Question

When an 18.6-g sample of solid potassium hydroxide dissolves in \(200.0 \mathrm{~g}\) of water in a coffee-cup calorimeter (Figure 5.18), the temperature rises from 23.7 to \(44.5^{\circ} \mathrm{C}\). (a) Calculate the quantity of heat (in kJ) released in the reaction. (b) Using your result from part (a), calculate \(\Delta H\) (in kJ/mol KOH) for the solution process. Assume that the specific heat of the solution is the same as that of pure water.

Short answer

The quantity of heat released in the reaction is 17.36864 kJ, and the enthalpy change (ΔH) for the solvation process of potassium hydroxide is 52.42 kJ/mol.

Step-by-step solution

Calculate the change in temperature (ΔT)

ΔT = Final temperature - Initial temperature ΔT = 44.5°C - 23.7°C ΔT = 20.8°C

Find the heat released (q) using the formula q = mcΔT

Here, we are given the mass of water (m) as 200.0 g. The specific heat capacity (c) of water is 4.184 J/g°C. q = (200.0 g)*(4.184 J/g°C)*(20.8°C) q = 17368.64 J Since we need the heat released in kilojoules (kJ), let's convert it from J to kJ: [q(kJ) = q(J) / 1000] q = 17.36864 kJ

Calculate moles of KOH dissolved

Now, we’ll find out how many moles of KOH were present in the 18.6-g sample: Molar mass of KOH = 39.1 (K) + 15.999 (O) + 1.007 (H) = 56.106 g/mol [Moles of KOH = mass / molar mass] moles of KOH = 18.6 g / 56.106 g/mol = 0.3314 mol

Calculate ΔH (enthalpy change) in kJ/mol KOH

[ΔH = Heat released (q) / moles of KOH] ΔH = 17.36864 kJ / 0.3314 mol ΔH = 52.42 kJ/mol Therefore, the enthalpy change for the solvation process of potassium hydroxide is 52.42 kJ/mol.

Key concepts

Calorimetry

Calorimetry is a technique used to measure the amount of heat absorbed or released during a chemical reaction. It is commonly conducted using a device called a calorimeter. The core principle behind calorimetry is the conservation of energy: the heat lost or gained by the system under investigation is equal to the heat gained or lost by the surroundings. This makes calorimetry a useful method for determining the enthalpy change (ΔH) of a reaction.
In a simple calorimeter setup, like the coffee-cup calorimeter, heat exchange with the environment is minimized. The chemical process takes place in a container (often a styrofoam cup), and the resulting temperature change is recorded. This temperature change, along with the known mass and specific heat capacity of the solution or reaction medium, allows us to calculate the amount of heat involved in the process.
Using the formula:

• q = mcΔT, where
• q = heat absorbed or released (in Joules),
• m = mass of the solution (in grams),
• c = specific heat capacity (in J/g°C), and
• ΔT = change in temperature (in °C).

Employing this technique requires careful attention to calibration and measurements to ensure accuracy of the results.

Potassium Hydroxide

Potassium hydroxide (KOH) is a strong base commonly used in various industrial and laboratory applications. When dissolved in water, it dissociates completely into potassium ( K^+ ) and hydroxide ( OH^− ) ions, which is indicative of its strong alkaline nature. This complete dissociation is significant in calorimetry experiments, as it typically results in significant heat exchange with the environment.
Known for its high reactivity, KOH solutions are often used in chemical synthesis, pH regulation, and as a cleaning agent. In the context of calorimetry and enthalpy change calculation, the solvation of KOH is an exothermic process, meaning it releases heat to the surroundings. This release of heat is evident from the increase in temperature observed in the surrounding water solution when KOH dissolves.
The molar mass of potassium hydroxide is a crucial factor in such experiments, helping to convert the measured heat into an enthalpy change per mole, reflecting the energy changes involved in dissolving a known quantity of the solute.

Specific Heat Capacity

Specific heat capacity, often denoted as 'c', is a property of a substance that indicates the amount of heat required to raise the temperature of one gram of the substance by one degree Celsius. Water, with a high specific heat capacity of 4.184 J/g°C, is commonly used in calorimetry because it can absorb substantial amounts of heat without a large change in temperature.
Its ability to hold heat makes it ideal for use in calorimetric calculations, where understanding how much energy is involved in chemical reactions is essential. When using specific heat capacity to calculate heat in a calorimetry experiment, the data rely on the assumption that the solution behaves similarly to water, even if other substances are involved.
In the context of the given solution, specific heat capacity allows us to calculate the heat change when potassium hydroxide dissolves. By knowing the specific heat, the mass of the water, and the change in temperature, we can determine the amount of heat exchanged with precision and proceed to calculate further energy changes, like the enthalpy change, per mole of the substance involved.