When 9.85 grams of potassium hydroxide (KOH) are dissolved in 150.0 grams of water at 25.0 °C in an insulated container, the temperature of the water increases to 40.1 °C. Assuming that the specific heat of the solution is 4.184 J/(g °C) and that no heat is gained or lost by the container, what is the AH of solution of KOH in kJ/mol?
Thermochemistry
Thermochemistry can be considered as a branch of thermodynamics that deals with the connections between warmth, work, and various types of energy, formed because of different synthetic and actual cycles. Thermochemistry describes the energy changes that occur as a result of reactions or chemical changes in a substance.
Exergonic Reaction
The term exergonic is derived from the Greek word in which ‘ergon’ means work and exergonic means ‘work outside’. Exergonic reactions releases work energy. Exergonic reactions are different from exothermic reactions, the one that releases only heat energy during the course of the reaction. So, exothermic reaction is one type of exergonic reaction. Exergonic reaction releases work energy in different forms like heat, light or sound. For example, a glow stick releases light making that an exergonic reaction and not an exothermic reaction since no heat is released. Even endothermic reactions at very high temperature are exergonic.
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![**Problem Statement:**
When 9.85 grams of potassium hydroxide (KOH) are dissolved in 150.0 grams of water at 25.0°C in an insulated container, the temperature of the water increases to 40.1°C. Assuming that the specific heat of the solution is 4.184 J/(g°C) and that no heat is gained or lost by the container, what is the ΔH of the solution of KOH in kJ/mol?
**Solution Approach:**
1. **Calculate the heat gained by the water (q):**
- Use the formula:
\[
q = m \cdot c \cdot \Delta T
\]
where
\( m \) = mass of the solution (150.0 g of water + 9.85 g of KOH = 159.85 g),
\( c \) = specific heat capacity (4.184 J/(g°C)),
\( \Delta T \) = change in temperature (40.1°C - 25.0°C = 15.1°C).
2. **Convert the heat energy \( q \) from joules to kilojoules.**
3. **Calculate the number of moles of KOH:**
- Use the molar mass of KOH (approximately 56.11 g/mol).
4. **Determine \(\Delta H\) for the dissolution of KOH in kJ/mol:**
- \(\Delta H = \frac{q \text{ in kJ}}{\text{moles of KOH}}\).
**Conclusion:**
This problem illustrates an application of thermochemistry, specifically calculating the enthalpy change of a reaction taking place in solution. The use of calorimetry to measure temperature changes helps infer the heat exchange and, ultimately, the energy associated with dissolving a compound.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb6887dc-5b49-4551-bc80-996c7c4ae414%2F226773d3-0dd5-4613-8c89-bc87cf387121%2F4hpc9u7_processed.jpeg&w=3840&q=75)
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