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 75

Chapter 12, Problem 75

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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Identify the heat required to melt the ice using the formula: \( q = m \times \Delta H_f \), where \( m \) is the mass of the ice and \( \Delta H_f \) is the heat of fusion for ice.

Calculate the heat \( q \) needed to melt the 10.5-g ice cube using the heat of fusion for ice, which is 334 J/g.

Determine the heat lost by the water using the formula: \( q = m \times c \times \Delta T \), where \( m \) is the mass of the water, \( c \) is the specific heat capacity of water (4.18 J/g°C), and \( \Delta T \) is the change in temperature.

Set the heat lost by the water equal to the heat gained by the ice: \( m_{\text{ice}} \times \Delta H_f = m_{\text{water}} \times c \times \Delta T \).

Solve for \( \Delta T \), the change in temperature of the water, by rearranging the equation: \( \Delta T = \frac{m_{\text{ice}} \times \Delta H_f}{m_{\text{water}} \times c} \).

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Key Concepts

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

Heat Transfer

Heat transfer is the process by which thermal energy moves from one object to another due to a temperature difference. In this scenario, the warmer water transfers heat to the colder ice cube, causing the ice to melt. Understanding this concept is crucial for calculating the temperature change in the water as it loses energy.

Latent Heat of Fusion

The latent 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. This concept is essential for determining how much energy the water must provide to completely melt the 10.5-g ice cube.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For water, this value is about 4.18 J/g°C. This concept is important for calculating the resulting temperature change in the water after it has lost energy to melt the ice.

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Textbook Question

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

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

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Textbook Question

Carbon disulfide has a vapor pressure of 363 torr at 25 °C and a normal boiling point of 46.3 °C. Find ΔH_vap for carbon disulfide.

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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.

Textbook Question

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

Textbook Question

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