Question

If the density of a gas at the sea level at 0° is 1·29 kg m^–3, what is the molar mass? (Assume that pressure is equal to 1 bar).

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Solution

Using ideal gas equation,

PVn space equals space RT space space space space space or space space space space straight P. straight M over straight d space equals space RT

or space space space space space straight M equals space dRT over straight P space space space space space.... left parenthesis 1 right parenthesis

Here space space space space space space space straight P space equals space 1 space bar space equals space 1.0 space cross times space 10 to the power of 5 Nm to the power of negative 2 end exponent space space space space space space space space space space space space space straight T space equals space 273.15 space straight K space space space space space space space space space space space space space straight R space equals space 8.314 space Nm space straight K to the power of negative 1 end exponent mol to the power of negative 1 end exponent space space space space space space space space space space space space space straight d space equals space 1.29 space kg space straight m to the power of negative 3 end exponent

Substituting the values in eq. (1), we have,

straight M space equals space fraction numerator left parenthesis 1.29 space kg space straight m to the power of negative 3 end exponent right parenthesis space cross times space left parenthesis 8.314 space straight N space mk to the power of negative 1 end exponent space mol to the power of negative 1 end exponent right parenthesis space cross times space left parenthesis 273.15 space straight K right parenthesis over denominator 1.0 space cross times space 10 to the power of 5 Nm to the power of negative 2 end exponent end fraction space space space space equals space fraction numerator 1.29 space cross times space 8.314 space cross times space 273.15 space kg space mol to the power of negative 1 end exponent over denominator 1 space cross times space 10 to the power of 5 end fraction space space space space equals space 0.0293 space kg space mol to the power of negative 1 end exponent space space space space equals space 29.3 space straight g space mol to the power of negative 1 end exponent therefore space space space Molar space mass space is space 29.3 space straight g space mol to the power of negative 1 end exponent

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