Molar heat capacity of ethanol is `110.4 JK^(-1)`. Its specific heat capacity is

Options

A. 2.4
B. 55.2
C. 5.078
D. 110.4

Explanation

To find the specific heat capacity of ethanol given its molar heat capacity, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Molar heat capacity (C_m) is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius (or one Kelvin).
- Specific heat capacity (c) is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius (or one Kelvin).

2. **Identify the Given Values**:
- Molar heat capacity of ethanol (C_m) = 110.4 J/K
- Molar mass of ethanol (M) = 46 g/mol

3. **Use the Relationship Between Molar Heat Capacity and Specific Heat Capacity**:
- The relationship is given by the formula:
\[ C_m = c \times M \]
- Rearranging this formula to find specific heat capacity (c):
\[ c = \frac{C_m}{M} \]

4. **Substitute the Known Values**:
- Substitute the values of C_m and M into the equation:
\[ c = \frac{110.4 \, \text{J/K}}{46 \, \text{g/mol}} \]

5. **Calculate the Specific Heat Capacity**:
- Performing the division:
\[ c = \frac{110.4}{46} \approx 2.4 \, \text{J/g·K} \]

6. **Conclusion**:
- Therefore, the specific heat capacity of ethanol is approximately **2.4 J/g·K**.