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?

1 Answer
Apr 2, 2018

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)