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.)

Verified step by step guidance

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.

Key Concepts

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

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.

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Textbook Question

A gaseous fuel mixture contains 25.3% methane (CH₄), 38.2% ethane (C₂H₆), and the rest propane (C₃H₈) by volume. When the fuel mixture contained in a 1.55 L tank, stored at 755 mmHg and 298 K, undergoes complete combustion, how much heat is emitted? (Assume that the water produced by the combustion is in the gaseous state.)

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Textbook Question

A gaseous fuel mixture stored at 745 mmHg and 298 K contains only methane (CH₄) and propane (C₃H₈). When 11.7 L of this fuel mixture is burned, it produces 769 kJ of heat. What is the mole fraction of methane in the mixture? (Assume that the water produced by the combustion is in the gaseous state.)

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Open Question

A copper cube with an edge measuring 1.55 cm and an aluminum cube with an edge measuring 1.62 cm are both heated to 55.0 °C and submerged in 100.0 mL of water at 22.2 °C. What is the final temperature of the water when equilibrium is reached? (Assume a density of 0.998 g/mL for water.)