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?

Apr 2, 2018

The final volume will be $\text{56 mL}$.

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

${V}_{1} = \text{93 mL}$

${T}_{1} = \text{144"^@"C + 273.15"="417 K}$ $\leftarrow$ Temp must be in Kelvins.

${T}_{2} = - {22}^{\circ} \text{C + 273.15"="251 K}$ $\leftarrow$ Temp must be in Kelvins.

Unknown

${V}_{2}$

Solution

Rearrange the formula to isolate ${V}_{2}$. Plug in the known values and solve.

${V}_{2} = \frac{{V}_{1} {T}_{2}}{T} _ 1$

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