Problem 64 - Chemistry Matter and Change

Question

Transportation Ethanol is being used as an additive to gasoline. The combustion of 1 mol of ethanol releases 1367 kJ of energy. How many Calories are released?

Step-by-Step Solution

Answer

The combustion of 1 mol of ethanol releases approximately 326,519 Calories of energy.

Step 1: Convert kilojoules to calories

First, we need to convert the energy released from the combustion of 1 mol of ethanol from kilojoules to calories. To do this, we'll use the conversion factor between kilojoules and joules and the conversion factor between joules and kilocalories: Energy in kilojoules = 1367 kJ Energy in joules = 1367 kJ * 1000 J/kJ = 1,367,000 J Now, convert joules to kilocalories: Energy in kilocalories = 1,367,000 J * 0.239006 kcal/J ≈ 326,519 kcal

Step 2: Convert kilocalories to Calories

Finally, we'll convert the energy in kilocalories to Calories. Since 1 kcal is equal to 1 Cal, the conversion is straightforward: Energy in Calories = 326,519 kcal So, the combustion of 1 mol of ethanol releases approximately 326,519 Calories of energy.

Key Concepts

Combustion of Ethanol

Combustion is a type of chemical reaction where a substance combines with oxygen to produce heat and light. In the case of ethanol (C2H5OH), the combustion process is particularly significant because it is widely used as a biofuel. When ethanol is burned, it reacts with oxygen in the air to produce carbon dioxide, water, and energy in the form of heat.

Here is the balanced chemical equation for the combustion of ethanol: \[ C_2H_5OH_{(l)} + 3O_2_{(g)} \rightarrow 2CO_2_{(g)} + 3H_2O_{(g)} + \text{energy} \]
Understanding this reaction is crucial for several industries, especially for those using ethanol as fuel, because it allows them to calculate how much energy can be obtained from a certain amount of ethanol.

Converting Energy Units

Energy can be measured in different units, and understanding how to convert between these units is fundamental in science, especially in the study of energy-related processes. The problem you encountered involves converting energy from kilojoules (kJ) to Calories (with a capital 'C', also known as food calories). One kilocalorie (kcal) is equivalent to one Calorie and to 4.184 kilojoules.

To convert from kilojoules to Calories, you can use the following equation: \[ \text{Calories} = \frac{\text{kilojoules}}{4.184} \]
By applying this conversion factor, students can easily transform energy values from one unit to another, which is essential for comparing energy outputs in different forms, such as how much energy is produced by the combustion of ethanol in our example.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is based on the conservation of mass where the total mass of the reactants equals the total mass of the products.

In the context of the combustion of ethanol, stoichiometry enables us to determine the amount of reactants needed to produce a certain amount of products, or vice versa. For example, knowing the balanced chemical equation allows us to calculate how much ethanol is needed to release a specific amount of energy. This is invaluable when planning the production of energy, creating efficient fuel mixtures, or even when complying with environmental regulations regarding emissions.

Thermochemistry

Thermochemistry is the study of heat changes that accompany chemical reactions and physical changes of state. It involves concepts such as enthalpy, entropy, and Gibbs free energy. The heat released by the combustion of a fuel like ethanol is an example of an exothermic reaction, which is a reaction that releases energy to the surroundings.

In this discipline, we speak of the heat of combustion, which is the amount of heat energy released when a substance combusts completely with oxygen under standard conditions. Thermochemical calculations, like those needed to determine the energy released from the combustion of ethanol, are essential for understanding how much energy different fuels can provide and how they can be used effectively and sustainably.