Question

Calculate the amount of energy released as heat by the freezing of 13.3 g of a liquid substance, given that the substance has a molar mass of 82.9 \(\mathrm{g} / \mathrm{mol}\) and a molar enthalpy of fusion of 4.60 \(\mathrm{kJ} / \mathrm{mol} .\)

Short answer

The amount of energy released is 0.738 kJ.

Step-by-step solution

- Calculate the number of moles

To find the number of moles of the substance, use the formula:

- Calculate the energy released

To find the amount of energy released, use the formula:

Key concepts

molar mass

The molar mass of a substance is the mass of one mole of its molecules. It's measured in grams per mole (g/mol). To find the molar mass, you sum the atomic masses of all atoms in one molecule. For instance, if you have a compound with a molar mass of 82.9 g/mol, it means 1 mole of that substance weighs 82.9 grams. This is vital for converting between grams and moles, making calculations on amounts of substances much easier.

moles calculation

To determine the number of moles from a mass, you use the relation: \[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} \ \] In our example, the given mass is 13.3 g and the molar mass is 82.9 g/mol. Plugging in these values: \[ \text{Number of moles} = \frac{13.3 \text{ g}}{82.9 \text{ g/mol}} = 0.160 \text{ moles} \ \] Now, you know how many moles of the substance you have. This step is essential as it connects the weight (mass) to the amount (moles).

molar enthalpy of fusion

The molar enthalpy of fusion (ΔH_fus) is the amount of energy required to melt one mole of a solid at its melting point. It's usually given in kilojoules per mole (kJ/mol). In our case, it is 4.60 kJ/mol. This value tells you how much energy per mole is involved in the phase change. If we reverse the process (freezing), the same amount of energy is released. Understanding this helps to calculate the total energy change during phase transitions.

energy calculation

To determine the energy released during freezing, use the formula: \[ \text{Energy} = \text{Number of moles} \times \text{Molar enthalpy of fusion} \ \] We already calculated the number of moles as 0.160. Using the molar enthalpy of fusion which is 4.60 kJ/mol: \[ \text{Energy} = 0.160 \text{ moles} \times 4.60 \text{ kJ/mol} = 0.736 \text{ kJ} \ \] So, when 13.3 g of the substance freezes, 0.736 kJ of energy is released as heat. Summing up, by knowing the molar mass, moles calculation, and molar enthalpy of fusion, we can accurately calculate energy changes in this process.