Question

Find \(\Delta H\) for the combustion of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\right)\) to carbon dioxide and liquid water from the following data. The heat capacity of the bomb calorimeter is \(34.65 \mathrm{kJ} / \mathrm{K},\) and the combustion of 1.765 \(\mathrm{g}\) of ethanol raises the temperature of the calorimeter from 294.33 \(\mathrm{K}\) to 295.84 \(\mathrm{K}\) .

Short answer

\( \Delta H \) for the combustion of ethanol is calculated by multiplying the heat absorbed per mole by the number of moles of ethanol burned.

Step-by-step solution

Determine the temperature change

Calculate the difference in temperature before and after the combustion of ethanol by subtracting the initial temperature from the final temperature.

Calculate the heat absorbed by the bomb calorimeter

Use the heat capacity of the bomb calorimeter and the temperature change to calculate the heat absorbed using the formula: Heat (q) = Heat Capacity (C) * \( \Delta T \) .

Convert the mass of ethanol to moles

The molar mass of ethanol (\( \mathrm{C}_2\mathrm{H}_6\mathrm{O} \) is about 46.07 g/mol. Calculate the number of moles of ethanol combusted by dividing the mass of ethanol by its molar mass.

Calculate \( \Delta H \) per mole of ethanol

Since \( q \) represents the heat for the combustion of the given mass of ethanol, you can find \( \Delta H \) per mole by dividing \( q \) by the number of moles of ethanol combusted.

Key concepts

Enthalpy Change (ΔH)

Enthalpy change, denoted as \(\Delta H\), is a measure of heat change during a chemical reaction at constant pressure. In the context of the combustion of ethanol, \(\Delta H\) refers to the amount of heat absorbed or released when ethanol is converted to carbon dioxide and water. A negative \(\Delta H\) would indicate an exothermic reaction, releasing heat to the surroundings, which is often the case in combustion reactions.

To calculate the enthalpy change for the combustion of a substance like ethanol, we monitor the temperature change in a calorimeter, a device that measures heat flow. By understanding the magnitude of \(\Delta H\), we can gauge the energy efficiency of fuels and their impact on the environment. For instance, a lower \(\Delta H\) means less heat is required for the reaction, making the fuel more efficient.

Bomb Calorimeter

A bomb calorimeter is an instrument designed to measure the heat of combustion of a substance. It consists of a strong container, or 'bomb,' where the combustion occurs, surrounded by a water jacket to absorb the heat released. The calorimeter is well-insulated to ensure minimal heat loss. In the combustion of ethanol, the bomb calorimeter helps to precisely measure the temperature rise due to the reaction. By calibrating the calorimeter with known heat quantities, we can calculate the actual heat of the reaction. The reliability of a bomb calorimeter makes it an essential tool in thermochemical experiments.

Key Components

• Sample holder: Where the substance (ethanol) is placed.
• Oxygen: Allows for complete combustion of the substance.
• Ignition system: Sparks combustion in the sample.
• Thermometer or temperature sensor: Records the temperature changes.

Heat Capacity

Heat capacity is an intrinsic property of any material or system that describes the quantity of heat required to raise its temperature by one degree. The heat capacity of a bomb calorimeter is a crucial factor in calculating enthalpy change as it dictates how much energy is absorbed by the calorimeter itself during the process. It is commonly expressed in units like joules per kelvin (J/K) or kilojoules per kelvin (kJ/K).

The heat capacity is factored into the calculations to ensure accurate determination of the heat associated with the chemical reaction. For precise measurements, it is important to calibrate the calorimeter and verify its heat capacity. Higher heat capacity indicates that the system can absorb more heat without significantly changing its temperature, which is an essential characteristic for calorimetry.

Molar Mass

Molar mass, the mass of one mole of a substance, is critical when translating between the mass of a substance and the amount of substance (in moles). The molar mass of ethanol (C₂H₆O) is 46.07 grams per mole. Understanding the molar mass enables chemists to calculate how many moles of ethanol undergo combustion.

To find the number of moles of ethanol used in a reaction, we divide the mass of ethanol by its molar mass. Accurate calculations of molar mass and the subsequent determination of moles are essential in stoichiometry for predicting the outcome of chemical reactions and for calculating specific heat changes, like enthalpy.

Temperature Change

Temperature change is the difference in temperature that occurs when a system absorbs or releases heat. In calorimetry, it's the observed alteration in the calorimeter's temperature before and after a reaction takes place. This temperature difference is denoted as \(\Delta T\) and is a direct indicator of energy exchange.

In our ethanol combustion example, we measure the initial temperature of the bomb calorimeter and after the combustion has occurred. The change in temperature, alongside the calorimeter's heat capacity, allows us to calculate the heat absorbed (q) during the reaction. An accurate assessment of temperature change is pivotal for determining the enthalpy change of a reaction with precision.