Question

A mixture of volatile components A and B has total vapour pressure (in torr) as $P = 254 - 119{X_A}$ , where ${X_A}$ is mole fraction of A in the mixture. Hence, ${P_A}^ \circ $ and ${P_B}^ \circ $ respectively are (in torr):
A. 254, 119
B. 119, 254
C. 135, 254
D. 154, 119

Answer 1

Hint:Dalton’s law of partial pressure states that the total pressure exerted by the mixture of inert gases is the equal to the sum of the partial pressure of each gas in the mixture. This Dalton’s law of partial pressure is applicable to ideal gases.

Complete answer:
The total pressure of a mixture of gases can be determined by adding the pressure of each individual gas. Mathematically it can be represented as-
 ${P_{total}} = {P_1} + {P_2} + {P_{3.}}....... + {P_n}$
The partial pressure of individual gas is equal to the total pressure multiplied by mole fraction of that gas. As we know, in the ideal gas equation the pressure depends on the number of moles of gas, not the kind of molecules the gas contains. Therefore Dalton’s law helps us to calculate the total pressure in a system from each gas’ individual gas pressure.
In this case, given is total pressure as ${P_{total}} = 254 - 119{X_A}$
We can write it as, ${P_{total}} = 254 - 119{X_A} = {P_A} + {P_B}$
Or ${P_{total}} = 254 - 119{X_A} = {P_A}^ \circ {X_A} + {P_B}^ \circ {X_B}$
We know that
$
  {X_A} + {X_B} = 1 \\
\Rightarrow {X_B} = 1 - {X_A}
 $
so putting the value of ${X_B}$ in above equation, we get
${P_{total}} = 254 - 119{X_A} = {P_A}^ \circ {X_A} + {P_B}^ \circ (1 - {X_A})$
On rearranging, ${P_{total}} = 254 - 119{X_A} = {P_B}^ \circ - ({P_B}^ \circ - {P_A}^ \circ ){X_A}$
Comparing the two equation, we have ${P_B}^ \circ = 254$ and ${P_B}^ \circ - {P_A}^ \circ = 119$ , or ${P_A}^ \circ = 254 - 119 = 135$

Therefore the correct option will be C.

Note:
For the purpose of gas exchange, oxygen and carbon dioxide are mainly considered due to their metabolic importance in gas exchange. Since gas flows from area from high to low pressure, atmospheric air has higher partial pressure of oxygen than lung’s air. Dalton’s law is applicable to ideal gases. Therefore most gases do not follow it.