Several properties of gases can be experimentally measured: temperature, pressure, volume, and the amount of the gas (i.e., the number of moles). The ideal gas law states that the relationship between these properties, or variables, in a mathematical formula.
The ideal gas law is PV = nRT.
P is the pressure in atmospheres (atm), V is the volume in liters (L), n is the number of moles, R is the gas constant (0.0821 L∙atm/(mol∙K)), and T is the temperature in Kelvins (K).
Using the ideal gas law, determine the temperature of a 2.63 mole sample of xenon gas, with a volume of 1.60 × 104 mL and under a pressure of 2.20 atm.
First, we need to convert the volume from milliliters (mL) to liters (L):
1.60 × 10^4 mL = 1.60 × 10^1 L
Now we plug in the values into the ideal gas law formula:
P = 2.20 atm
V = 1.60 × 10^1 L
n = 2.63 moles
R = 0.0821 L∙atm/(mol∙K)
PV = nRT
(2.20 atm)(1.60 × 10^1 L) = (2.63 mol)(0.0821 L∙atm/(mol∙K))(T)
35.2 = 0.215803 T
T = 35.2 / 0.215803
T ≈ 163.2 K
Therefore, the temperature of the xenon gas sample is approximately 163.2 K.