To solve this problem, you can use the Ideal Gas Law, which is represented by the equation:
PV = nRT
where:
- P is the pressure (in atmospheres),
- V is the volume (in liters),
- n is the number of moles,
- R is the ideal gas constant (0.0821 L.atm/(mol·K)),
- T is the temperature (in Kelvin).
First, you need to convert the volume from milliliters to liters, and the pressure from atm to Pa (1 atm = 101325 Pa).
V = 367 mL / 1000 L
P = 8.48 atm * 101325 Pa/atm
Now, you can rearrange the Ideal Gas Law to solve for temperature:
T = PV / nR
Substitute the known values:
T = (8.48 * 101325) * (367/1000) / (0.011 * 0.0821)
Now, calculate the temperature in Kelvin and round to the nearest whole number.
T ≈ (859468 * 0.367) / 0.0009021
T ≈ 315075.356 / 0.0009021
T ≈ 349745966.61
Now, round to the nearest whole number:
T ≈ 349745967
So, at a temperature of approximately 349,745,967 K, 0.011 mol of argon gas will have a volume of 367 mL at 8.48 atm.