Question

A \[200\text{ }cc\] flask contains oxygen at \[200\text{ }mm\] pressure and a \[300\text{ }cc\] flask contains nitrogen at \[100\text{ }mm\] pressure. The two flasks are connected so that each gas occupies the combined volume. The total pressure of the mixture in \[mm\] is:
A.\[60\]
B.\[80\]
C.\[140\]
D.\[300\]

Answer 1

Hint:Dalton’s law establishes a relationship between the partial pressures of individual liquid and the total pressure of the mixture as well as the volumes of the same.
The total volume of the mixture can be calculated by adding the volume of both flasks because the flasks are connected to each other .
Formula used: \[P_1V_1+P_2V_2=PVtotal\]
Where \[P_1\] is the partial pressure of gas \[1\]and \[{{P}_{2}}\] is the partial pressure of gas $2$. Similarly, ${{V}_{1}}$ is the volume of gas \[1\] and ${{V}_{2}}$ is the volume of gas $2$. And $P$ is the total pressure of a mixture of gases and $Vtotal$ is the total volume of the mixture.


Complete answer:
Dalton's law of partial pressures deals with the partial pressure of each substance present in a mixture of solution. It states that the partial pressure of ideal gas in a mixture of ideal gases is equal to the pressure gas would exert if it alone occupied the volume of the mixture at the temperature of the mixture. In other words, it states that the total pressure exerted by a mixture of various gases is the sum of the partial pressures of all the components involved in the mixture:
$Ptotal=Pgas1+Pgas2+Pgas3...$
where the partial pressures of each individual gases are the pressure that the same gas under consideration would exert if it was the only gas in the container.
According to Dalton's law of partial pressure, the sum of multiplication of individual partial pressures and volume of the components of gases present in a mixture is equal to the total volume into pressure of the mixture. This can be mathematically represented as,
\[P_1V_1+P_2V_2=PVtotal\]
Where \[P_1\] is the partial pressure of gas \[1\]and \[{{P}_{2}}\] is the partial pressure of gas $2$. Similarly, ${{V}_{1}}$ is the volume of gas \[1\] and ${{V}_{2}}$ is the volume of gas $2$. And $P$ is the total pressure of mixture of gases and $Vtotal$ is the total volume of the mixture.
Now the given values are
Here, \[P_1=200mm\],\[P_2=100mm\] ,\[V_1=200cc\] ,\[V_2=300cc\]
So we need to find out total pressure of the mixture which is $P$,while the total volume is given as $500mm$
\[200\times 200+300\times 100=P\times 500\]
After solving the above equation for the value of total pressure we get,
$P=140mm$
So the correct answer is, option C.

Note:
-In dalton's law, we assume there are no attractive forces between the gases, that is why we take the pressure exerted by individual gases, and when they are present in a mixture, we call it partial pressure.
-The absence of attractive force makes this law ideal .