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Molecular weight, also known as molar mass, is the mass of one molecule of a substance calculated based on the sum of atomic weights of its constituent atoms. It is expressed in atomic mass units (amu) or grams per mole. When considering molar heat capacity, it’s crucial to understand that it represents a property per mole of substance. Since it measures the heat needed to increase the temperature of one mole, the individual mass of the molecules doesn’t affect this value.
This is why the molecular weight doesn’t influence the molar heat capacity. Rather than a focus on mass, molar heat capacity essentially regards the quantity of substance in moles, maintaining consistency despite variations in molecular weight.

Atomicity refers to the number of atoms present within a single molecule of a substance. This concept is significant when evaluating the molar heat capacity of gases. The number of atoms in a molecule, or its atomicity, impacts the degrees of freedom available for motion.
Each additional atom increases the potential energy modes, such as translational, rotational, and vibrational, which in turn alters the molar heat capacity. For example:

• Monoatomic gases, like helium, have lower molar heat capacities as they primarily exhibit translational motion.
• Diatomic or polyatomic gases have higher heat capacities due to additional rotational and vibrational degrees of freedom.
  

Hence, the atomicity directly influences how much energy a gas can absorb as heat.

Temperature dependence refers to how a substance's physical property changes with temperature. When dealing with gases, their molar heat capacity can indeed vary with temperature. This variability is attributed to changes in the activity of molecules as they absorb more heat at higher temperatures.
At low temperatures, only a few degrees of freedom may be active. As temperature increases, additional rotational and vibrational motions become significant, amplifying heat capacity. Higher energy levels become accessible with rising temperatures, altering the total energy absorbed per mole. Understanding the temperature dependence of molar heat capacity helps predict how a gas will behave under different thermal conditions.

The conditions under which heat is supplied, such as constant pressure or constant volume, significantly impact the molar heat capacity of a gas. Molar heat capacity varies under different thermodynamic processes:

• At constant volume ( C_v ), no work is done by expansion, and all supplied heat increases the internal energy.
• At constant pressure ( C_p ), the gas expands as it is heated, performing work, requiring more energy per mole than at constant volume.

Additionally, specific processes like isothermal (constant temperature) or adiabatic (no heat exchange) conditions further modify how heat capacity is utilized. Each condition alters the energy requirements due to differences in how heat transforms into work or increases internal energy, thereby affecting calculations and applications of thermodynamic processes.