Question #95169

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Question #95169

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Answer 1 · 2016-07-25T08:52:14

The relative molecular mass of gas Z is 32

To get feasible result the volume of hydrogen gas diffused is considered $200 c m^{3}$ $200cm^3$ .

Explanation:

To solve this problem we are to apply Graham's law of diffusion which states that the rate of effusion or of diffusion (R)of a gas is inversely proportional to the square root of its molecular weight or relatve molecular mass (M) at constant temperature and pressure.

$Symbolically, R \propto \frac{1}{\sqrt{M}}$ $color(red)("Symbolically, "R prop 1/sqrtM)$

Let

$M_{Z} \to Relative molecular mass of gas Z = ?$ $M_Z->"Relative molecular mass of gas Z"=?$

$M_{H} \to Rel. molecular mass of Hydrogen = 2$ $M_H->"Rel. molecular mass of Hydrogen"=2$

$R_{Z} \to Rate diffusion of gas Z = \frac{100}{10} = 10 \frac{{cm}^{3}}{s}$ $R_Z->"Rate diffusion of gas Z"=100/10=10"cm"^3/s$

$R_{H} \to Rate diffusion of Hydrogen = \frac{200}{5} = 40 \frac{{cm}^{3}}{s}$ $R_H->"Rate diffusion of Hydrogen"=200/5=40"cm"^3/s$

Now by Graham's law

$\frac{R_{H}}{R_{Z}} = \sqrt{\frac{M_{Z}}{M_{H}}}$ $R_H/R_Z=sqrt(M_Z/M_H)$

$\Rightarrow \frac{40}{10} = \sqrt{\frac{M_{Z}}{2}}$ $=>40/10=sqrt(M_Z/2)$

$M_{Z} = 4^{2} \cdot 2 = 32$ $M_Z=4^2*2=32$

The relative molecular mass of gas Z is 32

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Question #95169

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