Which of the following statement(s) is/are true?
I. In a binary mixture, mole fraction of A is `chi_A = (n_A)/(n_A + n_B).`
II. For solution containing i number of components, `chi_i = (n_i)/(sumn_i)`
III. Sum of all mole fractions is one.
Select the option with true statements.

Options

A. I and II
B. II and III
C. III and I
D. All of the above

Answer

To determine which of the statements regarding mole fractions are true, let's analyze each statement step by step.

### Step 1: Analyze Statement I
**Statement I:** In a binary mixture, mole fraction of A is `chi_A = (n_A)/(n_A + n_B).`

- In a binary mixture, we have two components: A and B.
- The mole fraction of component A (denoted as `chi_A`) is defined as the ratio of the number of moles of A (`n_A`) to the total number of moles in the mixture (which is the sum of moles of A and B).
- Therefore, `chi_A = n_A / (n_A + n_B)` is indeed correct.

**Conclusion for Statement I:** True.

### Step 2: Analyze Statement II
**Statement II:** For a solution containing i number of components, `chi_i = (n_i)/(sumn_i)`

- Here, `chi_i` represents the mole fraction of component i in a solution with multiple components.
- The mole fraction of component i is defined as the number of moles of component i (`n_i`) divided by the total number of moles of all components in the solution.
- The total number of moles is represented as `sumn_i`, which is the sum of moles of all components.
- Thus, `chi_i = n_i / (sumn_i)` is also correct.

**Conclusion for Statement II:** True.

### Step 3: Analyze Statement III
**Statement III:** Sum of all mole fractions is one.

- The mole fractions of all components in a solution must add up to one. This is a fundamental property of mole fractions.
- If we have components A, B, C, ..., the sum of their mole fractions will be `chi_A + chi_B + chi_C + ... = 1`.

**Conclusion for Statement III:** True.

### Final Conclusion
All three statements are true. Therefore, the correct option is that all statements (I, II, and III) are true.

### Summary of True Statements
- **I:** True
- **II:** True
- **III:** True

### Final Answer
All statements are true.

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