Answered: A sample of gold weighing 227 grams is…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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A sample of gold weighing 227 grams is cooled then placed in a calorimeter containing 31 grams of water. The temperature of the water decreases from 20ᵒC to 19ᵒC. The specific heat of gold and water are 0.13 J/gᵒC and 4.18 J/gᵒC, respectively. What was the initial temperature (in degrees Celsius) of the gold sample? Express your answer using two decimal places.

Expert Solution

Step 1

Write the expression for heat of reaction as follows:
$Q = m C_{p} (T_{f} - T_{i}) . . . . . . (1)$

Step 2

Given,

mass of gold, $m_{g o l d} = 227 g$

heat capacity of gold, $C_{p} = 0.13 J / g \cdot ° C$

Initial temperature be $T_{i}$

final temperature, $T_{f} = 19 ° C$

Substitute the corresponding values in equation(1) and calculate heat of gold.

$Q_{g o l d} = m_{g o l d} C_{p} (T_{f} - T_{i}) Q_{g o l d} = 227 g \times 0.13 \frac{J}{g ° C} \times (19 ° C - T_{i}) Q_{g o l d} = 29.51 \times (19 ° C - T_{i}) \frac{J}{° C}$

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