Question

(a) When a 4.25 -g sample of solid ammonium nitrate dissolves in 60.0 g of water in a coffee-cup calorimeter (Figure 5.18), the temperature drops from 22.0 to \(16.9^{\circ} \mathrm{C}\) . Calculate \(\Delta H\left(\) in \(\mathrm{kJ} / \mathrm{mol} \mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) for the solution process: $$\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q)$$ Assume that the specific heat of the solution is the same as that of pure water. (b) Is this process endothermic or exothermic?

Short answer

The enthalpy change for the dissolution of NH₄NO₃ is \(-24.065\,\text{kJ/mol}\), and the process is exothermic.

Step-by-step solution

List the given information

- Mass of NH₄NO₃ (m₁) = 4.25g - Mass of H₂O (m₂) = 60.0g - Initial temperature (T₁) = 22.0°C - Final temperature (T₂) = 16.9°C - Specific heat capacity of water (c) = 4.18 J/(g°C) Note: The specific heat capacity of the solution is assumed to be the same as that of pure water.

Calculate the temperature change (∆T)

We will first calculate the temperature change by subtracting the final temperature from the initial temperature. ∆T = T₂ - T₁ = 16.9°C - 22.0°C = -5.1°C

Calculate the energy change (q)

Now, we will determine the energy change (q) using the equation q = mc∆T. Since the specific heat capacity of the solution is the same as that of pure water, we can use the mass of water (m₂) in our calculations. q = m₂ × c × ∆T = 60.0g × 4.18 J/(g°C) × (-5.1°C) q = -1277.64 J

Convert the mass of NH₄NO₃ to moles

To find the moles of NH₄NO₃, we will divide the mass (m₁) by the molar mass. Molar mass of NH₄NO₃ = (1 * 14.01 + 4 * 1.01) + (1 * 14.01 + 3 * 16.00) = 18.05 + 62.01 = 80.06 g/mol moles of NH₄NO₃ = m₁ / (molar mass) = 4.25g / 80.06 g/mol moles of NH₄NO₃ = 0.0531 mol

Calculate ∆H

Now, we will find ∆H by dividing the energy change (q) by the moles of NH₄NO₃ and converting the result to kJ/mol. ∆H = (q) / (moles of NH₄NO₃) = -1277.64 J / 0.0531 mol ∆H = -24,065 J/mol Since we need to convert the result to kJ/mol, divide by 1000: ∆H = -24.065 kJ/mol

Determine if the process is endothermic or exothermic

The value of ∆H is negative, which means the process is exothermic. This indicates that heat is released during the dissolution of NH₄NO₃. In conclusion, the enthalpy change for the dissolution of NH₄NO₃ is -24.065 kJ/mol, and the process is exothermic.

Key concepts

Coffee-Cup Calorimeter

A coffee-cup calorimeter is an essential tool in chemistry used to measure the heat changes during a reaction or process. Made from a simple coffee cup with a lid, it involves placing a sample in a liquid—often water—to observe the temperature change. This change helps determine the heat absorbed or released during a chemical reaction.

The setup takes advantage of the insulating properties of a coffee cup to minimize heat exchange with the environment. This way, we can assume that most of the heat transfer occurs between the solution and the substances inside the calorimeter.

A coffee-cup calorimeter operates under constant pressure conditions, which is ideal for studying processes that occur in solution, such as dissolving a solute like ammonium nitrate. By knowing the mass of the substances involved, the specific heat capacity, and the change in temperature, it allows us to calculate the energy change of the process.

Specific Heat Capacity

Specific heat capacity is a property of a material that defines how much heat energy it needs to change its temperature. For water, this value is 4.18 J/(g°C), meaning that it takes 4.18 joules of energy to raise the temperature of one gram of water by one degree Celsius.

In the context of our problem, we assume the solution's specific heat capacity is the same as water's. This simplification helps to calculate the heat gained or lost during the reaction easily. The equation used is:\[ q = m \times c \times \Delta T \]Where:

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

Despite being a simple concept, understanding specific heat capacity is vital as it allows us to determine how different substances respond to heat and how they affect temperature in reactions.

Endothermic and Exothermic Processes

In chemistry, reactions are typically categorized into endothermic and exothermic based on their heat exchange with the environment.

**Endothermic processes** absorb heat from their surroundings. These processes feel cold to the touch because they require energy. They have a positive enthalpy change (\(\Delta H\)). This means energy is taken in, essential when bonds are being broken or new product phases are being formed.

**Exothermic processes**, on the other hand, release heat into the surroundings. This release can often be felt as warmth. They have a negative enthalpy change (\(\Delta H\)), as seen in our problem where ammonium nitrate dissolves in water. This indicates that the process releases energy, generally because new bonds are being formed that are more stable.

Identifying whether a process is endothermic or exothermic is fundamental in understanding chemical reactions' energy dynamics and predicting their behavior under different conditions.