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

330336 J is required to melt all 16 ice cubes.

Step 1: Determine Energy for One Gram of Ice

The energy required to melt 1 gram of ice is given as 333 J. This is our starting point for calculations.

Step 2: Calculate Energy for One Ice Cube

Each ice cube has a mass of 62.0 g. To find the energy required to melt one ice cube, we multiply the energy per gram by the mass of the cube: \( 62.0 \, \text{g} \times 333 \, \text{J/g} = 20646 \, \text{J} \).

Step 3: Calculate Energy for All Ice Cubes in the Tray

A tray contains 16 ice cubes, each requiring 20646 J to melt. To find the total energy for the entire tray, we multiply the energy for one cube by the number of cubes: \( 20646 \, \text{J/cube} \times 16 \, \text{cubes} = 330336 \, \text{J} \).

Key Concepts

Energy Calculation

To calculate the energy needed to melt ice, we start by understanding the energy required for just one gram of it. The given energy to melt one gram of ice at 0°C is 333 joules. With this in hand, knowing the mass of the ice helps us determine the total energy needed for larger quantities.
For instance, if we have an ice cube that weighs 62 grams, we multiply the energy needed for one gram (333 J) by the cube's mass (62 g):

• Energy for one ice cube = 62 g × 333 J/g = 20646 J

This shows that 20,646 joules are required to melt just one ice cube.
When dealing with multiple ice cubes, like those in a full tray consisting of 16 ice cubes, we multiply the energy for one cube by 16:

• Total energy for the tray = 16 cubes × 20,646 J = 330,336 J

Each calculation builds on the one before, making it essential to start from the energy per gram and work up to the total mass.

Phase Change from Solid to Liquid

Understanding phase change, especially from solid to liquid, involves recognizing how energy input leads to the transformation of matter. For ice turning into water, this transition occurs at 0°C. During this phase change:

• The ice absorbs energy without a change in temperature.
• The absorbed energy breaks the bonds holding the solid structure together.

Unlike heating a substance, where temperature rises steadily with energy input, the energy used here helps ice transition to the same temperature state, except now as liquid water.
Once all the bonds are broken, and the ice has completely turned to liquid, adding more heat will eventually increase the water's temperature. However, during the phase change itself, the temperature remains constant even when heat is continually applied.

Latent Heat

When discussing the energy required for a phase change, latent heat is a key concept. It refers to the heat necessary for a substance to change its state without altering its temperature. With ice melting at 0°C, we focus on the latent heat of fusion, which is the energy required to convert solid to liquid. The specific latent heat of fusion for ice is 333 J/g. This means 333 joules are needed to melt each gram of ice into water at the same temperature. What makes latent heat important is that it characterizes the energy needed for phase transitions, affecting the calculations and understanding of energy balance during these transformations.
Recognizing latent heat's role helps clarify why heating doesn’t always result in temperature change and why substantial energy is required for phase changes without apparent temperature shifts.