Question

If 1 metric ton of CO2 goes from solid into a gas how much work does it do because of the change in volume? Assume the final state of the gas is standard temperature and pressure (STP).

Answer 1

1 metric ton = 1000 kg

1 metric ton CO₂ = 1000 kg CO₂ = 1 x 10⁶ g CO₂

moles of CO₂ = (mass of CO₂) / (molar mass CO₂)

moles of CO₂ = (1 x 10⁶ g) / (44 g/mol)

moles of CO₂ = 2.273 x 10⁴ mol

At STP, 1 mol of gas occupies 22.4 L space

Volume of CO₂ = (moles of CO₂) * (22.4 L/mol)

Volume of CO₂ = (2.273 x 10⁴ mol) * (22.4 L/mol)

Volume of CO₂ = 5.091 x 10⁵ L

Volume of CO₂ solid = (mass) / (density)

Volume of CO₂ solid = (1000 kg) / (1.6 kg/L)

Volume of CO₂ solid = 625 L

Change in volume = volume occupied by gaseous CO₂ - volume occupied by solid CO₂

Change in volume = 5.091 x 10⁵ L - 625 L

Change in volume = 5.085 x 10⁵ L

Pressure at STP = 1.00 atm

work done = pressure * change in volume

work done = (1.00 atm) * (5.085 x 10⁵ L)

work done = 5.085 x 10⁵ atm-L

work done = 5.085 x 10⁵ atm-L * (101.325 J / 1 atm-L)

work done = 5.15 x 10⁷ J

work done = 5.15 x 10⁴ kJ