Applying the Ideal Gas Law to Calculate Pressure in a Heated Canister

Q1. If I have a 1.0 liter canister that holds 2 moles of gas, and the campfire temperature is 1400°C, what is the pressure inside the canister?

Background

Topic: Ideal Gas Law

This question tests your ability to use the ideal gas law to predict the pressure inside a container when the temperature is extremely high. It also highlights the safety risks associated with heating pressurized containers.

Key formula:

$PV = nRT$

Where:

• $P$ = pressure (in atm)

• $V$ = volume (in liters)

• $n$ = number of moles (here, 2 moles)

• $R$ = ideal gas constant ($0.0821$ L·atm/mol·K)

• $T$ = temperature in Kelvin (must convert from Celsius)

Step-by-Step Guidance

1. Identify the known values: $V = 1.0$ L, $n = 2$ mol, $T = 1400\ ^\circ$C.

2. Convert the temperature from Celsius to Kelvin: $T = 1400 + 273 = 1673$ K.

3. Write the ideal gas law formula and rearrange to solve for pressure: $P = \frac{nRT}{V}$.

4. Check that all units are compatible with the gas constant $R$ (L, atm, mol, K).

5. Set up the calculation by plugging in the values: $P = \frac{(2)(0.0821)(1673)}{1.0}$.

Try solving on your own before revealing the answer!

Final Answer: 274.8 atm

$P = \frac{(2)(0.0821)(1673)}{1.0} \approx 274.8$ atm

The pressure inside the canister becomes extremely high, which explains why aerosol cans can explode when heated.