10 mL of hydrogen contains $2 \times 10^{3}$ molecules of hydrogen at certain pressure and temperature. Calculate the number of molecules of oxygen whose volume is 200 mL at the same temperature and pressure.

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Solution

By ideal gas equation, $P V = n R T$
$V \propto n$ at constant $P$ and $T$ .
But no. of moles $\propto$ no. of molecules.
Therefore, Volume $\propto$ No. of molecules.
$∴ \frac{V_{1}}{V_{2}} = \frac{M_{1}}{M_{2}}$
$∴ \frac{10}{200} = \frac{2 \times 10^{3}}{M_{2}}$
$∴ M_{2} = 4 \times 10^{4}$ molecules
Therefore, the number of molecules whose volume is $200 m l$ are $4 \times 10^{4}$ molecules

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10 mL of hydrogen contains 2×103 molecules of hydrogen at certain pressure and temperature. Calculate the number of molecules of oxygen whose volume is 200 mL at the same temperature and pressure.

By ideal gas equation, PV=nRTV∝n at constant P and T.But no. of moles ∝ no. of molecules.Therefore, Volume ∝ No. of molecules.∴V1V2=M1M2∴10200=2×103M2∴M2=4×104 moleculesTherefore, the number of molecules whose volume is 200ml are 4×104 molecules

10 mL of hydrogen contains $2 \times 10^{3}$ molecules of hydrogen at certain pressure and temperature. Calculate the number of molecules of oxygen whose volume is 200 mL at the same temperature and pressure.