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Which of the following is correct?...

Which of the following is correct?

A

The sum of mole fractions of all the components in a solution is always unity

B

Mole fraction depends upon temperature

C

Mole fraction is always negative

D

Mole fraction is independent of content of solute in solution

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AI Generated Solution

The correct Answer is:
To solve the question regarding the correctness of statements about mole fractions in a solution, we will analyze each statement step by step. ### Step-by-Step Solution: 1. **Understanding Mole Fraction**: - The mole fraction (x) of a component in a solution is defined as the ratio of the number of moles of that component to the total number of moles of all components in the solution. - Mathematically, for component A, it can be expressed as: \[ x_A = \frac{n_A}{n_A + n_B} \] - Where \( n_A \) is the number of moles of component A and \( n_B \) is the number of moles of component B. 2. **Sum of Mole Fractions**: - If we consider two components A and B, the mole fractions can be added: \[ x_A + x_B = \frac{n_A}{n_A + n_B} + \frac{n_B}{n_A + n_B} \] - Simplifying this gives: \[ x_A + x_B = \frac{n_A + n_B}{n_A + n_B} = 1 \] - Therefore, the sum of the mole fractions of all components in a solution is always equal to 1. 3. **Analyzing Each Statement**: - **Statement 1**: "The sum of the mole fraction of all the components in a solution is always unity." - This statement is **correct** based on our calculations. - **Statement 2**: "The mole fraction depends upon temperature." - This statement is **incorrect**. The mole fraction is a ratio that depends on the number of moles, which is related to mass and does not change with temperature for a given amount of substance. - **Statement 3**: "Mole fraction is always negative." - This statement is **incorrect**. Since mole fractions are ratios of moles, they can never be negative; they are always positive values. - **Statement 4**: "Mole fraction is independent of the content of solute in solution." - This statement is **incorrect**. The mole fraction is directly related to the amount of solute present in the solution; thus, it cannot be independent of it. 4. **Conclusion**: - The only correct statement is **Statement 1**: "The sum of the mole fraction of all the components in a solution is always unity." ### Final Answer: The correct option is **Statement 1**.
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