The density of a gas is found to be $2.07 {\mathrm{gL}}^{-1} \mathrm{at} {30}^{°}\mathrm{C}$and 2 atm pressure. What is its density at NTP 

The given data is as follows :

${\mathrm{d}}_1=2.07\mathrm{g}/\mathrm{lit}$

${\mathrm{T}}_1=30+273=303\mathrm{K}; {\mathrm{T}}_{\mathrm{K}}=°\mathrm{C}+273$

${\mathrm{T}}_2=273 \mathrm{K}; \mathrm{NTP}$ means normal Temp and Pressure

${\mathrm{P}}_1=2\mathrm{atm} {\mathrm{P}}_2=1 \mathrm{atm}$

$\mathrm{Then} {\mathrm{d}}_2=?$

From ideal gas equation,

PV=nRT 

$\mathrm{PV}=\frac{\mathrm{w}}{\mathrm{G}.\mathrm{M}.\mathrm{W}}\times \mathrm{RT};\mathrm{Since},\mathrm{n}=\frac{\mathrm{weight}}{\mathrm{Gram} \mathrm{molecular} \mathrm{weight}}$

$\mathrm{Then} \mathrm{P}\times \mathrm{GMW}=\mathrm{dRT}$

Consider the equation for same gas at two different conditions.

[ G.M.W is same]

$\frac{{\mathrm{d}}_1{\mathrm{T}}_1}{{\mathrm{P}}_1}=\frac{d_2{T}_2}{P_2}$

$\Rightarrow \frac{2.07\times 303}{2\times 273}=\frac{{\mathrm{d}}_2\times 273}{1}$

$\therefore d_2=\frac{2.07\times 303}{2\times 273}=1.149 g/lit$

$\therefore \mathrm{Density} \mathrm{of} \mathrm{a} \mathrm{gas} \mathrm{at} \mathrm{NTP} \mathrm{is} 1.149 \mathrm{g}/\mathrm{lit}$