It has been found that 221.4J is needed to heat 30g of ethanol from 150C to 180C. calculate (a) specific heat capacity, and (b) molar heat capacity of ethanol.

Explanation

To solve the problem, we need to calculate the specific heat capacity and the molar heat capacity of ethanol based on the given data. Let's break it down step by step.

### Given Data:
- Heat absorbed (Q) = 221.4 J
- Mass of ethanol (m) = 30 g
- Initial temperature (T1) = 15 °C
- Final temperature (T2) = 18 °C

### Step 1: Calculate the rise in temperature (ΔT)
\[ \Delta T = T2 - T1 = 18 °C - 15 °C = 3 °C \]

### Step 2: Calculate the specific heat capacity (c)
The formula for specific heat capacity is:
\[ c = \frac{Q}{m \cdot \Delta T} \]
Substituting the values:
\[ c = \frac{221.4 \, \text{J}}{30 \, \text{g} \cdot 3 \, \text{°C}} = \frac{221.4}{90} \approx 2.46 \, \text{J/g°C} \]

### Step 3: Calculate the molar heat capacity (C)
The molar heat capacity is calculated using the specific heat capacity and the molar mass of ethanol. The molar mass of ethanol (C2H5OH) can be calculated as follows:
- Carbon (C): 2 × 12 g/mol = 24 g/mol
- Hydrogen (H): 6 × 1 g/mol = 6 g/mol
- Oxygen (O): 1 × 16 g/mol = 16 g/mol

Total molar mass = 24 + 6 + 16 = 46 g/mol

Now, we can calculate the molar heat capacity:
\[ C = c \cdot \text{molar mass} \]
Substituting the values:
\[ C = 2.46 \, \text{J/g°C} \cdot 46 \, \text{g/mol} = 113.16 \, \text{J/mol°C} \]

### Final Answers:
(a) Specific heat capacity of ethanol = 2.46 J/g°C
(b) Molar heat capacity of ethanol = 113.16 J/mol°C

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