Question

How much heat is required to melt \(37.4 \mathrm{~g}\) of ice at \(0{ }^{\circ} \mathrm{C} ?\)

Short answer

The heat required to melt 37.4 g of ice at 0 degrees Celsius is 12487.6 J.

Step-by-step solution

Identify the Specific Heat of Fusion for Ice

The specific heat of fusion for ice is a constant value that represents the amount of heat required to melt a certain mass of ice at its melting point. This value for ice is approximately 334 J/g. This information is typically found in a physics or chemistry textbook or reference material.

Calculate the Amount of Heat Required

Use the formula for heat transfer during a phase change without a temperature change: \( Q = m \cdot \Delta H_f \), where \( Q \) is the heat energy, \( m \) is the mass of the substance, and \( \Delta H_f \) is the specific heat of fusion. For ice, the mass \( m \) is 37.4 g and \( \Delta H_f \) is 334 J/g.

Perform the Calculation

Substitute the given values into the equation: \( Q = (37.4 \, \text{g}) \times (334 \, \text{J/g}) \). Multiply the mass of the ice by the specific heat of fusion to find the heat required.

Compute the Heat Required

Multiplying the two values gives \( Q = 12487.6 \, \text{J} \). So, the heat required to melt 37.4 g of ice at \(0^\circ\text{C}\) is 12487.6 joules.

Key concepts

Specific Heat of Fusion

The specific heat of fusion refers to the amount of energy needed to change a substance from the solid phase to the liquid phase at its melting point, without changing its temperature. It's a unique value for each substance; for ice, this value is approximately 334 joules per gram (J/g).

During the melting process, this energy breaks the bonds between the molecules in the solid so they can move past each other as a liquid. In your textbook exercise, we see this concept in action as we calculate the heat required to melt ice. The higher a substance's specific heat of fusion, the more energy it requires to melt. This concept is crucial for understanding how different substances undergo phase changes.

Phase Change

A phase change is a transition of matter from one state (solid, liquid, gas) to another. In our exercise, the phase change in question is melting: the transition from solid (ice) to liquid (water).

Phase changes are isothermal processes when they occur at a substance's specific melting or boiling point, meaning that the temperature stays constant during the transition. The energy supplied (the heat of fusion) does not increase temperature, but rather overcomes intermolecular forces to allow the phase change to occur.

Heat Transfer

Heat transfer in the context of thermodynamics refers to the movement of thermal energy from one body or substance to another. During a phase change, such as melting, heat is transferred to a substance without causing a temperature increase.

In other words, this energy is used to facilitate the change in state. When calculating the heat needed for the ice to melt, it's important to remember that all of this energy goes into changing the phase, not increasing the temperature.

Energy Calculation

Energy calculation involves quantifying the amount of energy exchanged or required during a physical or chemical process. In this textbook exercise, the energy calculation was straightforward, as it solely depended on the mass of ice and its specific heat of fusion.

The calculation \( Q = m \cdot \Delta H_f \) effectively tells us how much heat, \( Q \), is needed to melt a given mass, \( m \) , of ice. The result provided the exact energy needed for the phase change, with no temperature change involved.

Thermochemistry

Thermochemistry is the study of the heat energy associated with chemical reactions and physical transformations. It plays a crucial role in calculating the heat required for transitions like melting and boiling.

Understanding thermochemistry is essential for solving exercises like the one with ice, as it encompasses the principles of heat transfer, phase changes, and the specific heat of substances. Through thermochemistry, we gain insight into how much energy is involved in breaking and forming bonds during phase changes.