How much work (in J) is involved in a chemical reaction if the volume decreases from 33.6 L to 11.2 L against a constant pressure of 90.5 kPa?

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Identify the formula for work done by or on a gas: \( W = -P \Delta V \), where \( W \) is work, \( P \) is 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: \( \Delta V = V_{\text{final}} - V_{\text{initial}} = 11.2 \text{ L} - 33.6 \text{ L} \).

Convert the pressure from kilopascals (kPa) to pascals (Pa) because the standard unit for pressure in the work formula is pascals. Recall that 1 kPa = 1000 Pa.

Substitute the values of pressure in pascals and the change in volume in liters into the work formula. Note that you need to convert the volume from liters to cubic meters (1 L = 0.001 m³) for consistency with the SI units.

Calculate the work using the formula \( W = -P \Delta V \) with the converted units to find 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 involving gases, work can be calculated using the formula W = -PΔV, where W is work, P is pressure, and ΔV is the change in volume. The negative sign indicates that work is done by the system when it expands and done on the system when it contracts.

Pressure-Volume Work

Pressure-volume work occurs when a gas expands or contracts against an external pressure. It is particularly relevant in chemical reactions involving gases, where changes in volume can significantly affect the energy of the system. The work done can be calculated by multiplying the constant pressure by the change in volume, ensuring that the units are consistent, typically converting pressure from kPa to atm or volume from liters to cubic meters as needed.

Units of Work

Work is measured in joules (J) in the International System of Units (SI). To convert pressure from kilopascals (kPa) to joules when calculating work, it is essential to ensure that volume is in cubic meters (m³). The conversion factor is 1 kPa = 1,000 N/m², and since 1 L = 0.001 m³, proper unit conversion is crucial for accurate calculations in thermodynamic problems.

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Consider a system consisting of two oppositely charged spheres hanging by strings and separated by a distance r1, as shown in the accompanying illustration. Suppose they are separated to a larger distance r2, by moving them apart. (a) What change, if any, has occurred in the potential energy of the system?

During a deep breath, our lungs expand about 2.0 L against an external pressure of 101.3 kPa. How much work is involved in this process (in J)?

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Open Question

(a) Under what condition will the enthalpy change of a process equal the amount of heat transferred into or out of the system? (b) During a constant-pressure process, the system releases heat to the surroundings. Does the enthalpy of the system increase or decrease during the process? (c) In a constant-pressure process, _x001F_H = 0. What can you conclude about _x001F_E, q, and w?

Open Question

Assume that 2 moles of water are formed according to the following reaction at constant pressure (101.3 kPa) and constant temperature (298 K): 2 H2(g) + O2(g) → 2 H2O(l). (b) Calculate _x001F_E for the reaction using your answer to (a).