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

Verified step by step guidance

1. 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.
2. Calculate the change in volume \( \Delta V \) by subtracting the final volume from the initial volume: \( \Delta V = V_{\text{final}} - V_{\text{initial}} = 11.2 \text{ L} - 33.6 \text{ L} \).
3. 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.
4. 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.
5. Calculate the work using the formula \( W = -P \Delta V \) with the converted units to find the work done in joules.

Key Concepts

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.