Question

A 26.5 g sample of nitrogen, N2 , has a volume of 50.0 L and a pressure of 640. mmHg . express answer in three sig figsWhat is the temperature of the gas in kelvins?What is the temperature of the gas in degrees Celsius?

Answer 1

To answer this question we have to usethe ideal gas law:

$PV=nRT$

Where P is the pressure, V is the volume, n is the number of moles, R is the constant of ideal gases (0.082atmL/molK) and T is the temperature (in Kelvin degrees).

The first step is to convert the given mass of N2 to moles using its molecular mass:

$26.5gN_2\cdot\frac{molN_2}{28gN_2}=0.95molN_2$

And convert the pressure from mmHg to atm (1atm=760mmHg):

$640mmHg\cdot\frac{1atm}{760mmHg}=0.84atm$

Finally, solve the initial equation for T and replace for the given values:

$\begin{gathered} T=\frac{PV}{nR} \\ T=\frac{0.84atm\cdot50.0L}{0.95mol\cdot0.082atmL/molK} \\ T=539.15K \end{gathered}$

The temperature of the gas is 539.15K.

Convert this temperature to Celsius by substracting 273.15 to the temperature in Kelvins:

$T=539.15-273.15=226$

The temperature of the gas is 226°C.