Problem 18 - Chemistry and Chemical Reactivity

Question

The energy required to melt \(1.00 \mathrm{g}\) of ice at \(0^{\circ} \mathrm{C}\) is 333 J. If one ice cube has a mass of \(62.0 \mathrm{g}\) and a tray contains 16 ice cubes, what quantity of energy is required to melt a tray of ice cubes to form liquid water at \(0^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

A total of 330336 J is required to melt the tray of ice cubes.

Step 1: Determine Energy to Melt One Ice Cube

First, calculate the energy required to melt the ice cube with mass 62.0 g. Given the energy required to melt 1.00 g of ice is 333 J, calculate the energy for 62.0 g:\[ \text{Energy for one ice cube} = 62.0 \text{ g} \times 333 \text{ J/g} = 20646 \text{ J}\]

Step 2: Calculate Total Energy for the Tray

Since the tray contains 16 ice cubes, calculate the total energy needed to melt all the ice cubes in the tray:\[ \text{Total energy} = 16 \times 20646 \text{ J} = 330336 \text{ J}\]

Key Concepts

Phase Changes

When talking about thermodynamics in chemistry, phase changes refer to the transformation of a substance from one state of matter to another. Common phase changes include melting, freezing, boiling, and condensing. For example, melting refers to the change from a solid to a liquid state. This process is important because it requires energy to overcome the forces holding the particles together in a solid.
In our scenario, ice (solid water) is being transformed into liquid water through melting. This requires heat energy to be added to the system. The amount of energy needed depends on the mass of the ice and its specific heat properties. Once the exact amount of energy is provided, the phase change completes at a consistent temperature, which for ice melting is 0°C.

Heat of Fusion

The heat of fusion is a term used to describe the amount of energy needed to change a unit mass of a solid into a liquid at its melting point without a change in temperature. It is an important factor when calculating the energy required to melt solids like ice.
For ice, the heat of fusion is 333 J/g. This means that it takes 333 joules of energy to melt one gram of ice at 0°C. Understanding this concept allows us to calculate the total energy required to melt a specific amount of ice. Multiply the heat of fusion by the mass of the ice to find out how much energy is needed. In our exercise, we took a single ice cube of 62 g and figured out how much energy was required to convert it entirely into liquid water.

Energy Calculations

Calculating the energy required for phase transformations like melting involves understanding both the heat of fusion and the total mass undergoing the transformation. In energy calculations, the formula \[ \text{Energy} = \text{mass} \times \text{heat of fusion} \] is commonly applied.
For our exercise, this formula helps determine the energy needed for a single ice cube first, and subsequently, for a whole tray. By knowing that each gram of ice requires 333 J to melt, multiplying this by the mass of each ice cube provides the energy needed to melt one cube. Then, by multiplying by the number of ice cubes in the tray, we can calculate the total energy required. This systematic approach ensures all energy calculations are precise and complete.