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Physics Question on kinetic theory

Molecular weight of oxygen is 32 amu32\, amu . At STPSTP , volume of 1 gm1\, gm of oxygen is 700 cm3700 \,cm^3 . What is the value of gas constant RR ?

A

18.23 J mol−1 K−118.23 \,J \,mol^{-1}\, K^{-1}

B

27.73 J mol−1 K−127.73 \,J \,mol^{-1}\, K^{-1}

C

37.97 J mol−1 K−137.97 \,J \,mol^{-1}\, K^{-1}

D

8.31 J mol−1 K−18.31 \,J \,mol^{-1}\, K^{-1}

Answer

8.31 J mol−1 K−18.31 \,J \,mol^{-1}\, K^{-1}

Explanation

Solution

PV=nRTPV=nRT At STPSTP, P=105P=10^{5}, T=273T=273, n=132n=\frac{1}{32}, V=700×10−6mV=700\times10^{-6}m R=PVnTR=\frac{PV}{nT} =105×700×10−6132×273=\frac{10^{5}\times700\times10^{-6}}{1 32\times273} ≃8.31 J mol−1 K−1\simeq 8.31\,J\,mol^{-1}\,K^{-1}