Heat capacity `(C_(p))` is an extensive property but specific heat (C) is an intensive property.What will be the relation between `C_(p)` and C for 1 mol of water? (Keep your answer in J/K and in two digits only)

Explanation

To find the relationship between the heat capacity \( C_p \) and the specific heat \( C \) for 1 mole of water, we can follow these steps:

### Step 1: Understand the Definitions
- **Heat Capacity (\( C_p \))**: This is an extensive property, meaning it depends on the amount of substance. It is the amount of heat required to raise the temperature of a substance by 1 K (or 1 °C).
- **Specific Heat (\( C \))**: This is an intensive property, meaning it does not depend on the amount of substance. It is defined as the amount of heat required to raise the temperature of 1 gram of a substance by 1 K (or 1 °C).

### Step 2: Identify the Molar Mass of Water
The molar mass of water (H₂O) is approximately 18 grams per mole.

### Step 3: Relate Heat Capacity to Specific Heat
The relationship between heat capacity and specific heat can be expressed as:
\[ C_p = C \times \text{(mass of substance)} \]
For 1 mole of water, the mass is 18 grams. Therefore, we can write:
\[ C_p = C \times 18 \text{ grams} \]

### Step 4: Substitute the Value of Specific Heat
The specific heat of water is approximately \( 4.18 \, \text{J/g·K} \). Substituting this value into the equation gives:
\[ C_p = 4.18 \, \text{J/g·K} \times 18 \, \text{g} \]

### Step 5: Calculate \( C_p \)
Now, perform the multiplication:
\[ C_p = 4.18 \times 18 = 75.24 \, \text{J/K} \]

### Step 6: Round to Two Digits
Finally, rounding \( 75.24 \, \text{J/K} \) to two digits gives:
\[ C_p \approx 75 \, \text{J/K} \]

### Final Answer
The relation between \( C_p \) and \( C \) for 1 mole of water is:
\[ C_p \approx 75 \, \text{J/K} \]