Q.3.39 - An Introduction to General, Organic, and Biological Chemistry

Question

Use the heat equation to calculate the energy for each of the following (see Table 3.11 ):

a. calories to heat 8.5g of water from ${15}^{\circ }\mathrm{C}\text{ to }{36}^{\circ }\mathrm{C}$

b. joules lost when 25g of water cools from ${86}^{\circ }\mathrm{C}\text{ to }{61}^{\circ }\mathrm{C}$

c. kilocalories to heat 150g of water from ${15}^{\circ }\mathrm{C}\text{ to }{77}^{\circ }\mathrm{C}$

d. kilojoules to heat  175 g of copper from ${28}^{\circ }\mathrm{C}\text{ to }{188}^{\circ }\mathrm{C}$

Step-by-Step Solution

Answer

a. $178.5 cal$

b. $-2615J$

c. $9.3kcal$

d. $6.063 kJ$

Step 1: introduction

joule, a unit of work or energy in the International System of Units (SI); it is equivalent to the work done by a power of one newton acting through one meter.

Step 2: explanation part (a)

given,

mass = $8.5g$

initial temperature = ${15}^{o}C$ final temperature = ${36}^{0}C$

Specific heat of water $C_p$= $1\mathrm{Cal}/g^{\circ }\mathrm{C}$

From the Specific heat formula,

$Q=m\times \left(t_f-t_i\right)\times C_p$

$$\begin{gathered} Q=8.5g\times (36-15{)}^{\circ }\mathrm{C}\times 1\mathrm{Cal}/g^{\circ }\mathrm{C} \\ \mathrm{Q}=178.5\mathrm{cal} \end{gathered}$$

Step 3: explanation part (b)

given,

mass = $25g$

initial temperature = ${86}^{o}C$ final temperature = ${61}^{0}C$

Specific heat of water $=4.184J/g^{\circ }\mathrm{C}$

from specific heat formula,

$\begin{array}{r}Q=m\times \left(t_f-t_i\right)\times C_p\\ Q=25g\times (61-86{)}^{\circ }\mathrm{C}\times 4.184\mathrm{J}/g^{\circ }\mathrm{C}\end{array}$

$Q=-2615J$

Step 4: explanation part (c)

given,

mass = $150g$

initial temperature = ${15}^{o}C$ final temperature = ${77}^{o}C$

Specific heat of water $C_p=1\mathrm{Cal}/g^{\circ }\mathrm{C}$

from the specific heat formula,

$Q=m\times \left(t_f-t_i\right)\times C_p$

$Q=150g\times (77-15{)}^{\circ }\mathrm{C}\times 1\mathrm{cal}/{\mathrm{g}}^{\circ }\mathrm{C}$

$Q=9.3kcal$

Step 5: explanation part (d)

given,

mass = $175g$

initial temperature = ${28}^{o}C$ final temperature = ${188}^{o}C$

Specific heat of copper $C_p=0.385\mathrm{J}/g^{\circ }\mathrm{C}$

From the specific heat formula,

$Q=m\times \left(t_f-t_i\right)\times C_p$

$Q=175g\times (118-28{)}^{\circ }\mathrm{C}\times 0.385\mathrm{J}/g^{\circ }\mathrm{C}$

$Q=6.06375\mathrm{kJ}$