TS EAMCET · Chemistry · Some Basic Concepts of Chemistry

If $\bar{M}_w$ is the weight average molecular weight and $\bar{M}_n$ is the number average molecular weight of a polymer, the poly dispersity index (PDI) of the polymer is given by

A $\frac{\bar{M}_n}{\bar{M}_w}$
B $\frac{\bar{M}_w}{\bar{M}_n}$
C $\bar{M}_w \times \bar{M}_n$
D $\frac{1}{\bar{M}_w \times \bar{M}_n}$

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Correct Answer

(B) $\frac{\bar{M}_w}{\bar{M}_n}$

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Detailed explanation

The ratio of weight average molecular weight and the number average molecular weight is called poly dispersity index (PDI). \[ \mathrm{PDI}=\frac{\bar{M}_w}{\bar{M}_n} \] where, $\bar{M}_w=$ weight average molecular weight $\bar{M}_n=$ number average molecular weight PDI is…

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

Following lists contain reactions and their corresponding equilibrium constants at different temperatures:

List - I (Reaction)	List - II $(K_{p})$
$2 {SO}_{2} (g) + O_{2} (g) ⇌ 2 {SO}_{3} (g) at 298 K$	$4.0 \times 10^{24}$
$2 {SO}_{2} (g) + O_{2} (g) ⇌ 2 {SO}_{3} (g) at 700 K$	$3.0 \times 10^{4}$
$N_{2} O_{4} (g) ⇌ 2 {NO}_{2} (g) at 298 K$	$0.98$
$N_{2} O_{4} (g) ⇌ 2 {NO}_{2} (g) at 500 K$	$1700$

∆ H_{1}^{0} and ∆ H_{2}^{0}

are the standard enthalpies for the reactions

2 {SO}_{2} + O_{2} ⇌ 2 {SO}_{3} and N_{2} O_{4} ⇌ 2 {NO}_{2}

respectively, then:

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If \(\bar{M}_w\) is the weight average molecular weight and \(\bar{M}_n\) is the number average molecular weight of a polymer, the poly dispersity index (PDI) of the polymer is given by

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