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100 g of liquid A (molar mass: 140 g mol-1) was dissolved in 1000 g of liquid B (molar mass:180 g mol-1). The vapour pressure of pure liquid B was found to be 500 torr. What will be the vapour pressure of pure liquid A and its vapour pressure in the solution, respectively, if the total vapour pressure of the solution is 475 torr?
  • a)
    28.7 torr and 32 torr
  • b)
    280.7 torr and 32 torr
  • c)
    28.7 torr and 3.2 torr
  • d)
    280.7 torr and 3.2 torr
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
100 g of liquid A (molar mass: 140 g mol-1) was dissolved in 1000 g...

Explanation:

Calculating the Vapour Pressure of Pure Liquid A:
- According to Raoult's Law, the partial vapour pressure of a component in a solution is directly proportional to its mole fraction in the solution.
- Let x be the mole fraction of liquid A in the solution.
- The mole fraction of liquid B will be (1-x).
- Using the formula for total vapour pressure of a solution:
Total Vapour Pressure = x * Vapour Pressure of A + (1-x) * Vapour Pressure of B
475 = x * Vapour Pressure of A + (1-x) * 500
475 = x * Vapour Pressure of A + 500 - 500x
Vapour Pressure of A = 500 - 500x + 475x
Vapour Pressure of A = 500 - 25x

Calculating the Vapour Pressure of Liquid A in the Solution:
- Using Dalton's Law of Partial Pressures, the total vapour pressure of the solution is the sum of the partial pressures of the components.
- The partial pressure of A can be calculated using the formula:
Partial Pressure of A = Mole Fraction of A * Vapour Pressure of A
Given that the total vapour pressure of the solution is 475 torr, and the vapour pressure of liquid B is 500 torr, we can substitute the values to find the mole fraction of A.
475 = x * (500 - 25x)
475 = 500x - 25x^2
25x^2 - 500x + 475 = 0
x^2 - 20x + 19 = 0
(x-1)(x-19) = 0
x = 1 or x = 19 (ignoring x=1 as it is not possible)
Therefore, x = 19
Vapour Pressure of A = 500 - 25(19) = 500 - 475 = 25 torr

Therefore, the vapour pressure of pure liquid A is 25 torr and its vapour pressure in the solution is 25 torr. Hence, the correct answer is option B.
Free Test
Community Answer
100 g of liquid A (molar mass: 140 g mol-1) was dissolved in 1000 g...
= 280.7 × 0.11 = 32 torr
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100 g of liquid A (molar mass: 140 g mol-1) was dissolved in 1000 g of liquid B (molar mass:180 g mol-1). The vapour pressure of pure liquid B was found to be 500 torr. What will be the vapour pressure of pure liquid A and its vapour pressure in the solution, respectively, if the total vapour pressure of the solution is 475 torr?a)28.7 torr and 32 torrb)280.7 torr and 32 torrc)28.7 torr and 3.2 torrd)280.7 torr and 3.2 torrCorrect answer is option 'B'. Can you explain this answer?
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