Question

When a \(4.00\)-g sample of magnesium metal is burned, it produces enough heat to raise the temperature of \(2010 \mathrm{~g}\) of water from \(24.00^{\circ} \mathrm{C}\) to \(33.10^{\circ} \mathrm{C}\). (a) How much heat did the magnesium release as it burned? (b) Calculate the heat of combustion of magnesium in units of \(\mathrm{kJ} / \mathrm{g}\).

Short answer

The heat released by the magnesium is the same as the heat absorbed by the water. The heat of combustion per gram of magnesium is calculated by dividing the heat released by the mass of magnesium.

Step-by-step solution

Calculate the heat absorbed by water)

The heat absorbed by water can be estimated using the equation \(q = m \cdot c \cdot \Delta T\), where 'q' is the heat, 'm' is the mass-water, 'c' is the specific heat capacity of water which equals \(4.18 \mathrm{~J/g^{\circ}C}\), and '\(\Delta T\)' is the change in temperature, subtract initial temperature from the final temperature.

Find the heat released by magnesium

The heat loss by the magnesium is equal to the heat gain by water due to the principle of conservation of energy. So, essentially the heat released by the magnesium will be equal to the heat absorbed by the water. Therefore, the value obtained in step 1 is the heat released by the magnesium.

Calculate the heat of combustion of magnesium per gram

Heat of combustion usually is given per mole of substance but in this case, the heat of combustion is required in terms of per gram. This can be done by dividing the heat released by the mass of magnesium.

Key concepts

Thermochemistry: The Study of Energy Changes

Thermochemistry is an essential branch of chemistry focusing on the study of energy changes, particularly heat, during chemical reactions and physical transformations. It involves understanding how energy is absorbed or released and the impact this has on the environment where the reaction occurs. An understanding of thermochemistry is crucial when analyzing the heat of combustion of substances, like the burning of magnesium in the provided exercise.

In relation to our exercise, when magnesium burns, it reacts with oxygen to form magnesium oxide, and this reaction releases a significant amount of heat. This heat transfer is the central interest in thermochemistry, helping us figure out the energy content of magnesium.

Specific Heat Capacity: A Measure of Thermal Inertia

The concept of specific heat capacity is at the heart of many thermochemical calculations, including the one described in the exercise. It is defined as the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius (or Kelvin). This property is intrinsic to each substance and is critically important because it tells us how much heat is needed to change the temperature of a specific quantity of the substance.

For water, the specific heat capacity is typically given as \(4.18 \mathrm{~J/g^\circ C}\), which is a relatively high value, indicating that water absorbs a lot of heat before its temperature rises significantly. The step-by-step solution makes use of this value to determine how much heat the water absorbed, thereby telling us how much heat the magnesium released.

Conservation of Energy: The Balancing Act of Heat Transfer

One of the most fundamental principles in science is the conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another. In the context of the given exercise, this principle ensures that all the heat released by the burning magnesium is absorbed by the water without any loss to the surroundings.

By applying this concept, we infer that the heat gained by the water has to equal the heat lost by the magnesium. The use of the conservation of energy allows us to conclusively determine the energy change of the magnesium as it burns, providing a clear understanding of the reaction's energetic.

Enthalpy Change: Accounting for Heat in Reactions

Enthalpy change, often symbolized as \(\Delta H\), is a measure of the total heat content change within a system during a chemical reaction at constant pressure. It is a central term in thermochemistry. A negative enthalpy change indicates an exothermic reaction, where heat is released to the surroundings, while a positive enthalpy change is indicative of an endothermic reaction, where heat is absorbed from the surroundings.

In our exercise, the burning of magnesium releases heat, indicating an exothermic reaction. This release is quantitatively expressed with the enthalpy change of the reaction. By calculating the heat of combustion per gram of magnesium, we are essentially measuring the enthalpy change for the burning of magnesium, which is an important piece of information for chemists and engineers.