Gas Laws: Calculating Volume Changes in Gas Samples

How can we determine the volume of a gas sample at STP?

Given data:

Pressure (P1): 150 kPa

Temperature (T1): 330 K

Volume (V1): 3.50 L

STP Pressure (P2): 101.3 kPa

STP Temperature (T2): 273 K

Answer:

The volume of the sample at STP is 4.29 L.

The volume of the sample can be calculated using the combined gas law equation:

[tex]\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}[/tex]

Where:

P₁ = initial pressure

V₁ = initial volume

T₁ = initial temperature

P₂ = final pressure at STP

V₂ = volume at STP (to be determined)

T₂ = final temperature at STP

Given information:

P1 = 150 kPa = 1.48 atm

T1 = 330 K

V1 = 3.50 L

At STP:

Pressure = 1 atm

Temperature = 273 K

Calculating the volume at STP:

[tex]\frac{1.48 \times 3.50}{330} = \frac{1 \times V_{2}}{273}

[tex]V_{2} = \frac{1.48 \times 3.50 \times 273}{1 \times 330}

[tex]V_{2} = 4.29 L

Hence, the volume of the sample at STP is 4.29 L.