Question

Calculate the ratio of kinetic energies of 3g of hydrogen and 4g of oxygen at a given temperature
The mean kinetic energy of a molecule at $O^0$ C is $5.621\times {10}^{-14}$ erg. Calculate Boltzmann's constant. If the value of $R=8.314\times {10}^7$erg, then also calculate the no. of molecules present in one mole of gas.

Answer 1

Kinetic energy $=\frac{3}{2}nRT$

$\therefore n_{H_2}=\frac{3}{2}$ and $n_{O_2}=\frac{4}{16}$

$\therefore$ ratio of $K.E$ of $3g$ $H_2$ and $4g$ $O_2=\frac{3}{2}:\frac{4}{16}=6:1$

Average $K.E.=\frac{3}{2}KT$

$\Rightarrow K=\frac{5.621\times {10}^{-14}\times 2}{3\times 273}=1.372\times {10}^{-16}erg{molecule}^{-1}{K}^{-1}$

$\therefore$ now of molecules present in one mole of gas, i.e.

Avogadro's number $=\frac{R}{K}=\frac{8.314\times {10}^7}{1.372\times {10}^{-16}}=6.059\times {10}^{23}$