Question

he time required for 0.010 moles of so 3 (g) to effuse through an opening was 22 seconds. under the same conditions, an unknown gas required 28 seconds. the unknown gas is most likely: a. xe(g) b. uf 6 (g) c. sif 4 (g) d. cf 4 (g) e. sf 6 (g)

Answer 1

The gas is most likely to be Xenon. So the correct option is (a)

What is The rate of diffusion?

The rate of diffusion, is the change in the number of diffusing molecules inside the cell over time i.e. $d_{n}$ / $d_{t}$. As the net movement of diffusing molecules depends on the concentration gradient then the rate of diffusion is directly proportional to the concentration gradient ($d_{C}$/$d_{t}$) across the membrane.

Since,  $\frac{1}{time}$ $\alpha$ $\frac{pressure}{\sqrt{molar weight} }$

In the given question time required for 0.010 moles of SO₃ is 22 s

Time required for 1 mole of SO₃ is  $\frac{22}{0.01}$ × 1 = 2200 s

Now,  $\frac{1}{2200}$ $\alpha$ $\frac{1}{\sqrt{80} }$

For unknown gas

$\frac{1}{2800}$ $\alpha$ $\frac{1}{\sqrt{m} }$

Now combining both the equation;

Since,

$\frac{1}{2200}$ × 2800 = $\frac{1}{\sqrt{80} }$ ×$\sqrt{m}$

m = 129.02 g/mole

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