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 \(\mathrm{kJ} / \mathrm{mol}\)

Short answer

The enthalpy change is approximately -91.58 kJ/mol.

Step-by-step solution

Calculate the Temperature Change

Determine the change in temperature by subtracting the initial temperature from the final temperature. \[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 28.8^{\circ} \mathrm{C} - 20.2^{\circ} \mathrm{C} = 8.6^{\circ} \mathrm{C} \]

Calculate Heat Absorbed by Water

Use the formula for heat absorbed by the water, which is \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of water, \( c \) is the specific heat capacity of water (\( 4.18 \ \mathrm{J/g}^{\circ} \mathrm{C} \)), and \( \Delta T \) is the temperature change. \[ q = 135 \ \mathrm{g} \times 4.18 \ \mathrm{J/g}^{\circ} \mathrm{C} \times 8.6^{\circ} \mathrm{C} \] \[ q = 4853.46 \ \mathrm{J} \] Convert this to kJ: \( 4.85346 \ \mathrm{kJ} \).

Convert Mass of H₂SO₄ to Moles

Convert the mass of sulfuric acid to moles using its molar mass (\( 98.08 \ \mathrm{g/mol} \)). \[ \text{Moles of } \mathrm{H}_{2}\mathrm{SO}_{4} = \frac{5.2 \ \mathrm{g}}{98.08 \ \mathrm{g/mol}} = 0.053 \ \mathrm{mol} \]

Calculate Molar Enthalpy Change

To find the enthalpy change per mole, divide the total heat absorbed by the moles of sulfuric acid. Use the formula \[ \Delta H = \frac{q}{n} \] where \( n \) is the number of moles. \[ \Delta H = \frac{4.85346 \ \mathrm{kJ}}{0.053 \ \mathrm{mol}} \approx 91.58 \ \mathrm{kJ/mol} \]

Analyze the Sign of Enthalpy Change

Since the temperature of the water increased, the dissolution is exothermic, meaning the enthalpy change should be negative. Thus, the final enthalpy change is: \[ \Delta H = -91.58 \ \mathrm{kJ/mol} \]

Key concepts

Exothermic Process

When chemicals react, they often release or absorb energy, typically in the form of heat. An exothermic process is one where heat is released into the surroundings, causing an increase in temperature of the environment. This is what happens when you dissolve sulfuric acid (\(\mathrm{H}_{2} \mathrm{SO}_{4}\)) in water. It's important to handle such chemicals with care since the heat release can be substantial. In the given exercise, adding 5.2 g of sulfuric acid to water resulted in a temperature increase, confirming the reaction was exothermic.

Key Points:

• Heat release leads to temperature rise, making the process exothermic.
• Reactions like the dissolution of sulfuric acid demonstrate the effect vividly.
• These reactions can be utilized to measure energy changes in chemistry.

Specific Heat Capacity

The specific heat capacity of a substance is a measure of how much heat energy it takes to raise the temperature of one gram of the substance by one degree Celsius. For water, this value is a well-known constant at 4.18 J/g°C.

In calorimetry, specific heat capacity helps us calculate the amount of heat absorbed or released during a chemical process. In this case, knowing the specific heat capacity of water allowed us to calculate how much heat the water absorbed as the acid dissolved.
Formula:

• Heat absorbed (\( q \)) = Mass (\( m \)) x Specific Heat Capacity (\( c \)) x Temperature Change (\( \Delta T \))

Using this formula, you can relate temperature changes to energy changes, which allows for the determination of reaction enthalpies in a calorimeter setup.

Molar Mass Conversion

To connect empirical mass data to chemical reactions, we frequently convert mass to a number of moles using molar mass. The molar mass of sulfuric acid (\( \mathrm{H}_{2} \mathrm{SO}_{4} \)) is 98.08 g/mol. This information is crucial in stoichiometry and energy calculations.

Steps for Molar Mass Conversion:

• Determine the mass of your sample (\(5.2 \, ext{g} \) in our exercise).
• Utilize the molar mass of the compound for the conversion.
• Calculate moles: \[ \text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

In our case, converting the mass of \( \mathrm{H}_{2} \mathrm{SO}_{4} \) to moles was a step toward understanding the amount of chemical involved in producing the measured heat change.

Coffee-Cup Calorimeter

A coffee-cup calorimeter is a simple device used to measure the heat changes in chemical reactions or physical changes. It typically consists of a polystyrene cup, a lid, a thermometer, and a stirrer. Despite its simplicity, it is a useful tool for acquiring precise measurements of temperature changes during chemical reactions.

Function and Usage:

• Designed to be an isolated system, it minimizes heat exchange with the surroundings.
• Measures the temperature change of the contents (usually water) to determine heat changes.
• Used especially in aqueous reactions to calculate enthalpy changes.

In the exercise, the calorimeter allowed for the accurate determination of the heat produced when sulfuric acid dissolved in water. By monitoring temperature increases inside the cup, we could calculate the energy change as the acid became aqueously dissolved.