Question

A .952 L container of gas is exerting a pressure of 108 kPa while at a temperature of 48 C. Calculate the pressure of this same amount of gas in a 1.236 L container at a temperature of 64 C.

Show Your Work

Answer 1

87.33 kPa (2 d.p.)

Step-by-step explanation:

To solve this problem, 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).

As we want to find the final pressure, rearrange the formula to isolate P₂:

`\sf P_2=(P_1V_1T_2)/(T_1V_2)`

As the temperatures have been given in Celsius, we need to first convert the temperatures from Celsius to kelvin by adding 273.15:

`\implies \sf T_1=48+273.15=321.15\;K`

`\implies \sf T_2=64+273.15=337.15\;K`

The given values are:

• P₁ = 108 kPa
• V₁ = 0.952 L
• T₁ = 321.15 K
• V₂ = 1.236 L
• T₂ = 337.15 K

Substitute the values into the formula and solve for P₂:

`\implies \sf \sf P_2=(108 \cdot 0.952 \cdot 337.15)/(321.15 \cdot 1.236)`

`\implies \sf \sf P_2=(34664.414)/(396.9414)`

`\implies \sf P_2=87.3287946...`

`\implies \sf P_2=87.33\;kPa\;(2\;d.p.)`

Therefore, the final pressure of the gas is 87.33 kPa (2 d.p.).