Question

In a \(250 \mathrm{~mL}\) solution, \(0.25 \mathrm{~mol}\) of \(\mathrm{KOH}(\mathrm{aq})\) and \(0.25 \mathrm{~mol}\) of \(\mathrm{HNO}_{3}(\mathrm{aq})\) are combined. The temperature of the solution increases from \(22.5^{\circ} \mathrm{C}\) to \(35.9^{\circ} \mathrm{C}\). Assume the solution has the same density and heat capacity of water. What is the heat of the reaction, and what is the \(\Delta H\) of the reaction on a molar basis?

Short answer

The heat of the reaction is -14.009 kJ, and \( \Delta H \) is -56.036 kJ/mol.

Step-by-step solution

Identify Parameters

First, we need to recognize the parameters given in the problem. We have 250 mL solution equating to 0.250 L. The number of moles of KOH and HNO₃ are both 0.25 mol. The temperature change is from 22.5°C to 35.9°C, resulting in a temperature change of 13.4°C. Assume the specific heat capacity, c, of water is 4.18 J/g°C, and the density of water is 1 g/mL.

Calculate Mass of Solution

Calculate the mass of the solution by using the volume and density of water. The volume is 250 mL, and the density is 1 g/mL, resulting in a mass of 250 g: \( \text{mass} = 250 \text{ mL} \times 1 \text{ g/mL} = 250 \text{ g} \).

Calculate Heat Absorbed by the Solution

Using the formula \( q = mc\Delta T \), where m is mass, c is specific heat capacity, and \( \Delta T \) is temperature change. Substituting the values: \( q = 250 \text{ g} \times 4.18 \text{ J/g°C} \times 13.4°C = 14009 \text{ J} \).

Calculate Heat of Reaction (\( q_{\text{rxn}} \))

The heat absorbed by the solution is equal to the heat released by the reaction, so \( q_{\text{rxn}} = -q \). Thus, \( q_{\text{rxn}} = -14009 \text{ J} \) or \( -14.009 \text{ kJ} \).

Calculate \( \Delta H \) on a Molar Basis

Since both substances fully react and have moles of 0.25 each, the \( \Delta H \) for the reaction per mole is calculated by dividing total heat (\( q_{\text{rxn}} \)) by moles involved: \( \Delta H = \frac{-14009 \text{ J}}{0.25 \text{ mol}} = -56036 \text{ J/mol} \) or \( -56.036 \text{ kJ/mol} \).

Key concepts

Enthalpy Change

Enthalpy change (\(\Delta H\)) is a key concept in thermochemistry that describes the heat content change during a chemical reaction. Essentially, it helps us understand how much energy is absorbed or released. When a reaction releases heat, it's called an exothermic reaction, and \(\Delta H\) is negative. Conversely, when a reaction absorbs heat, it's endothermic, making \(\Delta H\) positive.
In our exercise, the enthalpy change is negative (-56.036 kJ/mol), indicating that the reaction between KOH and HNO₃ is exothermic. Such reactions often make substances feel warmer because they release heat into the surroundings as they proceed.

Heat of Reaction

The heat of reaction (\(q_{\text{rxn}}\)) quantifies the energy exchanged as heat during a reaction. It is closely associated with enthalpy change, depending on whether energy is released or absorbed.
The calculation of \(q_{\text{rxn}}\) involves determining how much heat is gained or lost by the solution. This is measured using the formula \(q = mc\Delta T\), which uses factors like mass, specific heat capacity, and temperature change to quantify the energy exchange.
In the given problem, the heat of reaction is -14.009 kJ. This is derived from observing how much energy the solution absorbs, thereby matching how much heat the reaction releases, which in this case, turns out to be exothermic.

Specific Heat Capacity

Specific heat capacity (\(c\)) is an important term that describes how much heat energy is required to raise the temperature of one gram of a substance by one degree Celsius. Water, known for its stability, has a specific heat capacity of 4.18 J/g°C. This makes it uniquely effective at absorbing and releasing heat slowly, a fact that is incredibly useful in thermal calculations.
In the exercise, since the solution is assumed to have the specific heat capacity of water, we use this value in calculations. The specific heat capacity helps in determining how much energy a given mass of solution will absorb over a specified temperature change. This key factor is critical in accurately calculating the heat of reaction.

Chemical Reactions

Chemical reactions involve the transformation of substances into different substances through the breaking and forming of chemical bonds. These changes are always accompanied by energy changes, either requiring energy input or releasing energy.
The reaction between KOH and HNO₃ in this exercise is a classic example. It showcases an acid-base neutralization, where potassium nitrate and water are produced. This type of reaction is usually instantaneous and produces heat, characterizing it as exothermic. Understanding the energy dynamics in chemical reactions not only helps predict the temperature changes but also provides insights into the reaction's enthalpy change.