First slide

Thermometry

Question

Half a mole of helium at $27^{0} C$ and at a pressure of 2 atmosphere is mixed with 1.5 mole of $N_{2}$ at $77^{0}$ C and at a pressure of 5 atmosphere so that the volume of the mixture is equal to the sum of their initial volumes. If the temperature of the mixture is $69^{0}$ C, its pressure in atmosphere is

Moderate

A

3.5
B

3.8
C

3.95
D

4.25

Solution

PV = nRT $V = \frac{nRT}{P}$
From conservation of mole number
$n_{1} + n_{2} = n$
$n_{1} + n_{2} = \frac{P}{RT} (V_{1} + V_{2})$
$n_{1} + n_{2} = \frac{P}{RT} (\frac{n_{1} {RT}_{1}}{P_{1}} + \frac{n_{2} {RT}_{2}}{P_{2}})$
$n_{1} + n_{2} = \frac{P}{T} (\frac{n_{1} T_{1}}{P_{1}} + \frac{n_{2} T_{2}}{P_{2}})$
$0.5+1.5=2= \frac{P}{T} (\frac{0.5 T_{1}}{P_{1}} + \frac{1.5 T_{2}}{P_{2}})$
$2= \frac{P}{342} (\frac{0.5 (300)}{2} + \frac{1.5 (350)}{5})$
P = 3.8 atm

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