Densities of two gases are in the ratio 1:2 and their temperatures are in the ratio 2:1 then the ratio of their respective pressures is?

Hi Madhurima,

Please find below the solution to the asked query:

Ideal Gas equation gives: PV = nRT

$$\begin{gathered} \sin ce density \left(\rho \right)=\frac{m}{V}, then \\ PV=\frac{m}{M}RT \\ or PM=\frac{m}{V}RT=\rho RT \end{gathered}$$

​For two different gases, we have two different expression as: $$\begin{gathered} P_1{M}_1={\rho }_{1}R{T}_1 ----\left(i\right) \\ {P}_2{M}_2={\rho }_{2}R{T}_2 ----\left(ii\right) \\ Dividing equation \left(i\right) by \left(ii\right), we get \\ \frac{P_1{M}_1}{P_2{M}_2}=\frac{{\rho }_{1}R{T}_1 }{{\rho }_{2}R{T}_2} \\ \frac{P_1{M}_1}{P_2{M}_2}=\frac{{\rho }_{1}R2T_2 }{2{\rho }_{1}R{T}_2} [\sin ce, density are in ratio 1:2 and temperature are in ratio 2:1] \\ \frac{P_1{M}_1}{P_2{M}_2}=1 \\ \frac{{\mathbf{P}}_{\mathbf{1}}}{{\mathbf{P}}_{\mathbf{2}}}\mathbf{=}\frac{{\mathbf{M}}_{\mathbf{2}}}{{\mathbf{M}}_{\mathbf{1}}} \end{gathered}$$

Hence, ratio of their pressure is inverse of the ratio of their molecular masses.



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