First slide

Gaseous state

Question

At 400 k the Root Mean Square (RMS) speed of a gas ‘X’ (MW= 40) is equal to the most probable speed of a gas Y at 60K .The molecular weight of the gas = ___g.

Moderate

Solution

Given,
$r_{rms} = r_{mp}$
$\frac{3 R T_{x}}{M_{x}} = \frac{2 R T_{y}}{M_{y}} T_{x} = 400; M_{x} = 40$
$\Rightarrow \frac{3 \times 400}{40} = \frac{2 \times 60}{M_{y}} T_{y} = 60; M_{y} = ?$
$\Rightarrow M_{y} = 4$
root mean square (or) $C_{p} o f Y = \sqrt{\frac{2 R T_{y}}{M_{y}}}$

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