A) 96
B) 128
C) 32
D) 64
Correct Answer: D
Solution :
| Given, \[{{V}_{A}}={{V}_{B}}=50\,mL\] |
| \[{{T}_{A}}=150s\] |
| \[{{T}_{B}}=200s\] |
| \[{{M}_{B}}=36\] |
| \[{{M}_{A}}=?\] |
| From Graham's law of effusion |
| \[\frac{{{r}_{B}}}{{{r}_{A}}}=\sqrt{\frac{{{M}_{A}}}{{{M}_{B}}}}=\frac{{{V}_{B}}{{T}_{A}}}{{{T}_{B}}\cdot {{V}_{A}}}\] |
| \[\Rightarrow \] \[\sqrt{\frac{{{M}_{A}}}{36}}=\frac{{{V}_{A}}\times 150}{200\times {{V}_{A}}}\] |
| or \[\sqrt{\frac{{{M}_{A}}}{36}}=\frac{15}{20}=\frac{3}{4}\] |
| \[\frac{{{M}_{A}}}{36}=\frac{9}{16}\] |
| \[{{M}_{A}}=\frac{9\times 36}{16}=\frac{9\times 9}{4}=\frac{81}{4}=20.2\] |
| (No option is correct) |
| Note If \[{{T}_{A}}=200s\]and\[{{T}_{B}}=150s,\] the \[{{M}_{A}}=64\] |
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