The percentage composition (by weight) of a solution is `45% X, 15% Y`, and `40% Z`. Calculate the mole fraction of each component of the solution. (Molecular mass of `X = 18, Y = 60`, and `Z = 60)`

Explanation

To calculate the mole fraction of each component (X, Y, and Z) in the solution, we will follow these steps:

### Step 1: Understand the percentage composition
The percentage composition by weight of the solution is given as:
- X = 45%
- Y = 15%
- Z = 40%

This means that in 100 grams of the solution, there are:
- 45 grams of X
- 15 grams of Y
- 40 grams of Z

### Step 2: Calculate the number of moles of each component
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{Given mass (g)}}{\text{Molar mass (g/mol)}} \]

#### For X:
- Given mass of X = 45 g
- Molar mass of X = 18 g/mol
\[ n_X = \frac{45 \, \text{g}}{18 \, \text{g/mol}} = 2.5 \, \text{moles} \]

#### For Y:
- Given mass of Y = 15 g
- Molar mass of Y = 60 g/mol
\[ n_Y = \frac{15 \, \text{g}}{60 \, \text{g/mol}} = 0.25 \, \text{moles} \]

#### For Z:
- Given mass of Z = 40 g
- Molar mass of Z = 60 g/mol
\[ n_Z = \frac{40 \, \text{g}}{60 \, \text{g/mol}} = 0.6667 \, \text{moles} \quad (\text{approximately } 0.67) \]

### Step 3: Calculate the total number of moles
Now, we add the moles of all components:
\[ \text{Total moles} = n_X + n_Y + n_Z = 2.5 + 0.25 + 0.6667 = 3.4167 \, \text{moles} \]

### Step 4: Calculate the mole fraction of each component
The mole fraction (\(X_i\)) of each component is calculated using the formula:
\[ X_i = \frac{n_i}{\text{Total moles}} \]

#### For X:
\[ X_X = \frac{n_X}{\text{Total moles}} = \frac{2.5}{3.4167} \approx 0.731 \]

#### For Y:
\[ X_Y = \frac{n_Y}{\text{Total moles}} = \frac{0.25}{3.4167} \approx 0.073 \]

#### For Z:
\[ X_Z = \frac{n_Z}{\text{Total moles}} = \frac{0.6667}{3.4167} \approx 0.195 \]

### Final Mole Fractions:
- Mole fraction of X (\(X_X\)) ≈ 0.731
- Mole fraction of Y (\(X_Y\)) ≈ 0.073
- Mole fraction of Z (\(X_Z\)) ≈ 0.195

### Summary
The mole fractions of the components in the solution are:
- \(X_X \approx 0.731\)
- \(X_Y \approx 0.073\)
- \(X_Z \approx 0.195\)