A gas occupies a volume at 34.2 mL at a temperature of 15.0 C and a pressure of 800.0 torr. What will be the volume of this gas at STP?

The ideal gas law equation can be used to find the number of moles of the gas at given conditions

PV = nRT

where

P - pressure - 800.0 torr x 133.3 Pa/torr = 106 640 Pa

V - volume - 34.2 x 10⁻³ m³

n - number of moles

R - universal gas constant - 8.314 Jmol⁻¹K⁻¹

T - temperature in Kelvin - 15 °C + 273 = 288 K

substituting these values in the equation

106 640 Pa x 34.2 x 10⁻³ m³ = n x 8.314 Jmol⁻¹K⁻¹ x 288 K

n = 1.52 mol

molar volume is where 1 mol of any gas occupies a volume of 22.4 L at STP

therefore if 1 mol occupies - 22.4 L

then 1.52 mol occupies - 22.4 L/mol x 1.52 mol = 34.05 L

volume of the gas at STP is 34.05 L

The answer is 34.1 mL.

Solution:

Assuming ideal behavior of gases, we can use the universal gas law equation

P1V1/T1 = P2V2/T2

The terms with subscripts of one represent the given initial values while for terms with subscripts of two represent the standard states which is the final condition.

At STP, P2 is 760.0torr and T2 is 0°C or 273.15K. Substituting the values to the ideal gas expression, we can now calculate for the volume V2 of the gas at STP:

(800.0torr * 34.2mL) / 288.15K = (760.0torr * V2) / 273.15K

V2 = (800.0torr * 34.2mL * 273.15K) / (288.15K * 760.0torr)

V2 = 34.1 mL