Problem 44 - Chemistry The Molecular Science

Question

The enthalpy of fusion (melting) of water is \(6.0 \mathrm{~kJ} / \mathrm{mol}\). Calculate the quantity of energy that must be transferred to melt \(25.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\) at \(0{ }^{\circ} \mathrm{C}\).

Step-by-Step Solution

Answer

8.34 kJ of energy is required to melt 25.0 g of water at 0°C.

Step 1: Calculate Moles of Water

First, determine the number of moles of water. Use the molar mass of water, which is approximately \(18.0 \text{ g/mol}\). Calculate the moles using the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\). For \(25.0 \text{ g}\) of water, the moles are \(\frac{25.0 \text{ g}}{18.0 \text{ g/mol}} = 1.39 \text{ moles}\).

Step 2: Use Enthalpy of Fusion

Now, use the enthalpy of fusion value to calculate the total energy required. The enthalpy of fusion for water is \(6.0 \text{kJ/mol}\). Multiply this by the number of moles calculated in step 1: \(1.39 \text{ moles} \times 6.0 \text{ kJ/mol} = 8.34 \text{ kJ}\).

Step 3: Conclude with energy requirement

The total energy required to melt \(25.0 \text{ g} \text{ H}_2\text{O}\) at \(0{ }^{\circ} \text{C}\) is calculated to be \(8.34 \text{ kJ}\).

Key Concepts

Moles of Water

To begin understanding how much energy it takes to melt a substance, first, we need to understand the concept of moles. A mole is a unit that helps us relate the mass of a substance to the number of molecules it contains. For water, with the chemical formula \( \text{H}_2\text{O} \), the molar mass is approximately 18.0 grams per mole. This means that one mole of water weighs 18.0 grams.

In the context of this exercise, we have 25.0 grams of water that we want to melt. Our first task is to convert this mass into moles, which is done using the formula:

• \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \)

So for 25.0 grams of water, the number of moles is calculated as follows: \( \frac{25.0 \text{ g}}{18.0 \text{ g/mol}} = 1.39 \text{ moles} \). This conversion is essential because energy calculations during phase changes depend on the number of moles.

Energy Calculation

Once we have determined the number of moles of water, we can calculate the energy required to melt it. This process involves the enthalpy of fusion, which is the measure of energy needed to change a substance from a solid to a liquid at its melting point.

In this case, the enthalpy of fusion for water is given as 6.0 kJ/mol. This means that 6.0 kJ of energy is needed to melt one mole of water. With the calculated 1.39 moles of water, the total energy needed would be:

• \( 1.39 \text{ moles} \times 6.0 \text{ kJ/mol} = 8.34 \text{ kJ} \)

So, 8.34 kJ of energy must be absorbed to completely melt 25 grams of ice at \(0^{\circ} \text{C}\). This is a vital calculation as it forms the basis of understanding energy transformations during phase changes.

Phase Change

The concept of phase changes is crucial in thermodynamics and chemistry. A phase change is the transition of a substance from one state of matter to another, such as from solid to liquid or liquid to gas. During a phase change, the temperature of the substance does not change, even though energy is being transferred. This energy is used to break the intermolecular bonds that hold the molecules in a solid structure.

For water transforming from solid (ice) to liquid (water), energy must be absorbed without causing a rise in temperature, a process characterized by the enthalpy of fusion. In practical terms, the enthalpy of fusion tells us how much energy is needed to alter the phase per mole of the substance. For water, this is 6.0 kJ/mol.

• This process is crucial in natural phenomena and many industrial applications.
• Understanding how energy relates to phase changes helps explain why ice requires energy to melt and why the temperature remains constant during the melting.

This understanding provides foundational knowledge in fields such as meteorology, food science, and engineering, where the control of phase changes is often critical.