According to Maxwell's distribution of molecular speeds, for the below graph drawn for two different samples of gases A and B at temperature $T_{1}$ and $T_{2}$ respectively, which of the following statements is/are INCORRECT:

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If gas A is $O_{2}$ and gas B is $N_{2}$ , then considering them to be ideal gases, $T_{1}$ is necessarily less than $T_{2}$ .

If $T_{1} < T_{2}$ , then molecular mass of gas $B (M_{B})$ is necessarily less than molecular mass of gas $A (M_{A})$ .

If molecular mass of gas $A (M_{A})$ is equal to molecular mass of gas $B (M_{B})$ , then $T_{1} > T_{2}$ .

If $T_{1} = T_{2}$ , then molecular mass of gas $B (M_{B})$ is greater than molecular mass of gas $A (M_{A})$

answer is A, B, C, D.

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Detailed Solution

At constant temperature, decrease in molecular mass causes flattening of the graph. For same molecular mass of gas, increase in temperature causes flattering of the graph
${(V_{m p})}_{T_{1}} < {(V_{m p})}_{T_{2}}$
$∴ \frac{T_{1}}{M_{A}} < \frac{T_{2}}{M_{B}} ∴ \frac{T_{2}}{T_{1}} > \frac{M_{B}}{M_{A}}$
But , $\frac{M_{B}}{M_{A}}$ can be less than or greater than 1
Similarly, $\frac{M_{A}}{M_{B}} > \frac{T_{1}}{T_{2}}$
If gas A is $O_{2}$ and gas B is $N_{2}$ , then $M_{A} > M_{B}$