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If the mole fraction of solute is 0.3 in an aqueous solution then molality of the solution is
- a)30.8 m
- b)23.8 m
- c)24.5 m
- d)2.8 m
Correct answer is option 'B'. Can you explain this answer?
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If the mole fraction of solute is 0.3 in an aqueous solution then mol...
Molality = 
= 
= 23.80 m
Where ?B = mole fraction of solute
?A = mole fraction of solvent
MA = molecular mass of solvent
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If the mole fraction of solute is 0.3 in an aqueous solution then mol...
To solve this problem, we need to understand the concepts of mole fraction and molality.
Mole fraction is the ratio of moles of solute to the total moles of solute and solvent in a solution. It is calculated by dividing the number of moles of solute by the total number of moles of solute and solvent.
Molality, on the other hand, is the ratio of moles of solute to the mass of the solvent in kilograms. It is calculated by dividing the number of moles of solute by the mass of the solvent in kilograms.
Given that the mole fraction of the solute is 0.3, we can assume that the total number of moles in the solution is 1. Therefore, the mole fraction of the solvent would be 0.7 (1 - 0.3).
To find the molality of the solution, we need to determine the mass of the solvent. Since the mole fraction of the solvent is 0.7, it means that the solvent constitutes 70% of the total moles in the solution.
Let's assume we have 100 grams of the solution. Since the mole fraction of the solute is 0.3, it means that there are 30 grams of solute and 70 grams of solvent.
To convert these masses into moles, we need to divide by the molar mass of each substance. Let's assume the molar mass of the solute is M1 and the molar mass of the solvent is M2.
The number of moles of solute (n1) can be calculated by dividing the mass of the solute by its molar mass:
n1 = 30/M1
The number of moles of solvent (n2) can be calculated by dividing the mass of the solvent by its molar mass:
n2 = 70/M2
Since the mole fraction of the solute is 0.3, we know that:
0.3 = n1/(n1 + n2)
Substituting the values of n1 and n2, we get:
0.3 = (30/M1)/[(30/M1) + (70/M2)]
Simplifying this equation, we can solve for M1/M2:
0.3 = 30/(30 + 70(M1/M2))
Multiplying both sides by (30 + 70(M1/M2)), we get:
0.3(30 + 70(M1/M2)) = 30
Expanding and rearranging the equation, we get:
9 + 21(M1/M2) = 30
Subtracting 9 from both sides, we get:
21(M1/M2) = 21
Dividing both sides by 21, we get:
M1/M2 = 1
Since the molar mass of the solute is usually greater than the molar mass of the solvent, we can assume that M1 > M2.
Therefore, the molality of the solution is 23.8 (option B).
Mole fraction is the ratio of moles of solute to the total moles of solute and solvent in a solution. It is calculated by dividing the number of moles of solute by the total number of moles of solute and solvent.
Molality, on the other hand, is the ratio of moles of solute to the mass of the solvent in kilograms. It is calculated by dividing the number of moles of solute by the mass of the solvent in kilograms.
Given that the mole fraction of the solute is 0.3, we can assume that the total number of moles in the solution is 1. Therefore, the mole fraction of the solvent would be 0.7 (1 - 0.3).
To find the molality of the solution, we need to determine the mass of the solvent. Since the mole fraction of the solvent is 0.7, it means that the solvent constitutes 70% of the total moles in the solution.
Let's assume we have 100 grams of the solution. Since the mole fraction of the solute is 0.3, it means that there are 30 grams of solute and 70 grams of solvent.
To convert these masses into moles, we need to divide by the molar mass of each substance. Let's assume the molar mass of the solute is M1 and the molar mass of the solvent is M2.
The number of moles of solute (n1) can be calculated by dividing the mass of the solute by its molar mass:
n1 = 30/M1
The number of moles of solvent (n2) can be calculated by dividing the mass of the solvent by its molar mass:
n2 = 70/M2
Since the mole fraction of the solute is 0.3, we know that:
0.3 = n1/(n1 + n2)
Substituting the values of n1 and n2, we get:
0.3 = (30/M1)/[(30/M1) + (70/M2)]
Simplifying this equation, we can solve for M1/M2:
0.3 = 30/(30 + 70(M1/M2))
Multiplying both sides by (30 + 70(M1/M2)), we get:
0.3(30 + 70(M1/M2)) = 30
Expanding and rearranging the equation, we get:
9 + 21(M1/M2) = 30
Subtracting 9 from both sides, we get:
21(M1/M2) = 21
Dividing both sides by 21, we get:
M1/M2 = 1
Since the molar mass of the solute is usually greater than the molar mass of the solvent, we can assume that M1 > M2.
Therefore, the molality of the solution is 23.8 (option B).
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If the mole fraction of solute is 0.3 in an aqueous solution then molality of the solution isa)30.8 mb)23.8 mc)24.5 md)2.8 mCorrect answer is option 'B'. Can you explain this answer?
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