Question

Calculate the molar heat capacity of iron in \(\mathrm{J} \mathrm{mol}^{-1}{ }^{\circ} \mathrm{C}^{-1}\) Its specific heat is \(0.4498 \mathrm{Jg}^{-1}{ }^{\circ} \mathrm{C}^{-1}\).

Short answer

The molar heat capacity of iron is 25.1153 J/mol·°C.

Step-by-step solution

Find the molar mass of iron

To calculate the molar heat capacity, first, find the molar mass of iron, which is the mass of one mole of iron. Iron's molar mass is found on the periodic table and is approximately 55.85 grams per mole.

Calculate the molar heat capacity

Multiply the specific heat of iron by its molar mass to find its molar heat capacity. The molar heat capacity, C, is given by the formula: \[C = c \times M\] where c is the specific heat and M is the molar mass.

Insert values and solve

Insert the specific heat value for iron, 0.4498 \(\mathrm{Jg}^{-1}\)\(^{\circ}\mathrm{C}^{-1}\), and molar mass, 55.85 grams per mole, into the formula to get: \[C = 0.4498 \, \mathrm{Jg}^{-1}\,^{\circ}\mathrm{C}^{-1} \times 55.85 \, \mathrm{g/mol}\] and perform the multiplication to find the molar heat capacity.

Key concepts

Specific Heat

Specific heat, often symbolized as 'c', is a property that describes how much heat energy is required to raise the temperature of 1 gram of a substance by 1 degree Celsius. This physical quantity is critical in understanding how different materials respond to heat.

For example, water has a high specific heat capacity, meaning it can absorb a lot of heat before it starts to warm up. Metals like iron, on the other hand, generally have lower specific heat values, indicating they heat up more quickly.

In practice, knowledge of specific heat permits us to predict how substances will behave in various thermal environments, a crucial aspect in applications ranging from cooking to the design of radiators and even space shuttles.

Molar Mass

The molar mass of an element is the mass in grams of one mole of that element. A mole is Avogadro's number (\(6.022 \times 10^{23}\) atoms) of particles, whether they're atoms, molecules, ions, or electrons.

The molar mass is especially useful because it provides a bridge between the mass of a material and the number of moles present, which is a basic unit in chemistry for counting atoms and molecules. For instance, iron's molar mass is approximately 55.85 grams per mole, which means that one mole of iron—an ensemble of Avogadro's number of iron atoms—weighs 55.85 grams. Determining the molar mass is an essential step in many chemical calculations, including the computation of molar heat capacities.

Thermochemistry

Thermochemistry is the branch of chemistry that studies the heat energy involved in chemical reactions and physical transformations. This field examines the energy changes that accompany processes such as mixing, phase transitions, reaction formation, and even the often-discussed heat capacity of substances.

Key principles of thermochemistry include the laws of thermodynamics which, among other things, define how energy can be transformed and conserved in a system. Understanding thermochemistry is important for optimizing reactions, designing energy-efficient processes, and predicting how systems will behave when subjected to thermal stress.

Heat Capacity Calculations

Heat capacity calculations enable us to determine the amount of heat needed to change the temperature of an object. To move from the specific heat of a substance to its molar heat capacity, we employ the formula \[ C = c \times M\], where 'C' is the molar heat capacity, 'c' is the specific heat, and 'M' is the molar mass.

For a given substance, multiplying the specific heat by its molar mass provides the heat required to raise the temperature of one mole of the substance by one degree Celsius. In calculating the molar heat capacity of iron, understanding this relationship allowed us to convert from energy per mass to energy per mole, offering a more standardized unit that considers the number of particles involved.