Ch.12 - Liquids, Solids & Intermolecular Forces

Tro - Chemistry: A Molecular Approach 6th Edition

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Tro 6th Edition

Ch.12 - Liquids, Solids & Intermolecular Forces

Problem 76

Chapter 12, Problem 76

How much ice (in grams) would have to melt to absorb 155 kJ of energy?

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Identify the heat of fusion for ice, which is the amount of energy required to melt 1 gram of ice. The heat of fusion for ice is approximately 334 J/g.

Convert the energy from kilojoules to joules, since the heat of fusion is given in joules per gram. Remember that 1 kJ = 1000 J.

Use the formula: \( q = m \times \Delta H_f \), where \( q \) is the energy absorbed, \( m \) is the mass of the ice, and \( \Delta H_f \) is the heat of fusion.

Rearrange the formula to solve for the mass \( m \): \( m = \frac{q}{\Delta H_f} \).

Substitute the values for \( q \) (in joules) and \( \Delta H_f \) (334 J/g) into the equation to find the mass of ice that needs to melt.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Heat of Fusion

The heat of fusion is the amount of energy required to change a substance from solid to liquid at its melting point without changing its temperature. For ice, this value is approximately 334 J/g. Understanding this concept is crucial for calculating how much ice must melt to absorb a specific amount of energy.

Energy Transfer

Energy transfer refers to the movement of energy from one system to another, often in the form of heat. In this context, when ice melts, it absorbs energy from its surroundings, which is essential for the phase change. Recognizing how energy is absorbed during melting helps in determining the mass of ice needed to absorb a given amount of energy.

Calculating Mass from Energy

To find the mass of ice that must melt to absorb a certain amount of energy, one can use the formula: mass = energy absorbed / heat of fusion. This calculation allows for the direct conversion of energy (in joules or kilojoules) into mass (in grams), facilitating the solution to the problem presented.

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Nitrogen has a normal boiling point of 77.3 K and a melting point (at 1 atm) of 63.1 K. Its critical temperature is 126.2 K and its critical pressure is 2.55×10⁴ torr. It has a triple point at 63.1 K and 94.0 torr. Sketch the phase diagram for nitrogen. Does nitrogen have a stable liquid state at 1 atm?

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Textbook Question

A 10.5-g ice cube at 0°C is placed into 245-g of water. Calculate the temperature change in the water upon the complete melting of the ice. Assume that all of the energy required to melt the ice comes from the water.

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Consider the phase diagram shown here. Identify the states present at points a through g.

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The phase diagram for sulfur is shown here. The rhombic and monoclinic states are two solid states with different structures. b. Which of the two solid states of sulfur is more dense?

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Textbook Question

Calculate the amount of heat required to completely sublime 75.0 g of solid dry ice (CO₂) at its sublimation temperature. The heat of sublimation for carbon dioxide is 32.3 kJ/mol.

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How much energy is released when 75.2 g of water freezes?