Question

To warm \(400.0 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}, 0.050 \mathrm{~mol}\) of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) is burned. The water warms from \(24.6^{\circ} \mathrm{C}\) to \(65.6^{\circ} \mathrm{C}\). What is the heat of the reaction, and what is the \(\Delta H\) of the reaction on a molar basis?

Short answer

The heat of the reaction is \( 1370.08 \, \text{kJ/mol}\.\)

Step-by-step solution

Determine the Heat Absorbed by Water

First, let's calculate the amount of heat absorbed by the water using the formula:\[ q = mc\Delta T \] where \( q \) is the heat absorbed, \( m \) is the mass of the water, \( c \) is the specific heat capacity of water (which is \( 4.18 \, \text{J/g°C} \)), and \( \Delta T \) is the change in temperature.Substitute the given values:- \( m = 400.0 \, \text{g} \)- \( \Delta T = 65.6^{\circ} \text{C} - 24.6^{\circ} \text{C} = 41.0^{\circ} \text{C} \)\[q = 400.0 \, \text{g} \times 4.18 \, \text{J/g°C} \times 41.0^{\circ} \text{C} \]\[q = 68504 \, \text{J} \]

Calculate the Heat of Reaction per Mole

The heat absorbed by the water is equal to the heat released by the combustion of ethanol. To find the heat of the reaction on a molar basis, we need to calculate how much heat corresponds to burning 0.050 mol of ethanol.Given that the heat absorbed is \( 68,504 \, \text{J} \), and considering that for burning \( 0.050 \, \text{mol} \) of ethanol, this is the total heat:To find the heat of combustion per mole:\[\Delta H = \frac{68,504 \, \text{J}}{0.050 \, \text{mol}} = 1,370,080 \, \text{J/mol}\]

Convert the Heat of Reaction to kJ/mol

Usually, the heat of reaction is expressed in \( \text{kJ/mol} \), so we convert the value from \( \text{J/mol} \) to \( \text{kJ/mol} \):\[ \Delta H = \frac{1,370,080 \, \text{J/mol}}{1000} = 1370.08 \, \text{kJ/mol} \]

Key concepts

Heat of Reaction

The heat of reaction refers to the amount of heat energy released or absorbed during a chemical reaction. In our exercise, ethanol is burned to heat water, demonstrating an exothermic process where heat is released. During this process, the chemical bonds in the ethanol molecules break, releasing heat that raises the temperature of the water.
This energy exchange is quantified as the heat of reaction and is pivotal for understanding energy changes involved in chemical reactions. Calculating the exact amount of heat involved helps to understand the energetics of the reaction.

• The total heat released in this instance was calculated using the formula: \[ q = mc \Delta T \]
• Where \( m \) is the mass of water, \( c \) is its specific heat capacity, and \( \Delta T \) is the temperature difference.

This calculation showed that 68,504 joules were absorbed by the water, indicating that an equivalent amount of heat was released by the ethanol burning.

Specific Heat Capacity

Specific heat capacity is a material's property that defines how much heat energy is required to change the temperature of one gram of the material by one degree Celsius. It's crucial in calculating the heat used or transferred in a given process.
For water, this capacity is relatively high, at 4.18 J/g°C, which implies that water can store a lot of heat before its temperature changes. This characteristic is why water is often used as a heat reservoir in various applications.
In our example, the water’s ability to absorb the heat from burning ethanol without a steep increase in temperature showcases its high specific heat. Knowing the specific heat capacity allows us to determine the energy involved when the temperature changes by using the formula: \[ q = mc \Delta T \]
This formula helps us calculate how much heat is needed to warm the water from 24.6°C to 65.6°C, which consequently equals the heat released during the ethanol combustion.

Enthalpy Change

Enthalpy change, symbolized as \( \Delta H \), measures the heat content change in a system during a reaction at constant pressure. It's a central concept for understanding chemical energetics, differentiating between endothermic (where heat is absorbed) and exothermic reactions (where heat is released).
In our task, we calculated the change in enthalpy for the ethanol combustion process. We deduced that for each mole of ethanol burned, 1,370,080 joules of energy are released.

• This equates to an enthalpy change of \( -1370.08 \, \text{kJ/mol} \), where the negative sign signifies that the reaction is exothermic.
• The calculation involves dividing the total heat released by the number of moles of fuel burned, providing a molar basis for energy changes.

Understanding \( \Delta H \) on a molar basis allows chemists to predict how much energy is involved in reactions, crucial for both laboratory and industrial applications.