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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Heat Capacity

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