Question

What is the molar heat capacity of ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) in units of \(\mathrm{J} \mathrm{mol}^{-1}{ }^{\circ} \mathrm{C}^{-1}\), if its specific heat is \(0.586 \mathrm{cal} \mathrm{g}^{-1}{ }^{\circ} \mathrm{C}^{-1} ?\)

Short answer

The molar heat capacity of ethyl alcohol is approximately \(111.46 \mathrm{J}\mathrm{mol}^{-1}{ }^{\circ}\mathrm{C}^{-1}\).

Step-by-step solution

Understanding Specific Heat and Molar Heat Capacity

Specific heat is the amount of heat per unit mass required to raise the temperature of a substance by one degree Celsius. Molar heat capacity is the amount of heat needed to raise the temperature of one mole of a substance by one degree Celsius. Our goal is to find the molar heat capacity given the specific heat.

Convert Specific Heat from Calories to Joules

First, we convert the specific heat from calories to joules, since the desired molar heat capacity is in joules. Use the conversion factor: 1 cal = 4.184 J.

Calculate Molar Mass of Ethyl Alcohol

To find the molar heat capacity, we need to calculate the molar mass of ethyl alcohol, \( \mathrm{C}_{2}\mathrm{H}_{5} \mathrm{OH} \), using the atomic masses of carbon (C), hydrogen (H), and oxygen (O).

Find Molar Heat Capacity

Multiply the specific heat in \( \mathrm{J}\mathrm{g}^{-1}{ }^{\circ} \mathrm{C}^{-1} \) by the molar mass of ethyl alcohol to obtain the molar heat capacity in \( \mathrm{J}\mathrm{mol}^{-1}{ }^{\circ} \mathrm{C}^{-1} \).

Key concepts

Specific Heat

Specific heat, also known as specific heat capacity, is a property that describes how much heat energy is needed to raise the temperature of a given amount of a substance by one degree Celsius. It is unique for each substance and is crucial in understanding heat transfer in chemistry. This property allows us to predict how a substance will react when it comes into contact with a heat source or when it is mixed with other substances at different temperatures.

For example, water has a high specific heat capacity, which means it can absorb a lot of heat before it starts to get significantly warmer. This is why water is used as a coolant in car radiators or as an effective heat sink in various applications. Understanding specific heat is essential for many real-world applications, including climate science, culinary arts, and engineering.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance. It is a fundamental concept in chemistry as it bridges the gap between the microscopic scale of atoms and molecules and the macroscopic world we measure in grams and kilograms. The molar mass is calculated by summing the atomic masses of all the atoms in one molecule of a substance, as listed on the periodic table of elements.

For instance, to calculate the molar mass of water (H2O), we would add the mass of two hydrogen atoms with one oxygen atom. Accurately determining molar mass is essential for converting between grams and moles, allowing chemists to quantify the amount of a substance involved in a chemical reaction, assess purity, and calculate concentrations.

Heat Conversion

Heat conversion is the process of changing the unit of heat from one system to another. In chemistry, the most common heat conversions are between calories and joules. The calorie is a unit of energy that was originally defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius. On the other hand, the joule, which is the SI unit of energy, is more broadly used in science.

One calorie is equivalent to 4.184 joules, and this conversion factor is significant when working with thermal energies in real-life scenarios. For example, nutrition labels often use calories to quantify energy, while physicists and chemists usually employ joules. Without the ability to convert between these units, comparing and calculating energy values across different disciplines would be challenging.

Chemistry Thermodynamics

Chemistry thermodynamics is the branch of chemistry that deals with the relationships between heat, work, temperature, and energy transfer in chemical processes. It allows us to understand and predict the behavior of systems in thermal equilibrium and non-equilibrium states. The laws of thermodynamics govern the principles of energy conservation, efficiency, and spontaneity of reactions. A key concept is enthalpy, which is a measure of the total heat content in a chemical system and is essential in predicting whether a reaction will be exothermic (releasing heat) or endothermic (absorbing heat).

Thermodynamics aids in designing chemical reactions, engines, and refrigeration systems, ensuring that they operate with optimum efficiency. The field also helps explain biological processes like metabolism and has broad implications for the development of sustainable energy solutions.