Question

A cylinder contains helium at $2.5$ atmospheric pressure. Another identical cylinder contains argon at $1.5$ atmospheric pressure at the same temperature. If both the gases are filled in any one of the cylinders, the pressure of the mixture will be:
A . $1.5$ atm
B. $2.5$ atm
C . $4$ atm
D. none of these

Answer 1

Hint: In order to solve this numerical we need to apply the theory of Dalton’s. For non-reacting mixtures of gases the number of moles of each gas remains constant. So the pressure due to each gas remains constant. So that we can calculate the total pressure.

Complete step by step answer:
From the given data:
${P_{helium}}$=2.5atm
$\Rightarrow {P_{argon}}$=1.5atm

According to Dalton‘s law the total pressure of non- non-reacting mixture of gases that is exerted on the walls of the container is the sum of individual pressure or partial pressures of each gas.
Which is given by ${P_{total}} = \sum {{P_i}} $
Where ${P_i}$ is the individual partial pressure of each gas present in the mixture

So, by applying Dalton’s law here we get,
${P_{total}} = {P_{helium}} + {P_{argon}}$……… (1)
Where, ${P_{total}}$ = total pressure exerted by the mixture on the walls of the container,
${P_{helium}}$= partial pressure of helium gas
And ${P_{argon}}$=partial pressure of argon gas

$
{P_{total}} = 2.5 + 1.5 \\
\therefore {P_{total}} = 4atm \\ $
So, the total pressure of the mixture when both gases are filled in a cylinder will be 4 atm.Hence, the correct option is C.

Additional information:
The mole fraction of a specific gas in a mixture of gases is equal to the ratio of the partial pressure of that gas to the total pressure exerted by the gaseous mixture. This type of mole fraction is used to calculate the total number of moles of a gas when the total number of moles in the mixture of known value.

Note:Students must be aware that applying Dalton's theory is for a mixture of non-reacting gases so that it’s very easy to solve this kind of numerical. The physical conditions should be the same (like temperature) and it should be mentioned in the question that the gases are non-reacting.