Question

A $22.4L$ glass bulb has a total pressure of $760torr$ at $0^{\circ }C$ and contains three different gases,
nitrogen, helium and argon. If the partial pressure of nitrogen is $250torr$and the partial pressure
of argon is $130torr$ .
Given $R=62.363L.torr.mo{l}^{-1}{K}^{-1}$
Then the number of moles of helium in the bulb will be

• A. 0.5
• B. 1.5
• C. 2.5
• D. 1

Answer 1

The correct option is A 0.5

Given,
Total pressure = $760torr$
Partial pressure of $N_2,p_{N_2}=250torr$
Partial pressure of $Ar,p_{Ar}=130torr$

Dalton’s law of partial pressures is a gas law which states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by each individual gas in the mixture.
Hence,
Total pressure = $p_{N_2}+p_{Ar}+p_{H{e}_2}$
760 = 250 + 130 + $p_{H{e}_2}$
$p_{H{e}_2}=760-380=380torr$
The number of moles of He in the bulb is given by gas law,
PV = nRT
$R=62.363L.torr.mo{l}^{-1}{K}^{-1}$
$380\times 22.4=n_{He}\times 62.363\times 273$
$n_{He}=0.499mol\approx 0.5mol$

Hence, the correct answer is option (a).