If 1.8 g of glucose (molar mass = 180) is dissolved in 60 g of water the mole fraction of glucose is

Explanation

To find the mole fraction of glucose when 1.8 g of glucose is dissolved in 60 g of water, we can follow these steps:

### Step 1: Calculate the number of moles of glucose
To find the number of moles of glucose, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
Given that the mass of glucose is 1.8 g and its molar mass is 180 g/mol:
\[ \text{Number of moles of glucose} = \frac{1.8 \, \text{g}}{180 \, \text{g/mol}} = 0.01 \, \text{mol} \]

### Step 2: Calculate the number of moles of water
Next, we calculate the number of moles of water. The molar mass of water (H₂O) is approximately 18 g/mol. Given that the mass of water is 60 g:
\[ \text{Number of moles of water} = \frac{60 \, \text{g}}{18 \, \text{g/mol}} = 3.33 \, \text{mol} \]

### Step 3: Calculate the total number of moles in the solution
Now, we can find the total number of moles in the solution by adding the moles of glucose and the moles of water:
\[ \text{Total moles} = \text{moles of glucose} + \text{moles of water} = 0.01 \, \text{mol} + 3.33 \, \text{mol} = 3.34 \, \text{mol} \]

### Step 4: Calculate the mole fraction of glucose
The mole fraction of glucose (χ_glucose) is given by the formula:
\[ \chi_{\text{glucose}} = \frac{\text{moles of glucose}}{\text{total moles}} \]
Substituting the values we calculated:
\[ \chi_{\text{glucose}} = \frac{0.01 \, \text{mol}}{3.34 \, \text{mol}} \approx 0.00299 \]

### Final Answer
The mole fraction of glucose is approximately **0.00299**.

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