Latent heat of fusion of ice is `6.02 Kj "mol"^(-1)`. The heat capacity of water is `4.18 J g^(-1) C^(-1)`, 500 g of liquid water is to be cooled from `20^(@)` C to `0^(@)` C. Find the number of ice cubes (one mole each) required.

Answer

To solve the problem step by step, we will follow the outlined approach in the video transcript.

### Step 1: Calculate the heat released when cooling the water

We need to calculate the heat released when 500 g of water is cooled from 20°C to 0°C. The formula to calculate the heat (q) released is:

\[ q = m \cdot C \cdot \Delta T \]

Where:
- \( m \) = mass of water = 500 g
- \( C \) = specific heat capacity of water = 4.18 J/g°C
- \( \Delta T \) = change in temperature = \( 20°C - 0°C = 20°C \)

Substituting the values:

\[ q = 500 \, \text{g} \cdot 4.18 \, \text{J/g°C} \cdot 20°C \]

Calculating this gives:

\[ q = 500 \cdot 4.18 \cdot 20 = 41800 \, \text{J} \]

### Step 2: Convert the heat released from Joules to Kilojoules

Since the latent heat of fusion is given in kilojoules, we convert the heat released into kilojoules:

\[ q = \frac{41800 \, \text{J}}{1000} = 41.8 \, \text{kJ} \]

### Step 3: Calculate the number of moles of ice required

The latent heat of fusion of ice is given as \( 6.02 \, \text{kJ/mol} \). To find the number of moles of ice required to absorb the heat released by the water, we use the formula:

\[ \text{Number of moles of ice} = \frac{\text{Heat released}}{\text{Latent heat of fusion}} \]

Substituting the values:

\[ \text{Number of moles of ice} = \frac{41.8 \, \text{kJ}}{6.02 \, \text{kJ/mol}} \]

Calculating this gives:

\[ \text{Number of moles of ice} \approx 6.94 \, \text{mol} \]

Since we cannot have a fraction of a mole in terms of ice cubes, we round this to the nearest whole number, which is 7.

### Final Answer

The number of ice cubes (one mole each) required is **7**.

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