Question

If a gas is cooled from 523 K to 273 K and volume is kept constant

what final pressure would result if the original pressure was 745 mm
Hg?

Answer 1

388.88 mmHg (2 d.p.)

Step-by-step explanation:

To find the final pressure when the volume is kept constant, we can use Gay-Lussac's law.

Gay-Lussac's law

`\boxed{\sf (P_1)/(T_1)=(P_2)/(T_2)}`

where:

• P₁ is the initial pressure.
• T₁ is the initial temperature (in kelvins).
• P₂ is the final pressure.
• T₂ is the final temperature (in kelvins).

The values to substitute into the equation are:

• P₁ = 745 mmHg
• T₁ = 523 K
• T₂ = 273 K

Substitute the values into the equation and solve for P₂:

`\implies \sf (P_1)/(T_1)=(P_2)/(T_2)`

`\implies \sf (745)/(523 )=(P_2)/(273)`

`\implies \sf P_2=(745 \cdot 273)/(523 )`

`\implies \sf P_2=(203385)/(523 )`

`\implies \sf P_2=388.88145315...`

`\implies \sf P_2=388.88\;mmHg\;(2\;d.p.)`

Therefore, the final pressure would be 388.88 mmHg if a gas is cooled from 523 K to 273 K and the volume is kept constant, starting with an initial pressure of 745 mmHg.