What is the quantity of water that should be added to 16 gm. Methanol to make the mol fraction of methanol as 0.25?

Options

A. 27 gm
B. 12 gm
C. 18 gm
D. 36 gm

Answer

To solve the problem of determining the quantity of water that should be added to 16 grams of methanol to achieve a mole fraction of 0.25, we can follow these steps:

### Step 1: Calculate the moles of methanol
First, we need to find the number of moles of methanol (CH₃OH) present in 16 grams.

- The molar mass of methanol (CH₃OH) is calculated as follows:
- Carbon (C): 12 g/mol
- Hydrogen (H): 1 g/mol × 4 = 4 g/mol
- Oxygen (O): 16 g/mol
- Total = 12 + 4 + 16 = 32 g/mol

Now, we can calculate the moles of methanol:
\[ \text{Moles of methanol} = \frac{\text{mass of methanol}}{\text{molar mass of methanol}} = \frac{16 \text{ g}}{32 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 2: Set up the equation for mole fraction
The mole fraction of methanol (X) is given by the formula:
\[ X_{\text{methanol}} = \frac{\text{moles of methanol}}{\text{moles of methanol} + \text{moles of water}} \]
Let the moles of water be \( x \). According to the problem, we want the mole fraction of methanol to be 0.25:
\[ 0.25 = \frac{0.5}{0.5 + x} \]

### Step 3: Solve for the moles of water
Now we can solve the equation for \( x \):
\[ 0.25(0.5 + x) = 0.5 \]
Expanding this gives:
\[ 0.125 + 0.25x = 0.5 \]
Now, isolate \( x \):
\[ 0.25x = 0.5 - 0.125 \]
\[ 0.25x = 0.375 \]
\[ x = \frac{0.375}{0.25} = 1.5 \text{ moles of water} \]

### Step 4: Calculate the mass of water
To find the mass of water required, we use the molar mass of water (H₂O), which is 18 g/mol:
\[ \text{Mass of water} = \text{moles of water} \times \text{molar mass of water} = 1.5 \text{ moles} \times 18 \text{ g/mol} = 27 \text{ g} \]

### Final Answer
The quantity of water that should be added is **27 grams**.

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