Ch.5 - Thermochemistry

Problem 54a

Chapter 5, Problem 54a

Consider the data about gold metal in Exercise 5.26(b). (a) Based on the data, calculate the specific heat of Au(s).

Verified step by step guidance

Identify the data provided in Exercise 5.26(b) related to gold metal, such as mass, temperature change, and heat absorbed or released.

Recall the formula for specific heat capacity:

c = \frac{q}{m}

, where

q

is the heat absorbed or released,

m

is the mass of the substance, and

ΔT

is the change in temperature.

Substitute the values from the data into the formula:

c = \frac{q}{m}

. Ensure that the units are consistent, typically using joules for heat, grams for mass, and degrees Celsius for temperature change.

Perform the division to calculate the specific heat capacity of gold, ensuring that the calculation is done correctly according to the formula.

Interpret the result in the context of the problem, understanding that the specific heat capacity is a measure of how much heat energy is required to change the temperature of a given mass of a substance by one degree Celsius.

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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. It is a crucial property that varies between different materials and is essential for calculations involving heat transfer. Understanding specific heat allows for the determination of how much energy is needed to change the temperature of a substance, which is vital in thermodynamic processes.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another due to a temperature difference. This process can occur through conduction, convection, or radiation. In the context of calculating specific heat, it is important to understand how heat is absorbed or released by a substance, as this directly influences temperature changes and energy calculations.

Thermodynamic Equations

Thermodynamic equations, such as q = mcΔT, relate the heat absorbed or released (q) to the mass (m), specific heat capacity (c), and the change in temperature (ΔT) of a substance. These equations are fundamental in solving problems related to heat transfer and specific heat calculations. Mastery of these equations enables students to effectively analyze and predict the thermal behavior of materials.

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First Law of Thermodynamics

Related Practice

Textbook Question

(b) Calculate the energy needed for this temperature change.

Textbook Question

The specific heat of octane, C₈H₁₈(l), is 2.22 J•g/K. (a) How many J of heat are needed to raise the temperature of 80.0 g of octane from 10.0 to 25.0 °C?

Textbook Question

The specific heat of octane, C₈H₁₈(l), is 2.22 J•g/K. (b) Which will require more heat, increasing the temperature of 1 mol of C₈H₁₈(l), by a certain amount or increasing the temperature of 1 mol of H₂O(l) by the same amount?

Textbook Question

Consider the data about gold metal in Exercise 5.26(b). (b) Suppose that the same amount of heat is added to two 10.0-g blocks of metal, both initially at the same temperature. One block is gold metal, and one is iron metal. Which block will have the greater rise in temperature after the addition of the heat?

Textbook Question

Consider the data about gold metal in Exercise 5.26(b). (c) What is the molar heat capacity of Au(s)?

Textbook Question

When a 6.50-g sample of solid sodium hydroxide dissolves in 100.0 g of water in a coffee-cup calorimeter (Figure 5.18), the temperature rises from 21.6 to 37.8 °C (a) Calculate the quantity of heat (in kJ) released in the reaction.