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

Answer:

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)