Question

How many joules of heat are required to heat \(35.0 \mathrm{~g}\) of isopropyl alcohol from the prevailing room temperature, \(21.2^{\circ} \mathrm{C}\), to its boiling point, \(82.4^{\circ} \mathrm{C}\) ? (The specific heat of isopropyl alcohol is \(2.604 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}\).)

Short answer

5592.144 J of heat are required to heat 35.0 g of isopropyl alcohol from 21.2°C to its boiling point of 82.4°C.

Step-by-step solution

Understanding the problem

Determine the amount of heat energy required to raise the temperature of a substance using the formula: heat energy, Q = mass (m) * specific heat capacity (c) * change in temperature (∆T).

Plugging in the known values

Use the given mass of isopropyl alcohol (35.0 g), its specific heat capacity (2.604 J/g°C), and the change in temperature (∆T = final temperature - initial temperature = 82.4°C - 21.2°C) to calculate the heat energy (Q).

Performing the calculation

Calculate the heat energy using the formula: Q = m * c * ∆T. Here, ∆T = 82.4°C - 21.2°C = 61.2°C, so Q = 35.0 g * 2.604 J/g°C * 61.2°C.

Calculating the final result

Multiply the values to find Q, which is the total heat required: Q = 35.0 g * 2.604 J/g°C * 61.2°C = 5592.144 J.

Key concepts

Specific Heat Capacity

Specific heat capacity is a pivotal concept in understanding how substances interact with heat. It's defined as the amount of heat energy required to raise the temperature of one gram of a substance by one degree Celsius. This inherent property varies from one material to another, making it a unique identifier for the thermal behavior of substances. In practical terms, a high specific heat capacity means that a material will take more energy to heat up, explaining why water, with a high specific heat, takes longer to boil compared to metals.

In the case of the isopropyl alcohol mentioned in the exercise, knowing its specific heat capacity is crucial to determining how much energy is required to heat it from room temperature to its boiling point. With a value of 2.604 J/g°C, we can infer that isopropyl alcohol would require quite a bit of energy for every degree increase in temperature, indicative of its ability to absorb and hold heat.

Thermochemistry

Thermochemistry is the branch of chemistry that deals with the relationship between chemical reactions and heat change. Crucial to this field is the first law of thermodynamics, which asserts that energy cannot be created or destroyed – only transformed. This principle helps us understand how heat, a form of energy, is transferred during chemical processes, like when isopropyl alcohol is heated.

During heating, the energy supplied to the alcohol is not lost but stored within the substance as thermal energy, resulting in a temperature rise. Thermochemistry also teaches us about endothermic and exothermic reactions - processes that absorb or release heat, respectively. While our exercise isn't directly concerned with a chemical reaction, the principles of energy transfer are still at play.

Temperature Change

Temperature change is a measure of the difference in temperature as a substance absorbs or releases heat. It's a direct indicator of the thermal energy transfer that occurs during heating or cooling. The larger the temperature change, the greater the amount of heat energy involved in the process.

In our exercise, the temperature change is calculated by subtracting the initial temperature of the isopropyl alcohol (21.2°C) from its final temperature (82.4°C), yielding a change of 61.2°C. This significant change requires a substantial amount of heat, as the specific heat capacity of the alcohol dictates. Remember, the temperature change is directly proportional to the heat required; higher temperature changes demand more heat energy, a concept embodying the intimate tie between temperature and heat in thermochemical studies.