Calculate the amount of heat required to completely sublime 75.0 g of solid dry ice (CO₂) at its sublimation temperature. The heat of sublimation for carbon dioxide is 32.3 kJ/mol.

검증된 단계별 안내

Identify the given information: mass of dry ice (CO_2) is 75.0 g and the heat of sublimation is 32.3 kJ/mol.

Calculate the molar mass of CO_2. The molar mass of carbon (C) is approximately 12.01 g/mol and that of oxygen (O) is approximately 16.00 g/mol. Therefore, the molar mass of CO_2 is 12.01 + 2(16.00) g/mol.

Convert the mass of CO_2 from grams to moles using the formula: \( \text{moles of CO}_2 = \frac{\text{mass of CO}_2}{\text{molar mass of CO}_2} \).

Use the heat of sublimation to calculate the total heat required. Multiply the moles of CO_2 by the heat of sublimation: \( \text{heat required} = \text{moles of CO}_2 \times 32.3 \text{ kJ/mol} \).

The result from the previous step gives the total amount of heat required to completely sublime the given mass of dry ice.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Sublimation

Sublimation is the phase transition in which a substance changes directly from a solid to a gas without passing through the liquid phase. In the case of dry ice (solid CO2), it sublimates at temperatures below -78.5°C. Understanding sublimation is crucial for calculating the heat required for this process, as it involves energy changes associated with breaking intermolecular forces.

Heat of Sublimation

The heat of sublimation is the amount of energy required to convert one mole of a solid directly into a gas at a constant temperature and pressure. For carbon dioxide, this value is 32.3 kJ/mol, indicating the energy needed to overcome the forces holding the solid together. This concept is essential for calculating the total heat needed for the sublimation of a given mass of dry ice.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For carbon dioxide (CO2), the molar mass is approximately 44.01 g/mol. Knowing the molar mass is vital for converting the mass of dry ice (75.0 g) into moles, which allows for the application of the heat of sublimation in the heat calculation.

Calculate the amount of heat required to completely sublime 75.0 g of solid dry ice (CO2) at its sublimation temperature. The heat of sublimation for carbon dioxide is 32.3 kJ/mol.