Question

Calculate the universal gas constant R, if one mol of a gas at STP occupies 22.4 litres.

Answer 1

Answer:

$\boxed{\underline{\Huge{\mathtt{8.31\:J\:mol^{-1}\:K^{-1}}}}}$

Explanation:

$\mathtt{\:\:\:\:\:\:\:Standard\:Pressuse,\:P=0.76\:m\:of\:Hg=1.013 \times 10^5\:Nm^{-2}}\\\mathtt{Standard\:Temperature,\:T=273\:K}\\\mathtt{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:V=22.4 \times 10^{-3}\:m^3}\\\mathtt{From\:the\:gas\:equation,\:PV=RT}\\\mathtt{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\therefore R = \dfrac{PV}{T}=\dfrac{1.013\times 10^5\times 22.4\times10^{-3}}{273}}$

$\mathtt{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=8.31\:J\:mol^{-1}k^{-1}}$