To calculate the total energy required to convert a solid to a gas using heal ca

Question

To calculate the total energy required to convert a solid to a gas using heal capacity heat of fusion, and heat of vaporization. The amount of heat required to melt one mole of a solid is called the heat of fusion (delta H_fus). The amount of heat required to vaporize (boil) one mole of a liquid is carted the heat of vaporization (delta H_vap). The heat of fusion and the heat of vaporization can be used to calculate the amount of heat needed to melt or vaporize respectively, a given amount of substance. For example, the heat of fusion for H_2O is 6 02 kJ/moI. which means that 6.02 kJ of heat is needed to melt a mole of ice. Twice as much heat is needed to melt twice as much ice. as shown here: 2.00 mol times 6.02 kJ/mol = 12.0 kJ Heat of fusion (delta H_fus) is used for capitations involving a phase change between solid and liquid with no temperature change. For H_2O, delta H_fus = 6.02 kJ/mol. Specific heat capacity (C) is used tor calculations that involve a temperature change, but no phase change. For liquid water C = 4.184 J/(g degree C). Heat of vaporization (delta H_vap) is used for calculations involving a phase change between liquid and gas with no temperature change. For H_2O delta H_vap = 40.7 kJ/mol. How much heal is required to melt 52.5 g, of ice at its melting point? Express your answer numerically In kilojoules.

Explanation / Answer

We have 52.5 g ice. Molar mass of ice = 18 g/mol.

Therefore, moles of ice = (52.5 g)*(1 mol/18 g) = 2.9167 mol.

Heat of fusion of water, Hfus = 6.02 kJ/mol.

Therefore, heat required to melt 52.5 g ice at its melting point = (mols of ice melted)*Hfus = (2.9167 mol)*(6.02 kJ/mol) = 17.558 kJ (ans).

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