Question

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

Short answer

The work involved in the chemical reaction is \(2026.8 \mathrm{~J}\).

Step-by-step solution

Convert pressure to Pa

The pressure is given in kPa, but the SI unit for pressure is Pascal (Pa). To convert kPa to Pa, we can multiply the given pressure with 1000 since 1 kPa = 1000 Pa. So, the pressure in Pa is: 90.5 kPa × 1000 = 90500 Pa

Calculate the change in volume

We are given the initial volume (33.6 L) and the final volume (11.2 L). The change in volume ΔV is the difference between final and initial volumes: ΔV = V_final - V_initial ΔV = 11.2 L - 33.6 L ΔV = -22.4 L

Convert volume to m³

The SI unit for volume is cubic meters (m³), so we need to convert the volume ΔV from liters to m³. We can use the conversion factor that 1 L = 0.001 m³: ΔV_m³ = ΔV(L) × 0.001 ΔV_m³ = -22.4 L × 0.001 ΔV_m³ = -0.0224 m³

Calculate work done

Now, we can use the formula W = -PΔV to calculate the work done: W = - (90500 Pa) × (-0.0224 m³) W = 2026.8 J So, the work involved in the chemical reaction is 2026.8 J.

Key concepts

Work Done in Chemistry

In chemistry, the concept of work done is pivotal when studying reactions involving gases. When a gas expands or contracts, it exerts a force on its surroundings, and this is where the concept of work comes in. Work done (W) quantifies the energy transferred when a force moves an object. In chemical terms, work done refers to the amount of energy exchanged due to volume changes during reactions. For gases, this involves pressure and volume changes which are often described using the formula:
\[ W = - P \Delta V \]
This equation signifies that the work done (W) is equal to the negative of the external pressure (P) multiplied by the change in volume (\Delta V). The negative sign in the formula represents that work done by the system on its surroundings is considered negative. Conversely, if the system is compressed, work is done on the system, making it positive. Understanding this formula is crucial as it highlights the interplay between energy, work, and chemical changes that can often occur in reaction chambers or controlled environments.

• Work is a transfer of energy.
• In chemistry, it often involves gases and their volumes.
• The sign of work determines the direction of energy transfer.

Pressure-Volume Work

Pressure-volume work is a specific type of work done by or on the system when a chemical reaction occurs involving gases. It deals with changes in volume under constant pressure. Imagine you have a piston that compresses or expands within a cylinder as a gas inside reacts. This mechanical movement due to pressure differences reflects pressure-volume work.
This concept is essential in thermodynamics, as it allows us to understand how energy, in the form of work, helps drive chemical processes.

• Pressure remains constant during the reaction.
• A change in volume (\(\Delta V\)) indicates work done.
• This work is energy transferred due to volume changes.

By using the formula \(W = - P \Delta V\), we can calculate the amount of work done during chemical processes involving gases. Changes in volume can either be due to expansion, where the system does work on the surroundings, or compression, where the surroundings do work on the system. It serves as an excellent model for processes like the operation of internal combustion engines or even biological lungs during breathing.

Unit Conversion in Chemistry

Unit conversion is a crucial step in chemistry, especially when dealing with calculations involving work done, pressure, and volume. The primary goal of conversion is to ensure that all units match SI standards for accurate calculation. In the study exercise, converting pressure from kPa to Pa and volume from L to m³ was necessary for using the pressure-volume work formula.
Here's how to tackle unit conversion effectively:

• Always convert pressure to Pascals (Pa) – the SI unit of pressure – because 1 kPa equals 1000 Pa.
• Convert volumes to cubic meters (m³) when calculating work, as 1 L is equivalent to 0.001 m³.
• Consistent units throughout the calculation help prevent errors and yield accurate results.

Thus, converting units is more than just a step in calculations; it's a fundamental practice that ensures results are both accurate and meaningful in the context of scientific analysis and understanding. Proper unit conversion is a mark of precision and care in chemistry, reinforcing the basic principle that consistent units enable effective problem-solving.