COMEDK · Chemistry · 5. States of Matter

The ratio of average velocity of a gas molecule to the root mean square velocity at a particular temperature is

A 1 : 1.81
B 1.81 : 1
C 2 : 1.81
D 1.81 : 2

Verified Solution

Answer & Solution

Correct Answer

(A) 1 : 1.81

Step-by-step Solution

Detailed explanation

The expression for root mean square velocity is \(\left(\mu_{\mathrm{rms}}\right)=\sqrt{\frac{3 R T}{M}},\) and for average speed, \(\left(\mu_{\text {avg }}\right)=\sqrt{\frac{8 R T}{\pi M}}\) For a particular gas, at particular temperature \(M\) and \(T\) are constant.…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match the details given in Column I with those given in Column II

S.No.	Column I	S.No.	Column II
A	For complex reactions order is determined by	P	Rate of reaction.
B	For Zero order reaction unit of k is same as that of	Q	Slope \(= k/2.303\)
C	Mathematical expression which gives relationship between rate of reaction and concentrations of reactants is called	R	Slowest rate determining step.
D	For a first order reaction plot of \(\log[R_0]/[R]\) vs time gives	S	Rate law.

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