The mole fraction of water in `20% (wt.//wt.)` aqueous solution of `H_(2)O_(2)` is:

Options

A. `(77)/(68)`
B. `(68)/(77)`
C. `(20)/(80)`
D. `(204)/(231)`

Answer

To find the mole fraction of water in a 20% (wt/wt) aqueous solution of H₂O₂, we will follow these steps:

### Step 1: Understand the Composition of the Solution
A 20% (wt/wt) solution means that in 100 grams of the solution, there are 20 grams of H₂O₂ and 80 grams of water.

### Step 2: Calculate the Number of Moles of Water
To calculate the number of moles of water, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
The molar mass of water (H₂O) is approximately 18 g/mol. Therefore, the number of moles of water is:
\[ \text{Moles of water} = \frac{80 \text{ g}}{18 \text{ g/mol}} \approx 4.44 \text{ moles} \]

### Step 3: Calculate the Number of Moles of H₂O₂
The molar mass of H₂O₂ (hydrogen peroxide) is approximately 34 g/mol. Therefore, the number of moles of H₂O₂ is:
\[ \text{Moles of H₂O₂} = \frac{20 \text{ g}}{34 \text{ g/mol}} \approx 0.59 \text{ moles} \]

### Step 4: Calculate the Total Number of Moles
Now, we add the number of moles of water and H₂O₂ to find the total number of moles:
\[ \text{Total moles} = \text{Moles of water} + \text{Moles of H₂O₂} = 4.44 + 0.59 \approx 5.03 \text{ moles} \]

### Step 5: Calculate the Mole Fraction of Water
The mole fraction of water (Xₕ₂ₒ) is given by the formula:
\[ X_{H₂O} = \frac{\text{Moles of water}}{\text{Total moles}} = \frac{4.44}{5.03} \approx 0.88 \]

### Final Answer
Thus, the mole fraction of water in the 20% (wt/wt) aqueous solution of H₂O₂ is approximately:
\[ \frac{88}{100} = 0.88 \]