Should you carry out a chemical reaction under conditions of constant volume or constant pressure to obtain the largest possible amount of heat, if there is a large increase in the number of moles of gas? Explain.

Verified step by step guidance

Understand the difference between constant volume and constant pressure conditions. Under constant volume, the heat exchanged is equal to the change in internal energy (\( \Delta U \)), while under constant pressure, the heat exchanged is equal to the change in enthalpy (\( \Delta H \)).

Recall that for reactions involving gases, the change in enthalpy (\( \Delta H \)) is related to the change in internal energy (\( \Delta U \)) by the equation: \( \Delta H = \Delta U + \Delta n_{gas}RT \), where \( \Delta n_{gas} \) is the change in moles of gas, \( R \) is the ideal gas constant, and \( T \) is the temperature.

Consider the scenario where there is a large increase in the number of moles of gas (\( \Delta n_{gas} > 0 \)). This means that \( \Delta n_{gas}RT \) is positive, making \( \Delta H > \Delta U \).

Since \( \Delta H > \Delta U \) when there is an increase in moles of gas, more heat is absorbed or released under constant pressure conditions compared to constant volume conditions.

Therefore, to obtain the largest possible amount of heat, the reaction should be carried out under constant pressure conditions.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Enthalpy and Heat Transfer

Enthalpy is a thermodynamic property that reflects the total heat content of a system. In chemical reactions, the change in enthalpy (ΔH) indicates whether heat is absorbed or released. Under constant pressure, the heat exchanged is equal to the change in enthalpy, making it crucial for understanding how heat is produced or consumed during reactions.

Ideal Gas Law and Molar Volume

The Ideal Gas Law (PV=nRT) describes the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas. A large increase in the number of moles of gas during a reaction can significantly affect pressure and volume, influencing the conditions under which the reaction occurs and the heat produced.

Constant Volume vs. Constant Pressure Conditions

In a constant volume process, no work is done by the system, and the heat released corresponds to the internal energy change. Conversely, in a constant pressure process, the system can do work on the surroundings, which can lead to greater heat release when gas moles increase. Thus, the choice between these conditions affects the total heat output of the reaction.

Recommended video:

Guided course

02:35

Constant-Volume Calorimetry

Related Practice

Textbook Question

A 2.85-g lead weight, initially at 10.3 °C, is submerged in 7.55 g of water at 52.3 °C in an insulated container. What is the final temperature of both substances at thermal equilibrium?

views

Textbook Question

Two substances, A and B, initially at different temperatures, come into contact and reach thermal equilibrium. The mass of substance A is 6.15 g and its initial temperature is 20.5 °C. The mass of substance B is 25.2 g and its initial temperature is 52.7 °C. The final temperature of both substances at thermal equilibrium is 46.7 °C. If the specific heat capacity of substance B is 1.17 J/g•°C, what is the specific heat capacity of substance A?

views

Textbook Question

Exactly 1.5 g of a fuel burns under conditions of constant pressure and then again under conditions of constant volume. In measurement A the reaction produces 25.9 kJ of heat, and in measurement B the reaction produces 23.3 kJ of heat. Which measurement (A or B) corresponds to conditions of constant pressure? Explain.

Textbook Question

When 0.514 g of biphenyl (C₁₂H₁₀) undergoes combustion in a bomb calorimeter, the temperature rises from 25.8 °C to 29.4 °C. Find ΔE_rxn for the combustion of biphenyl in kJ/mol biphenyl. The heat capacity of the bomb calorimeter, determined in a separate experiment, is 5.86 kJ/°C.

views

Textbook Question

Mothballs are composed primarily of the hydrocarbon naphthalene (C₁₀H₈). When 1.025 g of naphthalene burns in a bomb calorimeter, the temperature rises from 24.25 °C to 32.33 °C. Find ΔE_rxn for the combustion of naphthalene. The heat capacity of the bomb calorimeter, determined in a separate experiment, is 5.11 kJ/°C.

Textbook Question

Zinc metal reacts with hydrochloric acid according to the balanced equation: Zn(s) + 2 HCl(aq) → ZnCl₂(aq) + H₂(g) When 0.103 g of Zn(s) is combined with enough HCl to make 50.0 mL of solution in a coffee-cup calorimeter, all of the zinc reacts, raising the temperature of the solution from 22.5 °C to 23.7 °C. Find ΔH_rxn for this reaction as written. (Use 1.0 g/mL for the density of the solution and 4.18 J/g•°C as the specific heat capacity.)

views