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°C can be melted by the addition of 500 J of heat, we can follow these steps:

### Step 1: Understand the given data
- Heat added (Q) = 500 J
- Molar heat of fusion for ice (L) = 6.02 kJ/mol

### Step 2: Convert the heat of fusion to joules
Since the heat added is in joules, we need to convert the heat of fusion from kJ to J:
\[ L = 6.02 \, \text{kJ/mol} = 6.02 \times 10^3 \, \text{J/mol} \]

### Step 3: Use the formula for heat required to melt ice
The formula to calculate the heat required to melt a mass (m) of ice is:
\[ Q = m \times L \]
Where:
- Q = heat added (in joules)
- m = mass of ice (in grams)
- L = heat of fusion (in J/g)

### Step 4: Convert the heat of fusion from per mole to per gram
To find the heat of fusion per gram, we need to divide the heat of fusion per mole by the molar mass of ice (water):
- Molar mass of ice (H₂O) = 18 g/mol
\[ L = \frac{6.02 \times 10^3 \, \text{J/mol}}{18 \, \text{g/mol}} = 334.44 \, \text{J/g} \]

### Step 5: Rearrange the formula to find the mass of ice
Now we can rearrange the formula to solve for mass (m):
\[ m = \frac{Q}{L} \]

### Step 6: Substitute the values
Substituting the values we have:
\[ m = \frac{500 \, \text{J}}{334.44 \, \text{J/g}} \]

### Step 7: Calculate the mass
Calculating the mass:
\[ m \approx 1.497 \, \text{g} \]

### Conclusion
Thus, the amount of ice that can be melted by the addition of 500 J of heat is approximately **1.497 grams**.

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