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  • We have two vessels of equal volume, one filled with hydrogen and the other with equal mass of Helium. The common temperature is <img alt="27^{\circ} \mathrm{C}" src="https://entrancecorner.oncodec

We have two vessels of equal volume, one filled with hydrogen and the other with equal mass of Helium. The common temperature is 27^{\circ} \mathrm{C}.

Question : If pressure of Hydrogen is 2 \mathrm{~atm}, what is the pressure of Helium ?

Option: 1

\mathrm{p}_{\mathrm{He}}=2 \mathrm{~atm}.


Option: 2

\mathrm{p}_{\mathrm{He}}=3 \mathrm{~atm}.


Option: 3

\mathrm{p}_{\mathrm{He}}=4 \mathrm{~atm}.


Option: 4

\mathrm{p}_{\mathrm{He}}=1 \mathrm{~atm}.


Answers (1)

best_answer

The equation of state for one mole of a gas is

\mathrm{pV}=\mathrm{RT}=\mathrm{Nk} \mathrm{T}

Where \mathrm{N} is Avogadro's number (no. of molecules in one mole) and \mathrm{k} is Boltzmann's constant. If a gas has \mathrm{n} molecules, the equation of state will be
\mathrm{\mathrm{pV}=\mathrm{nk} T}

For a given volume and a given temperature, we have
\mathrm{\mathrm{p} \propto \mathrm{n}}.

Since \mathrm{H}_{2} and \mathrm{He} have same volume and same temperature \left(27^{\circ} \mathrm{C}\right),  we have

\mathrm{\frac{\mathrm{p}_{\mathrm{H}}}{\mathrm{p}_{He}}=\frac{n_{H}}{n_{He}}= \frac{2}{1}}

\mathrm{Here \, \mathrm{p}_{\mathrm{H}}=2 \mathrm{~atm}}.

\mathrm{\therefore \quad \mathrm{pHe}=1 \mathrm{~atm} \text { }}.

Posted by

Sanket Gandhi

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