Question

A sample of gas occupies 17 mL at -112°C. What volume does the sample occupy at 70°C?

Answer 1

Use Charles' Law, which states that at a constant pressure, temperature and volume are proportional.

It is also written as

`("V"_1)/("T"_1)=("V"_2)/("T"_2)`

Before we define our values, note that temperature in gas law equations always use Kelvin, not Celsius.

To go from degrees Celsius to Kelvin, add `273`.

Thus, we have

`"V"_1="17 mL"`
`"T"_1=-112^@"C"="161 K"`

`"V"_2=???`
`"T"_2=70^@"C"="343 K"`

Thus, we have

`("17 mL")/("161 K")="V"_2/("343 K")`

Cross-multiply to solve for `"V"_2`:

`17 * "343 mL" * "K"="161 K" * "V"_2`

`"5831 mL"="161 V"_2`

`color(red)("V"_2="36.2173913043 mL"`

The question technically has `1` significant figure, since there's only one significant figure in `70^@"C"`.

This means the final answer is

`color(blue)("V"_2=4xx10^1` `color(blue)("mL"`