A) \[2.5\times {{10}^{25}}\]
B) \[-2.5\times {{10}^{25}}\]
C) \[-1.61\times {{10}^{23}}\]
D) \[1.38\times {{10}^{23}}\]
Correct Answer: B
Solution :
Using ideal gas equation PV = NRT (N is number of moles) \[{{P}_{0}}{{V}_{0}}={{N}_{i}}R\times 290\] ?.. \[[{{T}_{i}}=237+17=290K]\] After heating \[{{P}_{0}}{{V}_{0}}={{N}_{f}}R\times 300\] ?.. from equation [a] and [b] \[{{N}_{f}}-{{N}_{i}}=\frac{{{P}_{0}}{{V}_{0}}}{R}\left[ \frac{10}{290\times 300} \right]\] Hence \[{{n}_{f}}-{{n}_{i}}\]is \[=-\frac{{{P}_{0}}{{V}_{0}}}{R}\times \left[ \frac{10}{290\times 300} \right]\times 6.023\times {{10}^{23}}\] Putting \[{{P}_{0}}={{10}^{5}}{{P}_{A}}\]and \[{{V}_{0}}=30{{m}^{3}}\] Number of molecules \[{{n}_{f}}-{{n}_{i}}=-2.5\times {{10}^{25}}\]
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