Question

A 93mL sample of dry air cools from 144°C to -22°C while the pressure is maintained at 2.85 atm. What is the final volume?

Answer 1

The final volume will be `"56 mL"`.

Explanation:

This is an example of Charles' law, which states that the volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature . This means that if the volume increases, so does the temperature, and vice versa. The formula for this law is:

`V_1/T_1=V_2/T_2`,

where:

`V_1` is the initial volume, `V_2` is the final volume, `T_1` is the initial temperature, and `T_2` is the final temperature.

Organize the data:

Known

`V_1="93 mL"`

`T_1="144"^@"C + 273.15"="417 K"` `larr` Temp must be in Kelvins.

`T_2=-22^@"C + 273.15"="251 K"` `larr` Temp must be in Kelvins.

Unknown

`V_2`

Solution

Rearrange the formula to isolate `V_2`. Plug in the known values and solve.

`V_2=(V_1T_2)/T_1`

`((93"mL")xx(251color(red)cancel(color(black)("K"))))/(417color(red)cancel(color(black)("K")))="56 mL"` (rounded to two significant figures)