Question
When 2.215 g of AX (s) dissolves in 107 g of water in a coffee-cup calorimeter the temperature rises from 23.5 °C to 34.4 °C. Calculate the enthalpy change (in kJ/mol) for the solution process.
AX space left parenthesis s right parenthesis space rightwards arrow straight A to the power of plus left parenthesis a q right parenthesis space plus space straight X to the power of minus space left parenthesis a q right parenthesis
Assumptions for this calculation:
The specific heat of the solution is the same as that of pure water (4.18 J/gK)
The density of water = 1.000 g/mL
The liquid’s final volume is not changed by adding the solid
The calorimeter loses only a negligible quantity of heat.
The formula weight of AX = 59.1097 g/mol. Be sure you include the correct sign for the enthalpy change.
AX space left parenthesis s right parenthesis space rightwards arrow straight A to the power of plus left parenthesis a q right parenthesis space plus space straight X to the power of minus space left parenthesis a q right parenthesis
Assumptions for this calculation:
The specific heat of the solution is the same as that of pure water (4.18 J/gK)
The density of water = 1.000 g/mL
The liquid’s final volume is not changed by adding the solid
The calorimeter loses only a negligible quantity of heat.
The formula weight of AX = 59.1097 g/mol. Be sure you include the correct sign for the enthalpy change.
Answers
GPT-4o mini
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).
### 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).