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A polymer contains 50 molecules with molecular mass 5000, 100 molecules with molecular mass 10,000 and 50 molecules with molecular mass 15,000. Calculate number average molecular mass?
Options:
Solution:
2871 Upvotes
Verified Answer
The correct answer is:
10,000
$\because$ Number average molecular mass $(M n)$
$$
=\frac{N_2 M_2+N_2 M_2+N_3 M_3}{N_2+N_2+N_3}
$$
where, $N_2, N_2$ and $N_3$ are number of molecules and $M_2, M_2$ and $M_3$ are respectively their molecular masses.
Given,
$$
\begin{aligned}
& N_2=50 \text { and } M_2=5000 \\
& N_2=100 \text { and } M_2=10,000 \\
& N_3=50 \text { and } M_3=15,000
\end{aligned}
$$
Thus,
$$
\begin{aligned}
M \bar{n} & =\frac{N_1 M_1+N_2 M_2+N_3 M_3}{N_1+N_2+N_3} \\
& =\frac{(50 \times 5000)+(100 \times 10,000)+(50 \times 15000)}{50+100+50} \\
& =\frac{(25,0000)+(1,000,000)+(75,00,00)}{200} \\
M \bar{n} & =10,000
\end{aligned}
$$
Hence, option (3) is the correct answer.
$$
=\frac{N_2 M_2+N_2 M_2+N_3 M_3}{N_2+N_2+N_3}
$$
where, $N_2, N_2$ and $N_3$ are number of molecules and $M_2, M_2$ and $M_3$ are respectively their molecular masses.
Given,
$$
\begin{aligned}
& N_2=50 \text { and } M_2=5000 \\
& N_2=100 \text { and } M_2=10,000 \\
& N_3=50 \text { and } M_3=15,000
\end{aligned}
$$
Thus,
$$
\begin{aligned}
M \bar{n} & =\frac{N_1 M_1+N_2 M_2+N_3 M_3}{N_1+N_2+N_3} \\
& =\frac{(50 \times 5000)+(100 \times 10,000)+(50 \times 15000)}{50+100+50} \\
& =\frac{(25,0000)+(1,000,000)+(75,00,00)}{200} \\
M \bar{n} & =10,000
\end{aligned}
$$
Hence, option (3) is the correct answer.
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