To calculate the enthalpy change (ΔH) for the dissolution process of AX in water, we can follow these steps:
Step 1: Calculate the heat absorbed by the water (q_water)
The formula for calculating the heat absorbed or released by the water is:
\[ q_{\text{water}} = m \cdot c \cdot \Delta T \]
where:
- \( m \) = mass of the water (in grams)
- \( c \) = specific heat capacity of water (4.18 J/g·K)
- \( \Delta T \) = change in temperature (in °C or K)
Given Values:
- Mass of water, \( m = 107 , \text{g} \)
- Specific heat of water, \( c = 4.18 , \text{J/g·K} \)
- Initial temperature, \( T_{\text{initial}} = 23.5 , \text{°C} \)
- Final temperature, \( T_{\text{final}} = 34.4 , \text{°C} \)
Step 2: Calculate ΔT
\[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 34.4 , \text{°C} - 23.5 , \text{°C} = 10.9 , \text{°C} \]
Step 3: Substitute values into the q_water equation
\[ q_{\text{water}} = 107 , \text{g} \cdot 4.18 , \text{J/g·K} \cdot 10.9 , \text{K} \]
Calculating \( q_{\text{water}} \):
\[ q_{\text{water}} = 107 \cdot 4.18 \cdot 10.9 \approx 4,811.97 , \text{J} \]
Convert q_water to kJ
\[ q_{\text{water}} \approx 4.812 , \text{kJ} \]
Step 4: Calculate moles of AX dissolved
Now, using the formula weight of AX to calculate the amount in moles that was dissolved:
\[ \text{Molar mass of AX} = 59.1097 , \text{g/mol} \] \[ \text{moles of AX} = \frac{2.215 , \text{g}}{59.1097 , \text{g/mol}} \approx 0.03748 , \text{mol} \]
Step 5: Calculate the enthalpy change (ΔH)
The enthalpy change for the solution process can be calculated using:
\[ \Delta H = -\frac{q_{\text{water}}}{\text{moles of AX}} \]
Substituting the values:
\[ \Delta H = -\frac{4.812 , \text{kJ}}{0.03748 , \text{mol}} \approx -128.24 , \text{kJ/mol} \]
Final Result:
The enthalpy change for the solution process of AX is approximately:
\[ \Delta H \approx -128.2 , \text{kJ/mol} \]
Make sure to keep the sign in mind; the negative sign indicates that the dissolution process is endothermic (heat is absorbed).