Problem 10 - Chemistry in 30 days

Question

When \(10 \mathrm{ml}\) of \(0.1 \mathrm{M}\) soln. of \(\mathrm{HCl}\) is mixed with \(10 \mathrm{ml}\) of \(0.1 \mathrm{M}\) of \(\mathrm{KOH}\) solution, the rise in temperature was observed to be \(4^{\circ} \mathrm{C}\). If \(100 \mathrm{ml}\) of \(0.1 \mathrm{M} \mathrm{HCl}\) and \(100 \mathrm{ml}\) of \(0.1 \mathrm{M} \mathrm{KOH}\) are mixed in the same vessel, the rise in temperature would be (a) \(40^{\circ} \mathrm{C}\) (b) \(4^{\circ} \mathrm{C}\) (c) \(20^{\circ}\) (d) unpredictable

Step-by-Step Solution

Answer

(a) \(40^{\circ} \mathrm{C}\)

Step 1: Identify the Reaction

The reaction occurs between hydrochloric acid (HCl) and potassium hydroxide (KOH), forming water and potassium chloride: \( \mathrm{HCl} + \mathrm{KOH} \rightarrow \mathrm{H_2O} + \mathrm{KCl} \). This is an exothermic neutralization reaction.

Step 2: Calculate Initial Moles in Small-scale Mixing

For the initial reaction, 10 ml of 0.1 M HCl and 10 ml of 0.1 M KOH are mixed. The number of moles of each reactant is \( \text{volume (L)} \times \text{molarity} = 0.01 \times 0.1 = 0.001 \text{ moles} \).

Step 3: Calculate Heat Released for Initial Reaction

The release of heat in an exothermic reaction depends on the number of moles reacting. In this small-scale setup, the heat caused a temperature increase of \(4^{\circ} \mathrm{C}\).

Step 4: Calculate Moles in Large-scale Mixing

For the larger reaction, 100 ml of 0.1 M HCl and 100 ml of 0.1 M KOH are mixed, resulting in \(0.1 \times 0.1 = 0.01 \text{ moles} \) of each, which is 10 times the amount used in the original smaller reaction.

Step 5: Determine Temperature Rise for Larger Reaction

The temperature rise is proportional to the number of moles reacting. Since we now have 10 times more moles, the temperature rise will also be 10 times the initial rise: \(4^{\circ} \mathrm{C} \times 10 = 40^{\circ} \mathrm{C}\).

Step 6: Choose the Correct Multiple Choice Answer

Based on the calculation, the rise in temperature when mixing 100 ml of each solution is \(40^{\circ} \mathrm{C}\). Hence, the correct answer is (a) \(40^{\circ} \mathrm{C}\).

Key Concepts

Exothermic Reaction

An exothermic reaction is one in which energy is released into the surroundings as heat.
This heat release occurs because the energy needed to break the bonds in reactants is less than the energy released when new bonds are formed in the products.
In the neutralization reaction between hydrochloric acid (HCl) and potassium hydroxide (KOH), the products formed are water and potassium chloride. Here, heat is released as HCl and KOH neutralize each other, indicating an exothermic process.
The formula for this reaction is: \(\mathrm{HCl(aq) + KOH(aq) \rightarrow H_2O(l) + KCl(aq)} \).
Recognizing an exothermic reaction helps predict how the temperature of the system will change upon mixing, as the release of energy usually increases the temperature of the solution.

Molarity Calculation

Molarity is a way of expressing the concentration of a solution. It is defined as the number of moles of solute divided by the volume of solution in liters.
To calculate molarity, use the formula:\( \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \).
For example, in the exercise problem, both the HCl and KOH solutions have a molarity of 0.1 M.When 10 ml (or 0.01 L) of these solutions is used, the calculation for moles of solute is:

• Moles of HCl = \(0.1 \, \text{M} \times 0.01 \, \text{L} = 0.001 \, \text{moles} \)
• Moles of KOH = \(0.1 \, \text{M} \times 0.01 \, \text{L} = 0.001 \, \text{moles} \)

Calculating molarity is crucial for understanding how much solute is in a given volume, especially when predicting the outcomes of chemical reactions.

Temperature Change Calculation

Temperature change in a chemical reaction often indicates whether it is exothermic or endothermic.
In the exercise, when 10 ml of HCl is mixed with 10 ml of KOH, the temperature increased by \(4^{\circ} \text{C}\), showing exothermic behavior. To calculate the expected temperature change in a larger reaction, you correlate the heat released to the moles reacting.
In stepping up to 100 ml of each solution, we increased the number of moles tenfold. Therefore, the heat released - and consequently the temperature change - is also expected to multiply by ten.
The rise in temperature becomes: \(4^{\circ} \text{C} \times 10 = 40^{\circ} \text{C} \).
This shows the scalability in reactions, directly linking the amount of substances reacting to changes observed.

Heat Released in Chemical Reactions

The heat released in chemical reactions, especially exothermic ones, is a vital measure of the reaction's energy changes.
Thermodynamics tells us that the enthalpy change (heat change) accompanies many chemical reactions and can be calculated if certain other reaction conditions are known.
The standard unit for measuring heat changes in reactions is the joule (J).In an exothermic process like the neutralization of HCl and KOH, heat is released as the reaction proceeds. The amount of heat can also be indirectly calculated by measuring the temperature change, since the temperature increase is proportional to the heat released.
For reactions involving aqueous solutions, heat released per mole of reactants can be related to the specific heat capacity of water and the mass change:

• \( q = m \cdot c \cdot \Delta T \)

Where:

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

Understanding heat in reactions helps in predicting energy requirements and outcomes in chemical processes.