Mole fraction of `C_(3)H_(5)(OH)_(3)` in a solution of 36 g of water and 46 g of glycerine is :

Options

A. 0.46
B. 0.36
C. 0.2
D. 0.4

Answer

To find the mole fraction of glycerin (C₃H₅(OH)₃) in a solution containing 36 g of water and 46 g of glycerin, we can follow these steps:

### Step 1: Calculate the molar mass of glycerin (C₃H₅(OH)₃)
The molecular formula of glycerin is C₃H₅(OH)₃. To calculate its molar mass:
- Carbon (C): 3 atoms × 12 g/mol = 36 g/mol
- Hydrogen (H): 8 atoms (5 from C₃H₅ and 3 from (OH)₃) × 1 g/mol = 8 g/mol
- Oxygen (O): 3 atoms × 16 g/mol = 48 g/mol

Total molar mass of glycerin = 36 + 8 + 48 = 92 g/mol

### Step 2: Calculate the number of moles of glycerin
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
For glycerin:
\[ \text{Number of moles of glycerin} = \frac{46 \text{ g}}{92 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 3: Calculate the number of moles of water
The molar mass of water (H₂O) is:
- Hydrogen (H): 2 atoms × 1 g/mol = 2 g/mol
- Oxygen (O): 1 atom × 16 g/mol = 16 g/mol

Total molar mass of water = 2 + 16 = 18 g/mol

Now, calculate the number of moles of water:
\[ \text{Number of moles of water} = \frac{36 \text{ g}}{18 \text{ g/mol}} = 2 \text{ moles} \]

### Step 4: Calculate the mole fraction of glycerin
The mole fraction (X) of glycerin is given by:
\[ X_{\text{glycerin}} = \frac{\text{Number of moles of glycerin}}{\text{Number of moles of glycerin} + \text{Number of moles of water}} \]
Substituting the values:
\[ X_{\text{glycerin}} = \frac{0.5}{0.5 + 2} = \frac{0.5}{2.5} = 0.2 \]

### Final Answer
The mole fraction of glycerin in the solution is **0.2**.

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