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 added and the hole plugged. When lit the exploding gunpowder rapidly vaporizes the dry ice and immense pressure is built up. If 0.75kg of dry ice is placed in a cavity with a volume of 950mL and the ignited gunpowder heats the CO2 to 447 degrees Celsius, what is the final pressure inside the hole?

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 added and the hole plugged. When lit the exploding gunpowder rapidly vaporizes the dry ice and immense pressure is built up. If 0.75kg of dry ice is placed in a cavity with a volume of 950mL and the ignited gunpowder heats the CO2 to 447 degrees Celsius, what is the final pressure inside the hole?

R=0.0821 L.atm/mol.K

Answer 1

To find the final pressure inside the hole, we can use the ideal gas law equation:

PV = nRT

Where:
- P is the pressure
- V is the volume of the cavity
- n is the number of moles of CO2
- R is the ideal gas constant
- T is the temperature in Kelvin

First, let's convert the volume from milliliters (mL) to liters (L):
950 mL = 0.95 L

Next, we need to calculate the number of moles of CO2. We know that the mass of the dry ice is 0.75 kg, and the molar mass of carbon dioxide (CO2) is approximately 44 g/mol. We can use these values to find the number of moles:

mass = moles * molar mass

moles = mass / molar mass

mass = 0.75 kg = 750 g
molar mass = 44 g/mol

moles = 750 g / 44 g/mol ≈ 17.04 mol

Now, we have all the values needed to calculate the pressure. Substituting the known values into the ideal gas law equation:

PV = nRT

P * 0.95 L = 17.04 mol * 0.0821 L.atm/mol.K * 447 K

P = (17.04 mol * 0.0821 L.atm/mol.K * 447 K) / 0.95 L

Calculating this expression gives the final pressure (P) inside the hole.