Question

You mix \(125 \mathrm{mL}\) of \(0.250 \mathrm{M} \mathrm{CsOH}\) with \(50.0 \mathrm{mL}\) of \(0.625 \mathrm{M} \mathrm{HF}\) in a coffee-cup calorimeter, and the temperature of both solutions rises from \(21.50^{\circ} \mathrm{C}\) before mixing to \(24.40^{\circ} \mathrm{C}\) after the reaction. $$\mathrm{CsOH}(\mathrm{aq})+\mathrm{HF}(\mathrm{aq}) \longrightarrow \mathrm{CsF}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)$$ What is the enthalpy of reaction per mole of CsOH? Assume the densities of the solutions are all \(1.00 \mathrm{g} / \mathrm{mL}\) and the specific heats of the solutions are \(4.2 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\).

Short answer

The enthalpy of reaction per mole of CsOH is \(-68.2 \mathrm{kJ/mol}\).

Step-by-step solution

Calculate the change in temperature

The temperature change, \( \Delta T \), is the difference between the final and initial temperatures.\[\Delta T = 24.40^{\circ}\mathrm{C} - 21.50^{\circ}\mathrm{C} = 2.90^{\circ}\mathrm{C}\]

Calculate the total mass of the solution

The total volume of the solution is the sum of the volumes of CsOH and HF, which is \( 125 \mathrm{mL} + 50.0 \mathrm{mL} = 175 \mathrm{mL} \). Given the density is \( 1.00 \mathrm{g/mL} \), the mass is equal to the volume: \( 175 \mathrm{g} \).

Calculate the heat absorbed by the solution

The heat \( q \) absorbed by the solution can be calculated using the formula \[ q = m \cdot c \cdot \Delta T \] where \( m = 175 \mathrm{g} \), \( c = 4.2 \mathrm{J/g} \cdot \mathrm{K} \), and \( \Delta T = 2.90^{\circ} \mathrm{C} \). Plugging in these values: \[q = 175 \mathrm{g} \times 4.2 \mathrm{J/g} \cdot \mathrm{K} \times 2.90^{\circ} \mathrm{C} = 2131.5 \mathrm{J}\]

Calculate the moles of CsOH reacted

The number of moles of \( \mathrm{CsOH} \) can be calculated using its concentration and volume: \[\text{Moles of CsOH} = 0.250 \mathrm{M} \times 0.125 \mathrm{L} = 0.03125 \mathrm{mol}\]

Calculate the enthalpy change per mole of CsOH

The enthalpy change \( \Delta H \) for the reaction per mole of \( \mathrm{CsOH} \) is given by:\[\Delta H = -\frac{q}{\text{moles of CsOH}} = -\frac{2131.5 \mathrm{J}}{0.03125 \mathrm{mol}} = -68208 \mathrm{J/mol} = -68.2 \mathrm{kJ/mol}\]

Interpret the result

The negative sign indicates that the reaction is exothermic, meaning it releases heat.

Key concepts

Stoichiometry

When dealing with chemical reactions, stoichiometry allows us to calculate the relationships between the reactants and products. In the given exercise, stoichiometry helps us determine how much of a substance is used and produced. Here, we utilize the concept by calculating the moles of CsOH (cesium hydroxide) that participate in the reaction.

The moles of a substance can be found using its molarity (concentration) and the volume of solution it's in. In this instance, we multiply the molarity of CsOH (0.250 M) by its volume in liters (0.125 L). This simple multiplication gives us the moles of CsOH, which is 0.03125 mol.

• This step is crucial because it sets the stage for calculating how much energy is involved per mole of reactant in subsequent calculations.
• Always ensure that you're using the same units, liters for volume in this case, to avoid mistakes in your calculations.

Understanding stoichiometry is important because it directly impacts how we interpret and predict the outcomes of chemical reactions.

Calorimetry

Calorimetry is a technique used to measure the amount of heat absorbed or released during a chemical reaction. In this exercise, a coffee-cup calorimeter is used, which typically involves a simple setup suitable for reactions occurring at constant pressure.

By measuring the temperature change in the calorimeter, we can calculate the heat absorbed or released using the formula: \[ q = m \cdot c \cdot \Delta T \] Where:

• \( q \) is the heat absorbed or released, expressed in joules.
• \( m \) is the total mass of the solution, determined by the density and volume.
• \( c \) is the specific heat capacity, given as 4.2 J/g·K for this example.
• \( \Delta T \) is the change in temperature.

In the given problem, we calculate that 2131.5 J of heat is released. This heat exchange represents the reaction’s interaction with its surroundings, demonstrating the practicality and importance of calorimetric analysis.

Chemical Thermodynamics

Chemical thermodynamics focuses on the principles governing the energy and transformations within chemical reactions. It explores the nature of enthalpy changes, such as those calculated in the exercise.

The enthalpy change \( \Delta H \) is vital for understanding reaction energetics. A negative \( \Delta H \) implies that the reaction is exothermic, meaning it releases energy to the surroundings. In our exercise, we calculated the enthalpy change per mole of CsOH as \(-68.2 \ \text{kJ/mol}\). This confirms that heat is released when CsOH reacts with HF.

Chemical thermodynamics helps:

• Predict whether a reaction is energetically favorable.
• Understand how temperature, pressure, and concentration affect reactions.
• Explain why some reactions proceed spontaneously while others require external energy.

Understanding these thermodynamics principles provides valuable insights into the energy aspects of chemical reactions, crucial for broader scientific and industrial applications.