Problem 42 - Chemistry and Chemical Reactivity

Question

You should use care when dissolving \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in water because the process is highly exothermic. To measure the enthalpy change, \(5.2 \mathrm{g}\) of concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}(\ell)\) was added (with stirring) to 135 g of water in a coffee-cup calorimeter. This resulted in an increase in temperature from \(20.2^{\circ} \mathrm{C}\) to \(28.8^{\circ} \mathrm{C} .\) Calculate the enthalpy change for the process \(\mathrm{H}_{2} \mathrm{SO}_{4}(\ell) \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}),\) in kJ/mol.

Step-by-Step Solution

Answer

The enthalpy change is approximately 95.2 kJ/mol.

Step 1: Calculate the Total Mass of the Solution

Add the mass of the sulfuric acid to the mass of the water to get the total mass of the solution.Given: - Mass of \(\mathrm{H}_{2}\mathrm{SO}_{4} = 5.2\, \mathrm{g}\)- Mass of water = 135 gSo, Total mass of the solution = 135 g + 5.2 g = 140.2 g.

Step 2: Use Specific Heat Capacity to Calculate Heat Absorbed

The specific heat capacity \(c\) of water is approximately \(4.18\, \mathrm{J/(g\, ^\circ C)}\).Use the formula: \[ q = mc\Delta T \]Where:- \(m = \) total mass of the solution = 140.2 g- \(c = 4.18\, \mathrm{J/(g\, ^\circ C)}\)- \(\Delta T = \) change in temperature = \(28.8^\circ C - 20.2^\circ C = 8.6^\circ C\)Therefore, \[ q = 140.2\, \mathrm{g} \times 4.18\, \mathrm{J/(g\, ^\circ C)} \times 8.6^\circ C \approx 5047.02\, \mathrm{J}\]

Step 3: Convert Heat Absorbed to kJ

Since our final answer needs to be in kJ, we convert the heat absorbed from Joules to kJ. \[ 5047.02\, \mathrm{J} = \frac{5047.02}{1000}\, \mathrm{kJ} \approx 5.047\, \mathrm{kJ}\]

Step 4: Determine the Amount of Substance

Calculate the moles of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) used.Molar mass of \(\mathrm{H}_{2}\mathrm{SO}_{4} = 98.08\, \mathrm{g/mol}\).Therefore, moles of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) = \(\frac{5.2\, \mathrm{g}}{98.08\, \mathrm{g/mol}} \approx 0.0530\, \mathrm{mol}\).

Step 5: Calculate Enthalpy Change per Mole

To find the enthalpy change \(\Delta H\) per mole, divide the total heat change by the number of moles.\[ \Delta H = \frac{5.047\, \mathrm{kJ}}{0.0530\, \mathrm{mol}} \approx 95.2\, \mathrm{kJ/mol} \]

Key Concepts

Exothermic Reaction

When dissolving sulfuric acid (\(\text{H}_2\text{SO}_4\)) in water, the reaction is highly exothermic. An exothermic reaction is one that releases heat. This means the temperature of the surrounding environment increases as the reaction proceeds.
In such a reaction, the reactants convert into products, releasing energy in the form of heat. This release often makes the container of the reaction, like the coffee-cup calorimeter used here, hot to the touch.

• Example: Mixing sulfuric acid with water
• Outcome: Increased temperature
• Effect: Release of energy

Understanding exothermic reactions is crucial for safely conducting experiments involving significant heat release.

Specific Heat Capacity

Specific heat capacity is a property that tells us how much heat energy is required to raise the temperature of a substance by 1 degree Celsius. In this exercise, water's specific heat capacity is key.
The specific heat capacity of water is approximately 4.18 \(\text{J/(g}\,\!^\circ\text{C)}\). This value is used to calculate the amount of heat energy absorbed or released during a reaction.

• Formula: \( q = mc\Delta T \)
• \( m \) = mass of the solution
• \( c \) = specific heat capacity
• \( \Delta T \) = temperature change

Using this formula helps us determine how much heat the solution has absorbed when the temperature changes.

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). For sulfuric acid (\(\text{H}_2\text{SO}_4\)), the molar mass is 98.08 \(\text{g/mol}\).
This concept helps us convert between the mass of a substance and the amount of substance in moles. This conversion is crucial when calculating the enthalpy change per mole.

• Molar mass of \(\text{H}_2\text{SO}_4\)
• Importance: Linking mass to moles
• Application: \(\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\)

Accurate calculations of molar mass are vital for precise chemical calculations.

Calorimetry

Calorimetry is the science of measuring heat change in chemical reactions. In the given scenario, a coffee-cup calorimeter is used to measure the enthalpy change when \(\text{H}_2\text{SO}_4\) is dissolved in water.
A calorimeter helps capture and measure the heat absorbed or released, ensuring minimal heat loss to the environment.

• Instrument: Coffee-cup calorimeter
• Purpose: Measure temperature change
• Application: Calculate enthalpy change

By observing temperature changes, calorimetry allows calculations of the enthalpy change, providing insights into the reaction's energetics. This helps us understand the heat flow and energy involved in the process.