How many grams of ice at `0^@C` can be melted by the addition of 500 J of heat ? (The molar heat of fusion for ice is `6.02 Kamal^(-1))`

Options

A. 0.083 g
B. 1.50 g
C. 3.06 g
D. 12.0 g

Answer

To solve the problem of how many grams of ice at \(0^\circ C\) can be melted by the addition of 500 J of heat, we will use the formula that relates the energy required to melt ice to its mass and the latent heat of fusion.

### Step-by-Step Solution:

1. **Identify the given values:**
- Heat added (E) = 500 J
- Molar heat of fusion for ice (L) = 6.02 kJ/mol

2. **Convert the latent heat of fusion from kJ to J:**
\[ L = 6.02 \, \text{kJ/mol} = 6.02 \times 10^3 \, \text{J/mol} \]

3. **Use the formula for energy required to melt ice:**
The energy required to melt ice is given by:
\[ E = m \times L \]
where:
- \(E\) = energy (in joules)
- \(m\) = mass of ice (in grams)
- \(L\) = latent heat of fusion (in J/g)

4. **Rearrange the formula to solve for mass (m):**
\[ m = \frac{E}{L} \]

5. **Convert the latent heat of fusion from per mole to per gram:**
Since the molar heat of fusion is given per mole, we need to convert it to per gram. The molar mass of ice (H₂O) is approximately 18 g/mol. Thus:
\[ L = \frac{6.02 \times 10^3 \, \text{J/mol}}{18 \, \text{g/mol}} = 334.44 \, \text{J/g} \]

6. **Substitute the values into the equation:**
\[ m = \frac{500 \, \text{J}}{334.44 \, \text{J/g}} \approx 1.497 \, \text{g} \]

7. **Final answer:**
The mass of ice that can be melted by the addition of 500 J of heat is approximately 1.497 grams.