Question

At STP, a sample of gas occupies 0.225 L. Calculate the volume of this gas at a pressure of 2.7 atm and a temperature of 320 K.

Show Your Work

Answer 1

0.0976 L (3 s.f.)

Step-by-step explanation:

To find the final volume of the gas, use the combined gas law.

Combined Gas Law

`\boxed{\sf (P_1V_1)/(T_1)=(P_2V_2)/(T_2)}`

where:

• P₁ is the initial pressure.
• V₁ is the initial volume.
• T₁ is the initial temperature (in kelvin).
• P₂ is the final pressure.
• V₂ is the final volume.
• T₂ is the final temperature (in kelvin).

STP stands for Standard Temperature and Pressure.

The standard temperature is 273.15 K, and the standard pressure is 1 atm.

Therefore, the values to substitute into the formula are:

• P₁ = 1 atm
• V₁ = 0.225 L
• T₁ = 273.15 K
• P₂ = 2.7 atm
• T₂ = 320 K

Rearrange the formula to isolate V₂:

`\implies \sf V_2=(P_1V_1T_2)/(T_1P_2)`

Substitute the values into the formula and solve for V₂:

`\implies \sf V_2=(1 \cdot 0.225 \cdot 320)/(273.15 \cdot 2.7)`

`\implies \sf V_2=(72)/(737.505)`

`\implies \sf V_2=0.0976264567...`

`\implies \sf V_2=0.0976\;L\;(3\;s.f.)`

Therefore, the volume of the gas at the new pressure and temperature will be 0.0976 L (3 s.f.)