A solution containing 0.2 mole of each A, B and C. The sum of the mole fraction of A, B and C in an aqueous solutions is

Options

A. 0.6
B. 0.2
C. 1
D. 1.2

Answer

To solve the problem of finding the sum of the mole fractions of A, B, and C in an aqueous solution, we can follow these steps:

### Step 1: Identify the number of moles of each component
We are given that there are 0.2 moles of A, 0.2 moles of B, and 0.2 moles of C.

### Step 2: Calculate the total number of moles in the solution
To find the total number of moles in the solution, we add the moles of A, B, and C together:
\[ \text{Total moles} = n_A + n_B + n_C = 0.2 + 0.2 + 0.2 = 0.6 \text{ moles} \]

### Step 3: Calculate the mole fraction of each component
The mole fraction (x) of a component is calculated using the formula:
\[ x_A = \frac{n_A}{\text{Total moles}}, \quad x_B = \frac{n_B}{\text{Total moles}}, \quad x_C = \frac{n_C}{\text{Total moles}} \]

Calculating each:
\[ x_A = \frac{0.2}{0.6} = \frac{1}{3} \]
\[ x_B = \frac{0.2}{0.6} = \frac{1}{3} \]
\[ x_C = \frac{0.2}{0.6} = \frac{1}{3} \]

### Step 4: Sum the mole fractions
Now, we add the mole fractions together:
\[ x_A + x_B + x_C = \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1 \]

### Conclusion
The sum of the mole fractions of A, B, and C in the solution is:
\[ \text{Sum of mole fractions} = 1 \]

### Final Answer
The sum of the mole fractions of A, B, and C in the aqueous solution is **1**.

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