Question

$N_2$ gas is present in one litre flask at a pressure of $7.6\times {10}^{-10}mm$ of $Hg$. The number of $N_2$ gas molecules in the flask at $O^{o}C$ is?

• A. $2.68\times {10}^9$
• B. $2.68\times {10}^{10}$
• C. $1.34\times {10}^{28}$
• D. $2.68\times {10}^{22}$

Answer 1

Answer: (B)

$2.68\times {10}^{10}$

To calculate the number of moles of the gas under the given condition by the relation

$PV=nRT$

$P=7.6\times {10}^{-10}$

$=\frac{7.6\times {10}^{-10}}{760atm}=1\times {10}^{-12}atm$

$V=1litre$

$T=273+0=273K$

$R=0.082litratm/K/mol$

substituting the values in equation

$n=\frac{PV}{RT}=\frac{1\times {10}^{-12}\times 1}{0.082\times 273}moles$

Now since 1mole=$6.023\times {10}^{23}$

$\frac{{10}^{-12}}{0.082\times 273}=\frac{6.023\times {10}^{23}\times {10}^{-12}}{0.082\times 273}$

$=2.7\times {10}^{10}molecule$