What is the Qrxn of this acid/base neutralization reaction? 50 mL of 1 M NaOH is added into the calorimeter with a temperature of 23.5 degrees Celsius. 50 mL of 1 M HCl with a temperature of 23.6 degrees Celsius are added. The final temperature is 30.9 degrees Celsius.
a) -ΔH = Qrxn = – (m * ΔT * C), where m is the total moles of the reactants and C is the specific heat capacity of the solution.
b) ΔH = Qrxn = m * ΔT * C, where m is the total moles of the reactants and C is the specific heat capacity of the solution.
c) Qrxn = -m * ΔT * C, where m is the total moles of the reactants and C is the specific heat capacity of the solution.
d) ΔH = Qrxn = -m * ΔT * C, where m is the moles of the limiting reactant and C is the specific heat capacity of the solution.
The Correct Answer and Explanation is :
To determine the correct expression for the heat of the reaction ((Q_{\text{rxn}})) in this acid-base neutralization scenario, we need to analyze the provided information carefully.
Given:
- Volume of NaOH: 50 mL (1 M)
- Volume of HCl: 50 mL (1 M)
- Initial Temperature of NaOH: 23.5 °C
- Initial Temperature of HCl: 23.6 °C
- Final Temperature: 30.9 °C
Steps to Solve:
- Determine Total Moles of Reactants:
[
\text{Moles of NaOH} = 1 \, \text{mol/L} \times 0.050 \, \text{L} = 0.050 \, \text{mol}
]
[
\text{Moles of HCl} = 1 \, \text{mol/L} \times 0.050 \, \text{L} = 0.050 \, \text{mol}
]
Both NaOH and HCl are in equimolar amounts, so neither is limiting. - Calculate Temperature Change ((\Delta T)):
[
\Delta T = \text{Final Temperature} – \text{Initial Average Temperature}
]
[
\text{Initial Average Temperature} = \frac{23.5 + 23.6}{2} = 23.55 \, \text{°C}
]
[
\Delta T = 30.9 – 23.55 = 7.35 \, \text{°C}
] - Use the Specific Heat Capacity of Water:
For dilute aqueous solutions, (C) (specific heat capacity) can be approximated as (4.18 \, \text{J/g°C}). - Calculate Total Mass of Solution:
Assuming the density of the solution is approximately (1 \, \text{g/mL}), the total mass (m) of the solution is:
[
m = 100 \, \text{g} \quad (\text{50 mL NaOH + 50 mL HCl})
]
Determine Qrxn:
To calculate (Q_{\text{rxn}}), we can use the heat absorbed by the solution, which is given by:
[
Q_{\text{rxn}} = m \cdot C \cdot \Delta T
]
However, since this heat is released by the neutralization reaction, we represent it as:
[
Q_{\text{rxn}} = -m \cdot C \cdot \Delta T
]
Correct Answer:
The correct expression for (Q_{\text{rxn}}) in this context is:
c) (Q_{\text{rxn}} = -m \cdot \Delta T \cdot C), where (m) is the total moles of the reactants and (C) is the specific heat capacity of the solution.
Explanation:
In an acid-base neutralization reaction, the heat released by the reaction (exothermic) increases the temperature of the resultant solution. The negative sign indicates that the system (the calorimeter and the solution) is absorbing heat from the reaction. Thus, while the reaction releases heat, the surroundings (the water in the calorimeter) gain that heat, leading to the observed temperature rise. This relationship is crucial in calorimetry for determining reaction enthalpies, allowing for the calculation of heat transfer associated with the chemical process.