Question

When a \(6.50\)-g sample of solid sodium hydroxide dissolves in \(100.0 \mathrm{~g}\) of water in a coffee-cup calorimeter (Figure 5.17), the temperature rises from \(21.6\) to \(37.8^{\circ} \mathrm{C}\). (a) Calculate the quantity of heat (in \(\mathrm{kJ}\) ) released in the reaction. (b) Using your result from part (a), calculate \(\Delta H\) (in \(\mathrm{kJ} / \mathrm{mol} \mathrm{NaOH}\) ) for the solution process. Assume that the specific heat of the solution is the same as that of pure water.

Short answer

The heat released in the reaction is 7.169834 kJ, and the change in enthalpy for the solution process is 44.123 kJ/mol NaOH.

Step-by-step solution

Calculate the mass of the water and sodium hydroxide solution

First, we need to find the total mass of the solution, which is the sum of masses of the water and the sodium hydroxide. Total mass = mass of water + mass of sodium hydroxide Total mass = 100.0 g + 6.50 g Total mass = 106.5 g

Calculate the change in temperature

We are given the initial and final temperatures. To find the change in temperature, subtract the initial temperature from the final temperature. ΔT = T_final - T_initial ΔT = 37.8°C - 21.6°C ΔT = 16.2°C

Calculate the heat released

Now, we can use the formula q = mcΔT to calculate the heat released. q = (106.5 g) × (4.184 J/g°C) × (16.2°C) q = 7169.834 J To convert Joules to kJ, divide by 1000. q = 7.169834 kJ

Calculate the number of moles of sodium hydroxide

The molar mass of sodium hydroxide (NaOH) is 22.99 g/mol (Na) + 15.999 g/mol (O) + 1.0079 g/mol (H) = 40.00 g/mol. To find the number of moles of sodium hydroxide, divide the mass by its molar mass. moles of NaOH = 6.50 g / 40.00 g/mol moles of NaOH = 0.1625 mol

Calculate the change in enthalpy

To find the change in enthalpy per mole of sodium hydroxide, divide the heat released in kJ by the number of moles of NaOH. ΔH = q / moles of NaOH ΔH = 7.169834 kJ / 0.1625 mol ΔH = 44.123 kJ/mol The change in enthalpy for the solution process is 44.123 kJ/mol NaOH.

Key concepts

Enthalpy Change

Enthalpy change is a central concept in thermochemistry that represents the heat absorbed or released during a chemical reaction at constant pressure. In this exercise, the enthalpy change (\(\Delta H\)) for the dissolution of sodium hydroxide (NaOH) in water was calculated. This involves determining how much heat is transferred when NaOH is dissolved.

To understand this better, it is essential to consider \(\Delta H\) as a measure of how much the energy of the system changes due to the reaction. For the given process, the dissolution of NaOH releases heat, resulting in an exothermic reaction, hence the negative \(\Delta H\) indicates this release.

Calculating \(\Delta H\) requires knowing the amount of heat released and the number of moles of the substance involved, as shown in the exercise's conclusion where the heat release was divided by moles to get the enthalpy change per mole.

Heat Calculation

Calculating heat involves using the formula \(q = mc\Delta T\), which helps determine the amount of heat absorbed or released by a substance during a temperature change. Here, \(q\) is the heat energy, \(m\) is the mass, \(c\) is the specific heat capacity, and \(\Delta T\) is the temperature change.

In this exercise, the heat calculation was performed for the sodium hydroxide solution, using the sum of the masses of NaOH and water. It's important to note that the specific heat capacity of water was assumed for the solution, which is a common simplification in calorimetry experiments.

• Specific heat capacity of water: 4.184 J/g°C
• Total mass involved: 106.5 g
• Measured temperature change: 16.2°C

The calculated heat was found in Joules and then converted to kilojoules by dividing by 1000, leading to easier interpretability in terms of \(\Delta H\).

Calorimetry

Calorimetry is a technique used to measure the amount of heat involved in a chemical or physical process. In this exercise, it was employed using a coffee-cup calorimeter to assess the heat change during the dissolution of NaOH.

The coffee-cup calorimeter is a simple, user-friendly apparatus often used by students to learn basic calorimetry. It works by isolating the reaction in an insulated container, thus allowing for the direct measurement of temperature changes in the water surrounding the reactants.

• Advantages of calorimetry in the experiment:
• Direct measurement of temperature changes
• Simple and cost-effective setup
• Practical for observing exothermic and endothermic reactions

Using calorimetry provided the temperature rise from 21.6°C to 37.8°C, which then allowed for the determination of both the heat released and later the enthalpy change.

Dissolution Process

The dissolution process involves a solute, in this case, sodium hydroxide, dissolving in a solvent, water. This process can either absorb or release energy, described by the enthalpy change.

In the provided exercise, NaOH dissolves in water, releasing heat, evidenced by the temperature increase. This release of heat classifies the process as exothermic. The dissolution process not only involves the breaking and making of bonds between molecules but also the efficient mixing of solute and solvent, which in thermochemical terms is quantified by the change in enthalpy.

• Energy forms involved:
• Lattice energy: energy required to break the ions apart
• Hydration energy: energy released when ions interact with water molecules

The balance between these energy forms dictates whether the dissolution feels hot or cold, and is crucial in understanding real-world applications such as heat packs or solubilization processes in various industries.