Question

A sample of nitrogen dioxide has a volume of 28.6 L at 45.3°C and 89.9 kPa. What is its volume at STP?

Answer 1

`22.1` `"L"`

Explanation:

We can solve this problem using the combined gas law:

`(P_1V_1)/(T_1) = (P_2V_2)/(T_2)`

Standard temperature and pressure conditions are

• `100` `"kPa"`

• `0^"o""C"`

Remember that the temperatures must be in Kelvin, so we must convert the Celsius temperatures:

`0^"o""C" = 273.15` `"K"`

`45.3^"o""C" = 318.5` `"K"`

Since we're trying to find the volume at stp, let's rearrange this equation to solve for `V_2`:

`V_2 = (P_1V_1T_2)/(T_1P_2)`

Plugging in known values, we have

`V_2 = ((89.9cancel("kPa"))(28.6"L")(273.15cancel("K")))/((318.5cancel("K"))(100cancel("kPa"))) = color(red)(22.1` `color(red)("L"`

rounded to `3` significant figures, the amount given in the problem.

The volume of the nitrogen as sample at stp is thus `22.1` liters.