How do you calculate qcal, qrxn, and ΔH? I just need to know how to set it up. Can you provide a detailed example?
The Correct Answer and Explanation is:
To calculate q<sub>cal</sub>, q<sub>rxn</sub>, and ΔH, follow these steps using a calorimetry setup.
Key Formulas:
- q<sub>cal</sub> = C<sub>cal</sub> × ΔT
- C<sub>cal</sub> is the heat capacity of the calorimeter (J/°C)
- ΔT = T<sub>final</sub> – T<sub>initial</sub>
- q<sub>rxn</sub> = –q<sub>cal</sub>
- Assumes all heat released/absorbed by the reaction is gained/lost by the calorimeter.
- ΔH = q<sub>rxn</sub> / n
- n is the number of moles of limiting reactant.
Example Setup:
Suppose a reaction occurs in a bomb calorimeter.
- C<sub>cal</sub> = 5.00 kJ/°C
- T<sub>initial</sub> = 25.0°C
- T<sub>final</sub> = 28.2°C
- Mass of substance combusted = 1.00 g
- Molar mass of substance = 50.0 g/mol
Step-by-Step Calculation:
1. Calculate q<sub>cal</sub>: qcal=Ccal×(Tfinal−Tinitial)=5.00 kJ/°C×(28.2−25.0)°C=5.00×3.2=16.0 kJq_{cal} = C_{cal} \times (T_{final} – T_{initial}) = 5.00 \, \text{kJ/°C} \times (28.2 – 25.0)°C = 5.00 \times 3.2 = 16.0 \, \text{kJ}qcal=Ccal×(Tfinal−Tinitial)=5.00kJ/°C×(28.2−25.0)°C=5.00×3.2=16.0kJ
2. Determine q<sub>rxn</sub>: qrxn=−qcal=−16.0 kJq_{rxn} = -q_{cal} = -16.0 \, \text{kJ}qrxn=−qcal=−16.0kJ
The negative sign indicates that the reaction released heat (exothermic).
3. Calculate moles of reactant: n=1.00 g50.0 g/mol=0.0200 moln = \frac{1.00 \, \text{g}}{50.0 \, \text{g/mol}} = 0.0200 \, \text{mol}n=50.0g/mol1.00g=0.0200mol
4. Calculate ΔH: ΔH=qrxnn=−16.0 kJ0.0200 mol=−800 kJ/mol\Delta H = \frac{q_{rxn}}{n} = \frac{-16.0 \, \text{kJ}}{0.0200 \, \text{mol}} = -800 \, \text{kJ/mol}ΔH=nqrxn=0.0200mol−16.0kJ=−800kJ/mol
Explanation
In a calorimetry experiment, energy changes associated with chemical reactions are determined by measuring temperature changes. The heat absorbed or released by the calorimeter is calculated using the calorimeter’s heat capacity and the change in temperature.
The first quantity, q<sub>cal</sub>, represents the amount of heat gained or lost by the calorimeter. It depends directly on the heat capacity and the temperature change. If the temperature rises, heat has been absorbed; if it drops, heat has been lost.
Since the calorimeter is assumed to be isolated, the heat released or absorbed by the reaction (q<sub>rxn</sub>) must equal the negative of q<sub>cal</sub>. This reflects the law of conservation of energy—what the system loses, the surroundings gain.
To find ΔH (enthalpy change), the energy change per mole of reactant is calculated. This gives the molar enthalpy change, which provides a standardized measure of the heat involved in the reaction. Negative ΔH values indicate exothermic reactions; positive values indicate endothermic ones.
This process is essential in thermochemistry for determining reaction energetics in combustion, neutralization, and other enthalpy-driven processes.
