Answer to Question #64944 in General Chemistry for Shae

Question

Dry ice (solid CO2) has occasionally been used as an "explosive" in mining. A hole is drilled, dry ice and a small amount of gunpowder are placed in the hole, a fuse is added, and the hole is plugged. When lit, the exploding gunpowder rapidly vaporizes the dry ice, building up an immense pressure. Assume that 391 g of dry ice is placed in a cavity with a volume of 0.770 L and the ignited gunpowder heats the CO2 to 695 ∘C. What is the final pressure inside the hole?

Answer 1

Let’s use the ideal gas law:
PV=nRT or PV=m/M × RT

Following parameters are known:
V = 0.770 L = 0.770 × 10-3 m3, volume of the gas = volume of the cavity
m = 391 g, mass of CO2
M(CO2) = 44.009 g/mol, molar mass of CO2
R = 8.31 m3 × Pa ×  K−1 × mol−1, universal gas constant
T = 695 °C = 968.15 K, temperature of the gas

Hence,
P = mRT / MV = (391 × 8.31 × 968.15) / (44.009 × 0.770 × 10-3) = 92829969 Pa = 92.83 MPa