Question

If 5 mol of liquid A and 10 mol of liquid B are mixed to form an ideal solution then the total pressure of the solution toll be (P = 200 mm Hg and P400 mm Hg)
1)310 mm Hg
2)423 mm Hg
3)333.3 mm Hg
4)410 mm Hg​

Answer 1

Given :-

Number of moles of liquid A = 5 mol

Number of moles of liquid B = 10 mol

Vapour pressure of liquid A = 200 mm Hg

Vapour pressure of liquid B = 400 mm Ug

To Find :-

Total pressure of the solution

Solution :-

We know :-

$\underline{ \bf P_{total} = P_{A}^{\circ}X_{A} + P_{B}^{\circ}X_{B}}$

$\bullet \sf \: X_{A} = \dfrac{n_{A}}{n_{A} + n_{B}}$

$: \implies \sf \: X_{A} = \dfrac{5}{5 + 10}$

$: \implies \sf X_{A} = \dfrac{5}{15}$

$: \implies \sf X_{A} = \dfrac{1}{3}$

$\bullet \sf \: X_{B} = \dfrac{n_{B}}{n_{A} + n_{B}}$

$: \implies \sf X_{B} = \dfrac{10}{5 + 10}$

$: \implies \sf X_{B} = \dfrac{10}{15}$

$: \implies \sf X_{B} = \dfrac{2}{5}$

$\bf P_{total} = P_{A}^{\circ}X_{A} + P_{B}^{\circ}X_{B}$

$: \implies \sf P_{total} = 200 \times \dfrac{1}{3} + 400 \times \dfrac{2}{3}$

$: \implies \sf P_{total} = 66.67 + 266.67$

$: \implies \sf P_{total} = 333.3$

Total pressure :- 333.3 mm Hg

Correct option :- C

Answer 2

Answer:

Given :-

• 5 mol of liquid A and 10 mol of liquid B are mixed to form an ideal solution.
• [Pᴀ = 200 mm Hg, Pʙ = 400 mm Hg]

To Find :-

• What is the total pressure of the solution.

Formula Used :-

$\clubsuit$ Total Pressure Formula :

$\mapsto \sf\boxed{\bold{\pink{P_T =\: P^{\circ}_AX_A + P^{\circ}_BX_B}}}$

Solution :-

${\small{\bold{\purple{\underline{\leadsto\: In\: case\: of\: X_A\: :-}}}}}$

$\bigstar\: \: \sf\boxed{\bold{\pink{X_A =\: \dfrac{n_A}{n_A + n_B}}}}$

where,

• $\sf n_A$ = Number of Moles in liquid A
• $\sf n_B$ = Number of Moles in liquid B

Given :

• Number of Moles in liquid A = 5 moles
• Number of Moles in liquid B = 10 moles

According to the question by using the formula we get,

$\implies \sf X_A =\: \dfrac{5}{5 + 10}$

$\implies \sf X_A =\: \dfrac{\cancel{5}}{\cancel{15}}$

$\implies \sf X_A =\: \dfrac{1}{3}$

$\implies \sf\bold{\green{X_A =\: \dfrac{1}{3}}}$

${\small{\bold{\purple{\underline{\leadsto\: In\: case\: of\: X_B\: :-}}}}}$

$\bigstar\: \: \sf\boxed{\bold{\pink{X_B =\: \dfrac{n_B}{n_A + n_B}}}}$

where,

• $\sf n_A$ = Number of Moles in liquid A
• $\sf n_B$ = Number of Moles in liquid B

Given :

• Number of Moles in liquid A = 5 moles
• Number of Moles in liquid B = 10 moles

According to the question by using the formula we get,

$\implies \sf X_B =\: \dfrac{10}{5 + 10}$

$\implies \sf X_B =\: \dfrac{\cancel{10}}{\cancel{15}}$

$\implies \sf X_B =\: \dfrac{2}{3}$

$\implies \sf\bold{\green{X_B =\: \dfrac{2}{3}}}$

Now, we have to find the total pressure of the solution :

Given :

• Vapour Pressure Of Liquid A = 200 mm Hg
• Vapour Pressure Of Liquid B = 400 mm Hg

According to the question by using the formula we get,

$\longrightarrow \sf P_T =\: 200 \times \dfrac{1}{3} + 400 \times \dfrac{2}{3}$

$\longrightarrow \sf P_T =\: \dfrac{200}{3} + \dfrac{800}{3}$

$\longrightarrow \sf P_T =\: \dfrac{200 + 800}{3}$

$\longrightarrow \sf P_T =\: \dfrac{1000}{3}$

$\longrightarrow \sf\bold{\red{P_T =\: 333.3\: mm\: Hg}}$

$\therefore$ The total pressure of the solution is 333.3 mm Hg.

Hence, the correct options is option no (3) 333.3 mm Hg.