Ch.7 - Thermochemistry

Tro - Chemistry: A Molecular Approach 6th Edition

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Tro 6th Edition

Ch.7 - Thermochemistry

Problem 53

Chapter 7, Problem 53

How much work (in J) is required to expand the volume of a pump from 0.0 L to 2.5 L against an external pressure of 1.1 atm?

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Identify the formula for work done during expansion: \( W = -P_{\text{ext}} \Delta V \), where \( W \) is work, \( P_{\text{ext}} \) is the external pressure, and \( \Delta V \) is the change in volume.

Calculate the change in volume \( \Delta V \) by subtracting the initial volume from the final volume: \( \Delta V = V_{\text{final}} - V_{\text{initial}} = 2.5 \text{ L} - 0.0 \text{ L} \).

Convert the external pressure from atm to the SI unit of pressure, pascals (Pa), using the conversion factor: \( 1 \text{ atm} = 101325 \text{ Pa} \).

Convert the volume change from liters to cubic meters (m³) since 1 L = 0.001 m³.

Substitute the values into the work formula and solve for \( W \), ensuring all units are consistent (pressure in Pa and volume in m³).

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Key Concepts

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

Work in Thermodynamics

In thermodynamics, work is defined as the energy transferred when a force is applied over a distance. For gas expansion, the work done on or by the system can be calculated using the formula W = -P_extΔV, where P_ext is the external pressure and ΔV is the change in volume. The negative sign indicates that work is done by the system when it expands.

Pressure-Volume Work

Pressure-volume work occurs when a gas expands or contracts against an external pressure. It is a common type of work in chemical processes, particularly in engines and pumps. The work done can be expressed in units of energy, such as joules, and is directly related to the pressure exerted and the change in volume of the gas.

Unit Conversion

In this problem, it is essential to convert pressure from atmospheres to joules. The conversion factor is 1 atm = 101.325 J/L. This conversion allows for consistent units when calculating work, ensuring that the pressure and volume are compatible in the formula used to determine the work done during the expansion.

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Conversion Factors

Related Practice

Textbook Question

The average human lung expands by about 0.50 L during each breath. If this expansion occurs against an external pressure of 1.0 atm, how much work (in J) is done during the expansion?

Textbook Question

The air within a piston equipped with a cylinder absorbs 565 J of heat and expands from an initial volume of 0.10 L to a final volume of 0.85 L against an external pressure of 1.0 atm. What is the change in internal energy of the air within the piston?

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Textbook Question

A gas is compressed from an initial volume of 5.55 L to a final volume of 1.22 L by an external pressure of 1.00 atm. During the compression the gas releases 124 J of heat. What is the change in internal energy of the gas?

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Textbook Question

An unknown mass of each substance, initially at 23.0 °C, absorbs 1.95 × 10³ J of heat. The final temperature is recorded. Find the mass of each substance.

a. Pyrex glass (T_f = 55.4°C)

b. sand (T_f = 62.1°C)

c. ethanol (T_f = 44.2°C)

d. water (T_f = 32.4°C)

Textbook Question

How much heat is required to warm 2.50 kg of sand from 25.0 °C to 100.0 °C?

Textbook Question

Suppose that 25 g of each substance is initially at 27.0 °C. What is the final temperature of each substance upon absorbing 2.35 kJ of heat? c. aluminum

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