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(molN_2)/(28gN_2)=0.95molN_2`

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

`640mmHg\cdot(1atm)/(760mmHg)=0.84atm`

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

`\begin{gathered} T=(PV)/(nR) \\ T=(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.