Problem 56 - Chemistry The Central Science In Si Units

Question

(a) When an \(8.50-\mathrm{g}\) sample of solid ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}(s)\right)\) dissolves in \(120.0 \mathrm{~g}\) of water in a coffee-cup calorimeter (Figure 5.18 ), the temperature drops from 24.0 to \(18.9^{\circ} \mathrm{C}\). Calculate \(\Delta H\left(\right.\) in \(\left.\mathrm{k} / / \mathrm{mol} \mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) 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?

Step-by-Step Solution

Answer

The solution process is endothermic with \(\Delta H = 24.025 \text{ kJ/mol NH}_4\text{NO}_3\).

Step 1: Calculate Heat Absorbed by the Solution

First, determine the total change in temperature (\(\Delta T\)) by subtracting the final temperature from the initial temperature: \(\Delta T = 18.9^{\circ}\text{C} - 24.0^{\circ}\text{C} = -5.1^{\circ}\text{C}\). Since the temperature decreases, the process absorbs heat. Use the mass (\(m\)) of the water and its specific heat capacity (\(c = 4.18 \text{ J/g}\cdot\text{°C}\)) to calculate the heat absorbed (\(q\)): \[ q = m \cdot c \cdot \Delta T \].The mass of the water is \(120.0 \text{ g}\), hence:\[ q = 120.0 \cdot 4.18 \cdot (-5.1) = -2551.44 \text{ J} \].The negative result indicates heat absorption.

Step 2: Convert Heat Absorbed to kJ

The heat absorbed is measured in Joules, but we need it in kilojoules. Convert the heat from Joules to kilojoules by dividing by 1000:\[ q = \frac{-2551.44}{1000} = -2.551 \text{ kJ} \].

Step 3: Calculate Moles of NH₄NO₃

To find \(\Delta H\) per mole, we need the number of moles of ammonium nitrate. Using its molar mass (\(\text{NH}_4\text{NO}_3\), approximately 80.04 \(\text{g/mol}\)), calculate the moles from the mass given:\[ \text{moles NH}_4\text{NO}_3 = \frac{8.50 \text{ g}}{80.04 \text{ g/mol}} = 0.1062 \text{ mol} \].

Step 4: Calculate ΔH for the Dissolution Process

Determine \(\Delta H\) per mole of \(\text{NH}_4\text{NO}_3\) dissolved using the total heat absorbed and the number of moles:\[ \Delta H = \frac{-2.551 \text{ kJ}}{0.1062 \text{ mol}} = -24.025 \text{ kJ/mol} \].Since the calculation shows negative sign only because of convention for endothermic processes (heat absorbed), we take absolute value for positive \(\Delta H\). Thus, \(\Delta H = 24.025 \text{ kJ/mol} \).

Step 5: Determine if the Process is Endothermic or Exothermic

A process is endothermic if it absorbs heat and the \(\Delta H\) is positive. Here, as the process leads to a temperature drop in the water and \(\Delta H = 24.025 \text{ kJ/mol}\), it confirms that the process is endothermic.

Key Concepts

Calorimetry

Calorimetry is a fascinating and essential method used to measure the amount of heat absorbed or released during a chemical process. This technique is invaluable in thermochemistry, allowing us to quantify the energy changes involved in various reactions. A common tool used in calorimetry is the coffee-cup calorimeter, a simple yet effective device ideal for constant pressure experiments. Thanks to its design, it can effectively insulate the reaction mixture from outside influences. Thus, providing reliable data on heat changes.

In the coffee-cup calorimeter, substances are mixed, and the resultant temperature change is accurately recorded. This is because the heat effect is directly correlated to the temperature change observed. Through this, we can calculate the heat absorbed or evolved using the formula:

• \[ q = m \cdot c \cdot \Delta T \]

Here, \( q \) is the heat absorbed or released, \( m \) is the mass of the substance, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature. By knowing these values, we can fully analyze the thermodynamic properties of the substance involved. This makes calorimetry a powerful tool in understanding chemical energetics.

Endothermic Processes

Endothermic processes are chemical reactions or physical changes that absorb heat from their surroundings. In every endothermic reaction, heat is considered a reactant, as energy is needed to proceed with the process. This means the surroundings lose heat and usually result in a temperature drop as observed in a calorimeter.

An easy way to remember what entails an endothermic process is by internalizing that the prefix 'endo' suggests that heat is taken 'inside'. Therefore, if a process results in a decrease in ambient temperature, it is classified as endothermic. Common examples include the melting of ice cubes (achieving a change from solid to liquid) and the dissolution of certain salts, like ammonium nitrate in water.

• This absorption of heat is accompanied by a positive change in enthalpy, \( \Delta H \), because energy input is required for the process to occur.
• In thermodynamic terms, \( \Delta H > 0 \), emphasizing that the enthalpy of the products is higher than that of the reactants.

Knowing whether a process is endothermic helps predict shifts in temperature and energy usage, which is crucial in applications ranging from industrial chemical manufacturing to everyday life scenarios.

Molar Enthalpy

Molar enthalpy, represented as \( \Delta H \), is a concept that describes the heat change associated with one mole of a substance during a reaction at constant pressure. It is a crucial thermodynamic property that helps in determining how much energy is involved in chemical reactions per mole of reactant.

To calculate the molar enthalpy, we typically need a system structured similarly to a calorimetry setup. The formula involves the heat absorbed (or released), divided by the number of moles of the substance:

• \[ \Delta H = \frac{q}{\text{moles of substance}} \]

This formula allows for quantifying the energetic requirements or releases per mole. Such calculations are exceptionally useful in chemical manufacturing, providing insights into energy efficiency and potential heat management needs during processes.

For instance, in the solution process of ammonium nitrate, calculating molar enthalpy helps determine whether the reaction is feasible under desired conditions. This value is instrumental in many applications, including cooling packs. Consequently, understanding molar enthalpy is vital in both scientific research and practical applications across various fields of engineering and chemistry.