Introductory Chemistry (5th Edition)

Published by Pearson
ISBN 10: 032191029X
ISBN 13: 978-0-32191-029-5

Chapter 3 - Matter and Energy - Exercises - Cumulative Problems - Page 91: 108

Answer

The final temperature is; $T_{f} = 20.75^{\circ}C$

Work Step by Step

Using the equation $q=mcΔT$ and $-q_{system}, = q_{surroundings}$ we can solve for the final temperature of the system (i.e the ethanol and the water) provided the given information. First we must convert the volume of ethanol into its mass using its density; $25 mL\times \frac{0.789g}{ml}= 19.725 g$ Also the heat capacity of ethanol is 2.46 which is found online. $-q_{system}, = q_{surroundings}$ $-(19.725g)(2.46 \frac{J}{g\times^{\circ}C})(T_{f}-7^{\circ}C) = (35g)((4.184 \frac{J}{g\times^{\circ}C})(T_{f}-25.3^{\circ}C)$ $-48.5235T_{f}+339.6645 = 146.44T_{f}-3704.932$ $194.9635T_{f} = 4044.5965$ $T_{f} = 20.75^{\circ}C$
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