How much work (in J) is involved in a chemical reaction if the volume decreases from 5.00 to 1.26 L against a constant pressure of 0.857 atm?

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Identify the formula for work done in a chemical reaction involving gases: \( w = -P \Delta V \), where \( w \) is the work done, \( P \) is the pressure, and \( \Delta V \) is the change in volume.

Calculate the change in volume \( \Delta V \) by subtracting the final volume from the initial volume: \( \Delta V = V_{\text{final}} - V_{\text{initial}} = 1.26 \text{ L} - 5.00 \text{ L} \).

Convert the 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) using the conversion factor: \( 1 \text{ L} = 0.001 \text{ m}^3 \).

Substitute the values of pressure in pascals and volume change in cubic meters into the work formula to calculate the work done in joules.

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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 chemical reactions occurring at constant pressure, the work done by or on the system can be calculated using the formula W = -PΔV, where P is the pressure and ΔV is the change in volume. A negative sign indicates that work is done by the system when it expands.

Pressure-Volume Work

Pressure-volume work is a specific type of work associated with the expansion or compression of gases. It occurs when a gas changes its volume against an external pressure. The work done is directly proportional to the pressure and the change in volume, making it essential to understand how these variables interact in a chemical reaction.

Units of Work

In chemistry, work is typically measured in joules (J). To convert pressure from atmospheres to pascals (1 atm = 101.325 kPa) and volume from liters to cubic meters (1 L = 0.001 m³), it is crucial to ensure that all units are consistent when calculating work. This ensures accurate results in thermodynamic calculations.