2(g)$; $\Delta H^\ominus = -393.5 \text{ kJ mol}^{-1}$
2. $H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l)$; $\Delta H^\ominus = -285.8 \text{ kJ mol}^{-1}$
3. $C_2H_2(g) + \frac{5}{2}O_2(g) \rightarrow 2CO_2(g) + H_2O(l)$; $\Delta H^\ominus = -1299.6 \text{ kJ mol}^{-1}$

Calculate the standard enthalpy of reaction ($\Delta_r H^\ominus$) for the hydrogenation of ethene: $C_2H_4(g) + H_2(g) \rightarrow C_2H_6(g)$. Use the following bond enthalpy data:

• $C-H$: $414 \text{ kJ mol}^{-1}$
• $C=C$: $611 \text{ kJ mol}^{-1}$
• $H-H$: $436 \text{ kJ mol}^{-1}$
• $C-C$: $347 \text{ kJ mol}^{-1}$

Explain the concept of Gibbs energy (G) and its role as a criterion for spontaneity. (a) Write the Gibbs equation. (b) Describe the conditions for spontaneity and equilibrium in terms of $\Delta G$. (c) Explain why an endothermic process (positive $\Delta H$) can still be spontaneous.

Design a hypothetical two-step process to calculate the standard enthalpy of formation of carbon monoxide (CO) using Hess's Law. You are given the standard enthalpies of combustion for carbon (graphite) and carbon monoxide. Justify why a direct experimental measurement of the enthalpy of formation of CO is difficult.

Evaluate whether the Gibbs equation, $\Delta G = \Delta H - T\Delta S$, can be applied to a process that occurs under non-isothermal conditions. Justify your answer.

Justify that the free expansion of an ideal gas is a spontaneous process by analyzing the entropy changes involved. In your justification, evaluate $\Delta U, q, w$, and $\Delta S_{\text{system}}$, $\Delta S_{\text{surroundings}}$, and $\Delta S_{\text{total}}$ for this irreversible isothermal process.

(a) State the mathematical relationship between enthalpy change ($\Delta H$) and internal energy change ($\Delta U$). (b) Derive the expression $\Delta H = \Delta U + \Delta n_g RT$. (c) Under what condition is $\Delta H$ equal to $\Delta U$?

Given the reaction: $\text{N}_2\text{O}_4(\text{g}) \rightleftharpoons 2\text{NO}_2(\text{g})$. At 350 K, the equilibrium constant $K_p$ is 2.5. A chemist proposes that increasing the temperature will favor the formation of $\text{NO}_2$. Evaluate this proposal, given that the standard enthalpy of reaction, $\Delta_r H^\ominus$, is $+57.2 \text{ kJ mol}^{-1}$. Justify your answer using the relationship between Gibbs free energy, enthalpy, and the equilibrium constant.

Critique the statement: "A reaction with a positive $\Delta_r H^\ominus$ and a negative $\Delta_r S^\ominus$ can never be spontaneous." Justify your answer using the Gibbs free energy equation. Then, consider the reverse reaction. Formulate the expressions for its $\Delta_r H^\ominus$, $\Delta_r S^\ominus$, and $\Delta_r G^\ominus$, and evaluate its spontaneity.

An engineer is designing a process for the synthesis of ammonia: $\text{N}_2(\text{g}) + 3\text{H}_2(\text{g}) \rightleftharpoons 2\text{NH}_3(\text{g})$. The standard enthalpy of formation ($\Delta_f H^\ominus$) for $\text{NH}_3(\text{g})$ is $-46.1 \text{ kJ mol}^{-1}$ and the standard entropy change for the reaction ($\Delta_r S^\ominus$) is $-198.7 \text{ J K}^{-1}\text{mol}^{-1}$. (a) Create an expression for the standard Gibbs free energy change ($\Delta_r G^\ominus$) as a function of temperature (T). (b) Evaluate the temperature at which the reaction is at equilibrium under standard conditions. (c) Justify, using thermodynamic principles, why the industrial Haber-Bosch process operates at moderately high temperatures (e.g., 400-450°C) and high pressures, despite low temperatures favoring spontaneity.

Calculate the standard enthalpy of formation ($\Delta_f H^\ominus$) of liquid methanol ($CH_3OH(l)$) from the following data:

• $\Delta_f H^\ominus (CO_2, g) = -393.5 \text{ kJ mol}^{-1}$
• $\Delta_f H^\ominus (H_2O, l) = -285.8 \text{ kJ mol}^{-1}$
• The standard enthalpy of combustion of methanol is $\Delta_c H^\ominus = -726.0 \text{ kJ mol}^{-1}$. First, write the balanced thermochemical equation for the combustion of methanol. Then, use the data to solve for the enthalpy of formation.