Question

A 93-L sample of dry air is cooled from 145 oC to -22 oC at a constant pressure of 2.85 atmospheres). What is the final volume?

Answer 1

Answer:

56 L

Explanation:

We're dealing with a gas in this problem. We may, therefore, apply the ideal gas law for this problem:

$pV = nRT$

We now that we have a constant pressure. Besides, R, the ideal gas law constant, is also a constant number. Let's rearrange the equation so that we have all constant variables on the right and all changing variables on the left:

$\frac{V}{T} = \frac{nR}{p} = const$

This means the ratio between volume and temperature is a constant number. For two conditions:

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

Given initial volume of:

$V_1 = 93 L$

Convert the initial temperature into Kelvin:

$T_1 = 145^oC + 273.15 K = 418.15 K$

Convert the final temperature into Kelvin:

$T_2 = -22^oC + 273.15 K = 251.15 K$

Rearrange the equation for the final volume:

$V_2 = V_1 \cdot \frac{T_2}{T_1} = 93 L\cdot \frac{251.15 K}{418.15 K} = 56 L$