Question

The volume of a sample of a gas at 273 Kelvin and is 100.0 L. If the volume is decreased to 50.0 L at constant pressure, what will be the new temperature of the gas?

Answer 1

The new temperature will be `color(blue)("137 K")`.

Explanation:

This is an example of Charles' law, which states that the volume of a given amount of a gas is directly proportional to its Kelvin temperature. The formula to use for this law is `V_1/T_1=V_2/T_2`.

Given
`V_1="100.0 L"`
`T_1="273 K"`
`V_2="50.0 L"`

Unknown
`T_2`

Solution
Rearrange the formula to isolate `T_2`. Substitute the given values into the formula and solve.

`V_1/T_1=V_2/T_2`

`T_2=(T_1V_2)/V_1`

`T_2=(273"K" xx 50.0cancel"L")/(100.0cancel"L")`

`T_2="136.5 K"="137 K"` rounded to three significant figures

The proportionality between volume and temperature can be easily seen in this problem. As the volume decreased by half, the Kelvin temperature decreased by half.

A very good tutorial on the gas laws can be found at http://chemistry.bd.psu.edu/jircitano/gases.html.