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Standard XII

Mathematics

Existence of Limit

At what tempe...

Question

At what temperature will the rate of effusion of $N_{2}$ be 1.625 times that of $S O_{2}$ at $50^{\circ}$ C?

373 k

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273 k

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473 k

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127 k

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Solution

The correct option is A
373 k

$R a t e \propto \sqrt{T} \propto \frac{1}{\sqrt{M}}$

$∴$ Applying Graham’s Law of effusion ;

$r \propto \sqrt{\frac{T}{M}} (o r) \frac{r N_{2}}{r S o_{2}} = \sqrt{\frac{T_{N_{2}}}{T_{S O_{2}}} \times \frac{M_{S O_{2}}}{M_{N_{2}}}} 1.625 = \sqrt{\frac{T_{N_{2}}}{323} \times \frac{64}{28}} ∴ T_{N_{2}} = 373 K$

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At what temperature will the rate of effusion of N2 be 1.625 times that of SO2 at 50∘ C?

The correct option is A 373 k Rate∝√T∝1√M ∴ Applying Graham’s Law of effusion ; r∝√TM (or) rN2rSo2=√TN2TSO2×MSO2MN21.625=√TN2323×6428∴ TN2=373 K

At what temperature will the rate of effusion of $N_{2}$ be 1.625 times that of $S O_{2}$ at $50^{\circ}$ C?