The volume of a mass of gas at 37⁰C and a pressure of 75 cm of mercury is 620 c.c. Find the volume at N.T.P.

Volume of gas , V = 620cc 

Temperature , T = 37 +273 = 310K

Pressure , P = 75cm of Hg = $\frac{75}{76}$ atm [as 1 atm = 76cm Hg]

Using equation, PV = nRT

So,  $\mathrm{n}=\frac{{\displaystyle \raisebox{1ex}{$75$}\!\left/ \!\raisebox{-1ex}{$76$}\right.}\times 0.62}{\mathrm{R}\times 310}$.....(1)

at NTP ( normal temperature and pressure)

temperature , T' = 0° = 273K

pressure , P' = 1atm

applying equation, P'V' = nRT'

or, 1atm × V' = nR × (273K)

or, V' = nR(273)

from equation (1),

$\mathrm{V}\text{'}=\frac{{\displaystyle \raisebox{1ex}{$75$}\!\left/ \!\raisebox{-1ex}{$76$}\right.\times 620}}{310}\times 273=538.8\mathrm{cc}$