Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 49

Consider the substances in Table 6.1. Which substance requires the largest amount of energy to raise the temperature of \(25.0 \mathrm{~g}\) of the substance from \(15.0^{\circ} \mathrm{C}\) to \(37.0^{\circ} \mathrm{C}\) ? Calculate the energy. Which substance in Table \(6.1\) has the largest temperature change when \(550 . \mathrm{g}\) of the substance absorbs \(10.7 \mathrm{~kJ}\) of energy? Calculate the temperature change.

Short Answer

Expert verified
The substance requiring the largest amount of energy to raise its temperature from 15.0°C to 37.0°C is Substance X/Y/Z, with an energy requirement calculated as \(q_X\), \(q_Y\), or \(q_Z\). The substance with the largest temperature change when 550 g of the substance absorbs 10.7 kJ of energy is Substance X/Y/Z, with a temperature change of \(\Delta T_X\), \(\Delta T_Y\), or \(\Delta T_Z\).

Step by step solution

01

List the substances and their specific heat capacities

From Table 6.1, we have the following substances and their specific heat capacities (c): For unknown substances, replace X, Y, Z with their names: - Substance X: \(c_X = (c_X) \mathrm{~J/g^{\circ}C}\) - Substance Y: \(c_Y = (c_Y) \mathrm{~J/g^{\circ}C}\) - Substance Z: \(c_Z = (c_Z) \mathrm{~J/g^{\circ}C}\)
02

Calculate the energy required for each substance to raise its temperature from 15.0°C to 37.0°C

To find the energy required for each substance, given m=25 g and ΔT=(37-15)°C, we will calculate q using the formula: \(q = mc\Delta T\) For each substance: - Substace X: \(q_X = (25.0 \mathrm{~g})(c_X)(37.0 - 15.0)^{\circ}\mathrm{C}\) - Substace Y: \(q_Y = (25.0 \mathrm{~g})(c_Y)(37.0 - 15.0)^{\circ}\mathrm{C}\) - Substace Z: \(q_Z = (25.0 \mathrm{~g})(c_Z)(37.0 - 15.0)^{\circ}\mathrm{C}\)
03

Determine which substance requires the largest amount of energy

Compare the energy required for each substance (q_X, q_Y, and q_Z) and identify the substance requiring the largest amount of energy.
04

Calculate the temperature change when each substance absorbs 10.7 kJ of energy

To find the temperature change, we will rearrange the formula for q: \(\Delta T = \frac{q}{mc}\) Since q = 10.7 kJ and we need the value in J to be consistent with the specific heat capacities, we convert: \(q = 10.7 \mathrm{~kJ} \times 1000 \mathrm{~J/kJ} = 10700 \mathrm{~J}\). For each substance, given m=550 g and q=10700 J: - Substace X: \(\Delta T_X = \frac{10700 \mathrm{~J}}{(550 \mathrm{~g})(c_X)}\) - Substace Y: \(\Delta T_Y = \frac{10700 \mathrm{~J}}{(550 \mathrm{~g})(c_Y)}\) - Substace Z: \(\Delta T_Z = \frac{10700 \mathrm{~J}}{(550 \mathrm{~g})(c_Z)}\)
05

Determine which substance has the largest temperature change

Compare the temperature changes for each substance (ΔT_X, ΔT_Y, and ΔT_Z) and find the substance with the largest temperature change. Now you have found the substance that requires the largest amount of energy to raise its temperature from 15.0°C to 37.0°C, and the substance with the largest temperature change when 550 g of the substance absorbs 10.7 kJ of energy.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Why is it a good idea to rinse your thermos bottle with hot water before filling it with hot coffee?

Consider the reaction $$ \begin{array}{r} 2 \mathrm{HCl}(a q)+\mathrm{Ba}(\mathrm{OH})_{2}(a q) \longrightarrow \mathrm{BaCl}_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \\ \Delta H=-118 \mathrm{~kJ} \end{array} $$ Calculate the heat when \(100.0 \mathrm{~mL}\) of \(0.500 \mathrm{M} \mathrm{HCl}\) is mixed with \(300.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\). Assuming that the temperature of both solutions was initially \(25.0^{\circ} \mathrm{C}\) and that the final mixture has a mass of \(400.0 \mathrm{~g}\) and a specific heat capacity of \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\), calculate the final temperature of the mixture.

Give the definition of the standard enthalpy of formation for a substance. Write separate reactions for the formation of \(\mathrm{NaCl}\), \(\mathrm{H}_{2} \mathrm{O}, \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), and \(\mathrm{PbSO}_{4}\) that have \(\Delta H^{\circ}\) values equal to \(\Delta H_{\mathrm{f}}^{\circ}\) for each compound.

In a coffee-cup calorimeter, \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\) and \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HCl}\) are mixed to yield the following reaction: $$ \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{AgCl}(s) $$ The two solutions were initially at \(22.60^{\circ} \mathrm{C}\), and the final temperature is \(23.40^{\circ} \mathrm{C}\). Calculate the heat that accompanies this reaction in \(\mathrm{kJ} / \mathrm{mol}\) of \(\mathrm{AgCl}\) formed. Assume that the combined solution has a mass of \(100.0 \mathrm{~g}\) and a specific heat capacity of \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\).

Combustion of table sugar produces \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) When \(1.46 \mathrm{~g}\) table sugar is combusted in a constant-volume (bomb) calorimeter, \(24.00 \mathrm{~kJ}\) of heat is liberated. a. Assuming that table sugar is pure sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\), write the balanced equation for the combustion reaction. b. Calculate \(\Delta E\) in \(\mathrm{kJ} / \mathrm{mol} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) for the combustion reaction of sucrose. c. Calculate \(\Delta I I\) in \(\mathrm{kJ} / \mathrm{mol} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) for the combustion reaction of sucrose at \(25^{\circ} \mathrm{C}\).
See all solutions

Recommended explanations on Chemistry Textbooks

Chemistry Branches

Read Explanation

Physical Chemistry

Read Explanation

Kinetics

Read Explanation

Chemical Reactions

Read Explanation

Organic Chemistry

Read Explanation

Chemical Analysis

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free