Problem 21 - General Chemistry: Principles and Modern Applications

Question

A 0.205 g pellet of potassium hydroxide, \(\mathrm{KOH}\), is added to \(55.9 \mathrm{g}\) water in a Styrofoam coffee cup. The water temperature rises from 23.5 to \(24.4^{\circ} \mathrm{C}\). [Assume that the specific heat of dilute \(\mathrm{KOH}(aq)\) is the same as that of water.] (a) What is the approximate heat of solution of \(\mathrm{KOH}\) expressed as kilojoules per mole of \(\mathrm{KOH}?\) (b) How could the precision of this measurement be improved without modifying the apparatus?

Step-by-Step Solution

Answer

a) The approximate heat of solution of KOH is 57.5 kJ/mol. b) Precision can be improved by ensuring the initial temperature of the KOH pellet and the water is the same, stirring more thoroughly, and doing multiple trials for average value.

Step 1: Calculating the heat absorbed by the water

Let's calculate the amount of heat absorbed by the water using the formula \(q = mc\Delta T\).\nGiven: mass of water (m) = 55.9 g, Specific heat of water (c) = 4.18 J/g°C, Change in temperature (\(\Delta T\)) = \(24.4 °C - 23.5 °C = 0.9 °C\)\n Substituting these values into the formula gives: \(q = 55.9 \, g \times 4.18 \, J/g°C \times 0.9 °C = 209.8 J\). This is the heat absorbed by the water.

Step 2: Calculate moles of KOH used

The heat absorbed by the water equals the heat of solution of the KOH pellet. To determine the heat of solution per mole of KOH, calculate the number of moles in the 0.205 g pellet. This is done by dividing the mass of the pellet by the molar mass of KOH:\n Molar mass of KOH = 39.1g (for K) + 16.0g (for O) + 1.01g (for H) = 56.11g/mol\n Therefore, the number of moles = 0.205 g / 56.11 g/mol = 0.00365 mol

Step 3: Calculating the heat of solution of KOH

To find the heat of solution of KOH, one must divide the quantity of heat absorbed by the number of moles of KOH:\n Heat of solution (q) = 209.8 J / 0.00365 mol = 57449.32 J/mol, which can be approximated to 57.5 kJ/mol after converting from Joules to kiloJoules.

Step 4: Improving the precision of the measurement

Some ways to improve the precision of the measurement without modifying the apparatus include ensuring that the initial temperature of the KOH pellet and the water is the same to minimize heat exchange prior to mixing, stirring the solution more thoroughly to ensure that the KOH fully dissolves and distributes the heat evenly, and performing the experiment multiple times to obtain an average value.

Key Concepts

Heat of Solution

When you dissolve a substance in water, it can either release or absorb heat. This is known as the 'heat of solution'. In the exercise, we are interested in finding out how much heat is released or absorbed when potassium hydroxide (KOH) dissolves in water.
To calculate this, we measure the heat change in the surrounding water. The assumption here is that the heat absorbed by the water is equal to the heat of solution of KOH. This means when KOH dissolves in water, it either warms the solution if heat is released (exothermic) or cools it if heat is absorbed (endothermic).
We use the formula: \[ q = m \cdot c \cdot \Delta T \] Where:

• \( q \) is the heat absorbed or released
• \( m \) is the mass of the water
• \( c \) is the specific heat capacity of water
• \( \Delta T \) is the change in temperature

By calculating \( q \) for the water, we indirectly determine the heat of solution for KOH.

Specific Heat Capacity

Specific heat capacity refers to how much heat energy is needed to change the temperature of a certain mass of a substance by 1 degree Celsius. Water's specific heat capacity is a well-known constant, 4.18 J/g°C.
In this exercise, the problem assumes that the specific heat capacity of the KOH solution is the same as pure water. This is a common assumption for dilute solutions, simplifying the calculation of heat absorbed by the water.
The formula \( q = m \cdot c \cdot \Delta T \) uses specific heat capacity to relate the temperature change of an object to the amount of heat it absorbs or releases. Elements with high specific heat capacities, like water, require a lot of heat for each degree of temperature change. This makes water an ideal medium for calorimetry exercises because it reflects small heat changes accurately.

Molar Mass Calculations

The molar mass is a crucial factor in converting between grams of a substance and moles, which allows us to perform various chemical calculations. To find the molar mass, sum up the atomic masses of all atoms in a molecule.
For KOH, the molar mass calculation is as follows:

• Potassium (K): 39.1 g/mol
• Oxygen (O): 16.0 g/mol
• Hydrogen (H): 1.01 g/mol

Adding these gives a molar mass of 56.11 g/mol for KOH.
Using the molar mass, you can convert the mass of a KOH pellet (given in grams) into moles using the formula: \[ ext{moles of KOH} = \frac{ ext{mass of KOH in grams}}{ ext{molar mass of KOH in g/mol}} \] For 0.205 g of KOH, this becomes 0.00365 mol. This conversion is key in finding the heat of solution per mole of KOH, giving us insight into the energy changes occurring during the dissolution process.