Suggested Response - Q3

*Determine the density of nitrogen at standard temperature and pressure.

Response:

Standard temperature and pressure are 0°C and 101,325 Pa, respectively.

Expressing the universal gas law with the specific gas constant RSpecific:

P V space equals space m R subscript S p e c i f i c end subscript T

Rearranging for density ρ (m/V):

rho space equals space fraction numerator P over denominator left parenthesis R subscript S p e c i f i c end subscript T right parenthesis end fraction

Remembering the definition for RSpecific:

R subscript S p e c i f i c space end subscript equals space fraction numerator R over denominator M. M a s s end fraction space equals space fraction numerator 8 comma 314.5 over denominator 2 space cross times space 14 end fraction space equals space 296.9 space J divided by k g K

The density of nitrogen at STP is given by:

rho space equals space fraction numerator 101 comma 325 over denominator 296.9 space cross times space left parenthesis 273.15 space plus space 0 right parenthesis end fraction space equals space 1.25 space k g divided by m cubed

Alternatively, you may have adopted a slightly different approach by considering the concept of molar volume where 1 kmol of any gas occupies 22.4 m3 at STP. In this case, we know that the molar volume at STP is 22.4 m3 and we know that the molar mass of N2 is 28 kg/kmol. Therefore, the density of N2 is given by:

rho subscript N subscript 2 end subscript space equals space m over V space equals space fraction numerator 28 over denominator 22.4 end fraction space equals space 1.25 space k g divided by m cubed

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