A pure gold ring and a pure silver ring have a total mass of 14.9 g. The two rings are heated to 62.0 °C and dropped into 15.0 mL of water at 23.5 °C. When equilibrium is reached, the temperature of the water is 25.0 °C. What is the mass of each ring? (Assume a density of 0.998 g/mL for water.)

Name: Chemistry: A Molecular Approach
Author: Tro
ISBN: 9780134112831

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Identify the specific heat capacities of gold and silver, which are approximately 0.129 J/g°C and 0.235 J/g°C, respectively.

Use the formula for heat transfer: \( q = mc\Delta T \), where \( q \) is the heat absorbed or released, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

Calculate the heat gained by the water using its mass (15.0 mL \( \times \) 0.998 g/mL) and its temperature change (25.0 °C - 23.5 °C).

Set up the equation for heat lost by the rings: \( q_{gold} + q_{silver} = -q_{water} \), where the negative sign indicates that the rings lose heat while the water gains it.

Use the total mass of the rings (14.9 g) and solve the system of equations to find the individual masses of the gold and silver rings.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Heat Transfer and Thermal Equilibrium

Heat transfer occurs when two objects at different temperatures come into contact, leading to a flow of thermal energy from the hotter object to the cooler one until they reach thermal equilibrium. In this scenario, the gold and silver rings transfer heat to the water until all three reach the same final temperature, which is crucial for calculating the mass of each ring.

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. Each material has a unique specific heat capacity, which affects how much heat is absorbed or released during temperature changes. For this problem, knowing the specific heat capacities of gold and silver is essential to determine how much heat each ring contributes to the water.

Mass and Density Relationship

The relationship between mass, volume, and density is defined by the equation density = mass/volume. In this question, the density of water is provided, allowing for the conversion of the water's volume into mass. This mass is then used in conjunction with the heat transfer calculations to solve for the unknown masses of the gold and silver rings.