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Question

Physics Question on kinetic theory

What is the fraction of molecular volume to the actual volume occupied by oxygen gas at STPSTP ? Given, the diameter of oxygen molecule is 2 ?2\,? .

A

1.75×10−41.75\times 10^{-4}

B

1.5×10−41.5\times 10^{-4}

C

12×10−412\times 10^{-4}

D

1.125×10−41.125\times 10^{-4}

Answer

1.125×10−41.125\times 10^{-4}

Explanation

Solution

Volume of oxygen gas at STP =22.4 L=22.4\, L
=22.4×10−3m3…=22.4 \times 10^{-3} m^{3} \ldots (i)
⇒\Rightarrow Volume of oxygen molecules at STP
=N0×43πr3=N_{0} \times \frac{4}{3} \pi r^{3}
=6.02×1023×43π(10−10)3=6.02 \times 10^{23} \times \frac{4}{3} \pi\left(10^{-10}\right)^{3}
=6.02×43×π×10−7=6.02 \times \frac{4}{3} \times \pi \times 10^{-7}
=25.20×10−7m3=25.20 \times 10^{-7} m^{3}
⇒ Volume (oxygen molecules at STP)  Volume (oxygen gas at STP) \Rightarrow \frac{\text { Volume (oxygen molecules at STP) }}{\text { Volume (oxygen gas at STP) }}
=25.20×10−722.4×10−3=\frac{25.20 \times 10^{-7}}{22.4 \times 10^{-3}}
=1.125×10−4=1.125 \times 10^{-4}