Question

Calculate the amount of heat required to completely sublime \(50.0 \mathrm{~g}\) of solid dry ice \(\left(\mathrm{CO}_{2}\right)\) at its sublimation temperature. The heat of sublimation for carbon dioxide is \(32.3 \mathrm{~kJ} / \mathrm{mol}\).

Short answer

The heat required to sublime 50.0 g of solid dry ice is 36.1 kJ.

Step-by-step solution

Convert mass to moles

To find the amount of heat required, first convert the mass of dry ice to moles using the molar mass of \text{CO}_2, which is approximately 44.01 g/mol. The number of moles of \text{CO}_2 is calculated using the formula: \[ \text{number of moles} = \frac{\text{mass in grams}}{\text{molar mass in g/mol}}. \]

Calculate the heat required

After obtaining the number of moles of \text{CO}_2, multiply it by the heat of sublimation to find the total heat required for sublimation. Use the formula: \[ \text{heat required (kJ)} = \text{number of moles} \times \text{heat of sublimation (kJ/mol)}. \]

Key concepts

Understanding Sublimation Temperature

Sublimation temperature is the point at which a substance transitions directly from a solid to a gas without passing through the liquid phase. This temperature is specific to each substance and has a fixed value under a given set of conditions, often at atmospheric pressure. For dry ice, which is solid carbon dioxide (CO2), sublimation occurs at approximately -78.5°C (-109.3°F).

During sublimation, particles gain enough energy to break free from their fixed positions in the solid state and disperse, becoming a gas. The sublimation temperature is crucial in calculations involving the phase change because it indicates the exact conditions under which the heat of sublimation applies.

Enthalpy Change During Sublimation

Enthalpy change, in the context of sublimation, refers to the amount of heat required or released when a substance sublimates at constant pressure. It is an essential concept for understanding how energy is absorbed or released during phase transitions. For sublimation, the enthalpy change corresponds to the heat of sublimation.

The heat of sublimation is an intrinsic property and can be thought of as the 'energy cost' to overcome the forces holding the solid together. It is usually given in kilojoules per mole (kJ/mol). The provided exercise requires the understanding of this concept to calculate the heat needed to sublimate CO2 from solid to gas at its sublimation temperature.

The Role of Molar Mass in Calculations

Molar mass is the weight of one mole of a chemical compound or element, typically expressed in grams per mole (g/mol). It is fundamental in converting between the mass of a substance and the amount of substance in moles—which is necessary for stoichiometric calculations and thermochemical equations.

Utilizing the molar mass of CO2, which is approximately 44.01 g/mol, we can calculate the number of moles of CO2 present in any given mass. As illustrated in the exercise, the mass of dry ice is first transformed into its mole equivalent by dividing by the molar mass. This step allows us to interface the physical quantity of the substance (its mass) with the chemical quantity (moles), which then enables the calculation of energy changes during sublimation via the heat of sublimation.