Ch.5 - Thermochemistry

Problem 106d

Chapter 5, Problem 106d

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at 25.1°C A 121.0-g block of copper metal is heated to 100.4°C by putting it in a beaker of boiling water. The specific heat of Cu(s) is 0.385 J/g-K The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of 30.1°C (d) What would be the final temperature of the system if all the heat lost by the copper block were absorbed by the water in the calorimeter?

Verified step by step guidance

Identify the principle of conservation of energy, which states that the heat lost by the copper block will be equal to the heat gained by the water.

Use the formula for heat transfer: \( q = m \cdot c \cdot \Delta T \), 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 lost by the copper block using its mass, specific heat capacity, and the change in temperature from its initial temperature to the final temperature.

Calculate the heat gained by the water using its mass, specific heat capacity, and the change in temperature from its initial temperature to the final temperature.

Set the heat lost by the copper equal to the heat gained by the water and solve for the final temperature of the system.

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Key Concepts

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

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius (or Kelvin). It is a crucial property that varies between different materials, influencing how they absorb and release heat. In this problem, the specific heat of copper is given, which will be used to calculate the heat lost by the copper block as it cools down.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another due to a temperature difference. In this scenario, heat is transferred from the hot copper block to the cooler water in the calorimeter until thermal equilibrium is reached. Understanding this concept is essential for calculating the final temperature of the system based on the heat lost by the copper and gained by the water.

Thermal Equilibrium

Thermal equilibrium occurs when two objects in contact reach the same temperature, resulting in no net heat flow between them. In the context of this question, the final temperature of the system is the point at which the heat lost by the copper equals the heat gained by the water. This concept is fundamental for solving calorimetry problems, as it allows for the application of the principle of conservation of energy.

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Related Practice

Textbook Question

A house is designed to have passive solar energy features. Brickwork incorporated into the interior of the house acts as a heat absorber. Each brick weighs approximately 1.8 kg. The specific heat of the brick is 0.85 J/g•K. How many bricks must be incorporated into the interior of the house to provide the same total heat capacity as 1.7⨉10³ gal of water?

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Textbook Question

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at 25.1°C A 121.0-g block of copper metal is heated to 100.4°C by putting it in a beaker of boiling water. The specific heat of Cu(s) is 0.385 J/g-K The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of 30.1°C. (a) Determine the amount of heat, in J, lost by the copper block.

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Textbook Question

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at 25.1°C A 121.0-g block of copper metal is heated to 100.4°C by putting it in a beaker of boiling water. The specific heat of Cu(s) is 0.385 J/g-K The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of 30.1°C (b) Determine the amount of heat gained by the water. The specific heat of water is 4.184 J/1gK.

(b) Assuming that there is an uncertainty of 0.002 °C in each temperature reading and that the masses of samples are measured to 0.001 g, what is the estimated uncertainty in the value calculated for the heat of combustion per mole of caffeine?

The corrosion (rusting) of iron in oxygen-free water includes the formation of iron(II) hydroxide from iron by the following reaction: Fe(s) + 2 H2O(l) → Fe(OH)2(s) + H2(g). (b) Calculate the number of grams of Fe needed to release enough energy to increase the temperature of 250 mL of water from 22 to 30 °C.

Open Question

Burning acetylene in oxygen can produce three different carbon-containing products: soot (very fine particles of graphite), CO(g), and CO2(g). (a) Write three balanced equations for the reaction of acetylene gas with oxygen to produce these three products. In each case assume that H2O(l) is the only other product. Determine the standard enthalpies for the reactions in part (a).