Two liquids of vapour pressure p1 and p2 in pure state in the ratio of...
Two liquids of vapour pressure p1 and p2 in pure state in the ratio of...
Solution:
Given,
Liquids with vapour pressure p1 and p2 in pure state in the ratio of 2:1.
Molar ratio of liquids in the mixture = 1:2.
To find: The ratio of their moles in the vapour state.
Let us assume that we have '2x' moles of liquid 1 and 'x' moles of liquid 2 in pure state.
In the vapour state, the partial pressure of liquid 1 (p1) = mole fraction of liquid 1 in vapour state × total pressure.
Similarly, the partial pressure of liquid 2 (p2) = mole fraction of liquid 2 in vapour state × total pressure.
From Raoult's law, we know that mole fraction of liquid 1 in vapour state = moles of liquid 1 in vapour state / total moles in vapour state.
Total moles in vapour state = 2x + x = 3x.
Moles of liquid 1 in vapour state = (molar ratio of liquid 1 in the mixture) × (total moles in vapour state) = (1/3) × 3x = x.
Similarly, moles of liquid 2 in vapour state = (molar ratio of liquid 2 in the mixture) × (total moles in vapour state) = (2/3) × 3x = 2x.
Therefore, the ratio of their moles in the vapour state = x : 2x = 1:2.
Hence, the correct option is (B) 1:2.
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Solution:
Given,
Liquids with vapour pressure p1 and p2 in pure state in the ratio of 2:1.
Molar ratio of liquids in the mixture = 1:2.
To find: The ratio of their moles in the vapour state.
Assumptions:
Let us assume that we have '2x' moles of liquid 1 and 'x' moles of liquid 2 in pure state.
Calculation:
Partial pressure of liquid 1 (p1) = mole fraction of liquid 1 in vapour state × total pressure.
Partial pressure of liquid 2 (p2) = mole fraction of liquid 2 in vapour state × total pressure.
Mole fraction of liquid 1 in vapour state = moles of liquid 1 in vapour state / total moles in vapour state.
Total moles in vapour state = 2x + x = 3x.
Moles of liquid 1 in vapour state = (molar ratio of liquid 1 in the mixture) × (total moles in vapour state) = (1/3) × 3x = x.
Moles of liquid 2 in vapour state = (molar ratio of liquid 2 in the mixture) × (total moles in vapour state) = (2/3) × 3x = 2x.
Answer:
Ratio of their moles in the vapour state = x : 2x = 1:2.
Hence, the correct option is
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