Question

A gaseous mixture contains three gases A, B and C with a total number of $10$ moles and total pressure of $10$ $atm$. The partial pressures of A and B are $3$ $atm$ and \ [1\] atm respectively and if C has molecular weight of $2g/mol$. Then, the weight of C present in the mixture will be:
A.$8g$
B.$12g$
C.$3g$
D.$6g$

Answer 1

Hint: Use Dalton ‘s law to find the weight of C present in mixture. This law states that the partial pressure of gas in a mixture is directly proportional to the mole fraction of that gas multiplied by total pressure of the gas.

Complete step by step answer:
First, we will write down the information provided to us.
Total number of moles = $10$
Partial pressure of A = $3$ atm
Partial pressure of B = \[1\] atm
Molecular weight of C = $2g/mol$
From Dalton ‘s law we have the following equation: ${P_A} + {P_B} + {P_C} = {P_{Total}} $
$\therefore {P_C} = {P_{Total}} - ({P_A} + {P_B}) $
$ \Rightarrow {P_C} = 10 - (3 + 1) $ = $6$$atm$
Now making use of the equation, ${P_C} = {Y_C} \times {P_T} $
 Where, ${P_C} $= Partial pressure of C, ${Y_C} $= mole fraction of C and ${P_T} $ = Total pressure
We have,\[\]$\dfrac{{{n_c}}}{{{n_T}}} = \dfrac{{{P_C}}}{{{P_T}}}$ $\dfrac{{{n_c}}}{{{n_T}}} = \dfrac{{{P_C}}}{{{P_T}}}$
$ \Rightarrow \dfrac{{{W_C}}}{{{M_C}}} = \dfrac{{{P_C} \times {n_T}}}{{{P_T}}}$ = $\dfrac{{6 \times 10}}{{10}}$= $6$
$ \Rightarrow {W_C} = 6 \times {M_C} = 6 \times 2$=$12g$
So the weight of gas C in the given mixture is $12g$.
So, the correct option is B.

Additional information: At a constant temperature, the pressure exerted by the vapours of a liquid on its surface when liquid and vapours are in equilibrium, is known as vapour pressure. The various factors which affect vapour pressure are: (a) nature of liquid (b) Temperature.

Note:
Always remember that in case of gases, Dalton law is applied and in case of liquids, Raoult ’s law is applied which states that for a solution of volatile liquids the partial vapour pressure of any component at constant temperature is equal to vapour pressure of pure component multiplied by mole fraction of that component in the solution.