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Question

In a container of capacity 1 litre, there are 1023 molecules each of mass 10−22 g. If the root mean square speed is 105 cm/s then calculate the pressure of the gas.

A
13×107 Pa
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B
1×107 Pa
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C
1 atm
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D
1 torr
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Solution

The correct option is A 13×107 PaWe know the root mean square speed is given as: urms=√3RTM or using PV=nRT urms=√3PVnM urms=√3PVw (using n=w/M) now, PV=13w U2rms we have N=1023 molecules so total mass becomes m×N PV=13m N U2rms P=?; V=1L=10−3 m3 m=10−25 kg; N=1023 mol−1 urms=105 cm/s=103 m/s u2rms=106 m2/s2 P×10−3=13×10−25×1023×106 P=13×10−2×106×103 P=13×107 Pascals

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