1g of H₂ gas expand at STP to occupy double it's volume . What is thework done during the process?

To calculate the work done during the expansion of 1 g of hydrogen gas (H2) at standard temperature and pressure (STP), we can use the formula for work done in an isothermal expansion of an ideal gas. Let’s break this down step by step.

Understanding the Concept of Work in Gas Expansion

In thermodynamics, when a gas expands, it can perform work on its surroundings. The work done (W) by the gas during expansion can be defined mathematically as:

W = -PΔV

Where:

• P is the pressure of the gas
• ΔV is the change in volume, which is the final volume minus the initial volume

Calculating the Initial and Final Volumes

At STP (Standard Temperature and Pressure), which is defined as 0 degrees Celsius (273.15 K) and 1 atm, one mole of an ideal gas occupies 22.4 liters. First, we need to determine the amount of hydrogen gas we have:

Molar mass of H2 = 2 g/mol

Since we have 1 g of H2, we can find the number of moles:

Number of moles (n) = mass / molar mass = 1 g / 2 g/mol = 0.5 mol

At STP, the volume occupied by 0.5 moles of H2 is:

Volume = n × 22.4 L = 0.5 × 22.4 L = 11.2 L

When this gas expands to double its volume, the final volume becomes:

Final Volume (Vf) = 2 × 11.2 L = 22.4 L

The change in volume (ΔV) is:

ΔV = Vf - Vi = 22.4 L - 11.2 L = 11.2 L

Determining the Pressure

Since the gas is expanding at STP, the pressure (P) is constant at 1 atm. To use this in our work formula, we need to convert atmospheres to a more convenient unit for work calculations, which is often in liters-atm:

P = 1 atm = 1 L·atm

Calculating the Work Done

Now we can calculate the work done using the formula:

W = -PΔV = -1 atm × 11.2 L = -11.2 L·atm

To convert this to joules (since 1 L·atm is approximately 101.3 J):

W = -11.2 L·atm × 101.3 J/L·atm ≈ -1131.6 J

Final Thoughts

The negative sign indicates that work is done by the system (the gas) on the surroundings as it expands. Therefore, the work done during the expansion of 1 g of hydrogen gas at STP, as it doubles its volume, is approximately -1131.6 joules.