using hess’s law to determine enthalpy...

60 MHR ● Chemistry 12 Solutions Manual 978-0-07-106042-4

Using Hess’s Law to Determine Enthalpy Change

(Student textbook page 316)

41. Nitrogen dioxide, NO2(g), is an emission resulting from the burning of gasoline in an

automobile engine that contributes to the formation of smog and acid rain. It can be

converted to dinitrogen tetroxide as shown below:

2NO2(g) N2O4(g)

a. Use Hess’s law and the following equations to determine the enthalpy change for

this reaction.

(1) N2(g) + 2O2(g) 2NO2(g) ∆Ho = 66.4 kJ

(2) N2(g) + 2O2(g) N2O4(g) ∆Ho = 11.1 kJ

b. Write the thermochemical equation for the overall reaction.

What Is Required?

You need to determine the enthalpy change of a reaction by using two other reactions.

What Is Given?

You are given the overall equation. You are given two equations and their

corresponding enthalpy changes that can be manipulated to represent the individual

steps that occur to reach the overall equation.

Plan Your Strategy

a. Apply Hess’s law. The given equations can be manipulated so that their reactants

and products match the reactants and products in the overall equation.

To manipulate the equations, reverse (1).

When an equation is reversed, the sign of ∆Ho is reversed. If the stoichiometric

coefficients in a given equation are multiplied by an integer or a fraction, multiply

∆Ho for that equation by the same integer or fraction.

Act on Your Strategy

o

2 2 2o

2 2 2 4

1 (1) : 2NO (g) N (g) + 2O (g) 66.4 kJ

(2): N (g) + 2O (g) N O (g) 11.1 kJ

H

H

- ´ ® D = -

® D =

Plan Your Strategy

To determine the overall reaction, add the manipulated equations together, cancelling

species that are common to both sides.

Add the ∆Ho values together to find the enthalpy change for the overall reaction.

Unit 3 Part B ● MHR 61


2 2 2NO (g) N (g)® 2 + 2O (g) o

2

66.4 kJ

N (g)

HD = -

2 + 2O (g) o

2 4

o

2 2 4

N O (g) 11.1 kJ

2NO (g) N O (g) 55.3 kJ

H

H

® D =

® D = -

Plan Your Strategy Act on Your Strategy

b. Write the thermochemical

equation for the overall reaction. 2NO2(g) N2O4(g) + 55.3 kJ

Check Your Solution

Since the equations add to give the overall equation, the given individual equations

must have been manipulated correctly. Check that the correct sign has been carried

through with each ∆Ho term. The overall ∆H

o shows the same precision as the least

precise used in the calculation with one digit to the right of the decimal point.


42. Ethyne, C2H2(g), can be converted to benzene, C6H6(ℓ), over a palladium catalyst.

3C2H2(g) Pd¾¾®C6H6(ℓ)

Determine the enthalpy of reaction for this process from the equations below that

show the combustion of C2H2(g) and C6H6(ℓ) at standard conditions.

(1) C2H2(g) + 5

2O2 (g) 2CO2(g) + H2O(g) ∆H

o = –1301.1 kJ

(2) C6H6(ℓ) + 15

2 O2(g) 6CO2(g) + 3H2O(g) ∆H

o = –3267.6 kJ

What Is Required?


What Is Given?

You are given the overall equation. You are given two equations and their



Plan Your Strategy

Apply Hess’s law. The given equations can be manipulated so that their reactants and

products match the reactants and products in the overall equation.

Manipulate the equations by multiplying the coefficients in (1) by 3 and reversing

(2).





( )

o

2 2 2 2 2

o

2 2 6 6

153 (1) : 3C H (g) + O (g) 6CO (g) + 3H O(g) 3903.3 kJ

21 (2): 6CO (g) 3H O g C H ( ) 3267.6 kJ

H

H

´ ® D = -

- ´ + ® D =( ) ( )( )


Plan Your Strategy





2 2 2

15 3C H (g) + O (g)

226CO (g)® 2 + 3H O(g) o 3903.3 kJHD = -

2 6CO (g) ( )2 3H O g+ 6 6 2

15C H ( ) O (g)

2® +

15( ) O6 6 26 6 2

156 6 26 6 2( )( )6 6 26 6 26 6 2

o 3267.6 kJHD =

o

2 2 6 6 C H (g) C H ( ) –635.7 kJH® D =) )

Check Your Solution







43. Hydrazine, N2H4(ℓ), is a high-energy compound used as a rocket propellant. Use

Hess’s law to determine the enthalpy of reaction when this compound reacts as

follows:

N2H4(ℓ) + 2H2O2 (ℓ) N2(g) + 4H2O(ℓ)

Use the following information:

(1) H2(g) + 1

2O2(g) H2O(ℓ) ∆H

o = –285.8 kJ

(2) N2H4(ℓ) + O2(g) N2(g) + 2H2O(ℓ) ∆Ho = –622.0 kJ

(3) H2(g) + O2(g) H2O2(ℓ) ∆Ho = –188.0 kJ

What Is Required?

You need to determine the enthalpy change of a reaction by using three other

reactions.

What Is Given?

You are given the overall equation.

You are given three equations and their corresponding enthalpy changes that can be

manipulated to represent the individual steps that occur to reach the overall equation.

Plan Your Strategy



Manipulate the equations by multiplying the coefficients in (1) by 2. Then, reverse

(3) and multiply the coefficients in that equation by 2.





2 2 22 (1): 2H (g)+ O (g) 2H O( ) 571.6 kJH´ ® D ° = -( ) ( )

2 4 2 2 21 (2): N H ( ) + O (g) N ( ) + 2H O( ) 622.0 kJ g H´ ® D ° = -( ) + O ( ) N ( ) + 2H O( ) 622.02 4 2 2 22 4 2 2 2 HO( ) 2 22 22 2 ( ) + O (g) N ( ) + 2H O( )g N2 4 2 2 22 4 2 2 2 6 6( ) + 2H O( ) ( ) +2 22 22 2

2 2 2 22 (3) : 2H O ( ) 2H (g) + 2O (g) 376.0 kJ H- ´ ® D ° =2 2 22 2 2( ) 2H (( ) 2H (22 2 22 2 22 2 2


Plan Your Strategy





2 2H (g) 2 + O (g) 22H O( ) 571.6 kJH® D ° = -( ) ( )( )

2 4 2 N H ( ) + O (g)( ) + O (g2 4 22 4 2 2 2N ( ) + 2H O( ) 622.0 kJ g H® D ° = -( ) ( )( )( )

2 2 2 2H O ( ) 2H (g)®( ) 2H2 2 22 2 22 2 22 2 2 2 + 2O (g) 376.0 kJ HD ° =

2 4 2 2 2 2N H ( ) 2H O ( ) N (g) 4H O( ) 817.6 kJ H+ ® + D ° = -( ) 2H O ( ) N (g) 4H O( ) 2 4 2 2 2 22 4 2 2 2 2 2H O ( ) N (g) 4H O( ) 2H O ( ) N (g) 4H O( ) 2 4 2 2 2 22 4 2 2 2 22 4 2 2 2 2

Check Your Solution







44. Synthetic rubber can be manufactured from the hydrocarbon 1,3-butadiene, C4H6(g).

This compound reacts with hydrogen to produce butane(g), C4H10(g), as shown in the

equation below:

C4H6(g) + 2H2(g) C4H10(g)

Use Hess’s law and the equations that follow to determine the enthalpy change for this

reaction.

(1) C4H6(g) + 11

2O2(g) 4CO2(g) + 3H2O(g) ∆H

o = –2541.5 kJ

(2) C4H10(g) + 13

2O2(g) 4CO2(g) + 5H2O(g) ∆H

o = –2877.6 kJ

(3) H2(g) +1

2O2(g) H2O(g) ∆H

o = –241.8 kJ

What Is Required?

You need to determine the enthalpy change of a reaction by using three other reactions.

What Is Given?

You are given the overall equation. You are given three equations and their



Plan Your Strategy



Manipulate the equations by reversing (2). Then, multiply the coefficients in (3) by 2.





( ) o

4 6 2 2 2

111 1 : C H (g) + O (g) 4CO (g) 3H O(g) –2541.5 kJ

2H´ ® + D =

( ) o2 2 4 10 2

13

21 2 : 4CO (g) + 5H O(g) C H (g) O (g) 2877.6 kJH- ´ ® + D =

( ) o

2 2 22 3 : 2H (g) O (g) 2H O(g) –483.6 kJ H´ + ® D =

Plan Your Strategy






4 6 2

11 C H (g) + O

22(g) 4CO (g)® 2 3H O(g)+ o –2541.5 kJHD =

24CO (g) 2 + 5H O(g) 4 10 2

13

2 C H (g) O (g)® + o 2877.6 kJHD =

2 2 2H (g) O (g)+ 2 2H O(g)® o –483.6 kJ HD =

o

4 6 2 4 10 C H (g) 2H (g) C H (g) –147.5 kJH+ ® D =

Check Your Solution







45. Ethylene, C2H4(g), is commonly used as an agent to hasten the ripening of fruit, such

as bananas. It can also be used to prepare 1,2-dichloroethane, C2H4Cl2(ℓ), which is

used to make vinyl chloride. Use Hess’s law to determine the enthalpy of reaction for

the preparation of C2H4Cl2(ℓ).

C2H4(g) + Cl2(g) C2H4Cl2(ℓ)

Given:

(1) 4HCl(g) + O2(g) 2Cl2(g) + 2H2O(ℓ) ∆Ho = –202.4 kJ

(2) 2HCl(g) + C2H4(g) + 1

2O2(g) C2H4Cl2(ℓ) + H2O(ℓ) ∆H

o = –320.8 kJ

What Is Required?


What Is Given?


You are given two equations and their corresponding enthalpy changes that can be


Plan Your Strategy



Manipulate the equations by reversing (1). Then, divide the coefficients of (1) by 2.





( ) o

2 2 2

1 1(1) : Cl (g) H O 2HCl(g) O (g) 101.2 kJ

2 2H- ´ + ® + D =2 2 22 2 2)2 2 2))) 2HC)2 2 22 2 22 2 2))

o

2 4 2 2 4 2 2

1(2): 2HCl(g) C H (g) O ( ) C H Cl ( ) H O( ) –320.8 kJ

2g H+ + ® + D =o) H O( ) –o

HO( ) 2 ) H O( ) o) H O( ) ) H22

Plan Your Strategy






( )2 2 Cl (g) H O+ ) 2HCl(g)® 2

1 O (g)

2+ o 101.2 kJ HD =

2HCl(g) 2 4 2

1 C H (g) O (g)

2+ + 2 4 2 2C H Cl ( ) H O( ) ® + 2) H O( ) 22)) o –320.8 kJHD =

o

2 4 2 2 4 2 C H (g) Cl (g) C H Cl ( ) –219.6 kJH+ ® D =( ) ( )( )

Check Your Solution







46. Carbon monoxide, CO(g), can react with hydrogen, H2(g), to produce methane,

CH4(g), and water vapour.

CO(g) + 3H2(g) CH4(g) + H2O(g)

Given the following equations, use Hess’s law to determine the enthalpy of reaction.

(1) H2(g) + 1

2O2(g) H2O(g) ∆H

o = –241.8 kJ

(2) CO(g) + 1

2O2(g) CO2(g) ∆H

o = –283.0 kJ

(3) 2CO(g) + 2H2(g) CH4(g) + CO2(g) ∆Ho = –247.1 kJ

What Is Required?


reactions.

What Is Given?




Plan Your Strategy



Manipulate the equations by reversing (2).

When an equation is reversed, the sign of ∆Ho is reversed.


( ) o

2 2 2

1(1): H (g) O (g) H O g –241.8 kJ

2H+ ® D =

o

2 2

11 (2): CO (g) CO(g) O (g) 283.0 kJ

2H- ´ ® + D =

o

2 4 2(3): 2CO(g) 2H (g) CH (g) CO (g) –247.1 kJ H+ ® + D =

Plan Your Strategy






2 2

1 H (g) O (g)

2+ ( ) o

2H O g –241.8 kJH® D =

2 CO (g) CO(g)® 2

1 O (g)

2+ o 283.0 kJHD =

2 2 4 2CO(g) 2H (g) CH (g) CO (g)+ ® + o –247.1 kJ HD =

o

2 4 2CO(g) + 3H CH (g) + H O(g) = 205.9 kJH® D -

Check Your Solution







47. The following thermodynamic equations have been obtained from reference sources:

(1) H2(g) + 1

2O2(g) H2O(ℓ) + 285.8 kJ

(2) H2(g) + S(s) H2S(g) + 20.6 kJ

(3) S(s) + O2(g) SO2(g) + 296.8 kJ

Use Hess’s law to determine the enthalpy change for the reaction below:

2H2S(g) + 3O2(g) 2SO2(g) + 2H2O(ℓ)

What Is Required?


reactions.

What Is Given?




Plan Your Strategy



Manipulate the equations by first multiplying the coefficients of (1) by 2. Then,

reverse (2) and multiply the coefficients of that equation by 2. Finally, multiply the

coefficients of (3) by 2.



( ) o

2 2 22 (1): 2H (g) O (g) 2H O –571.6 kJH´ + ® D =) ) )

o

2 22 (2): 2H S(g) 2H (g) 2S(g) 41.2 kJH- ´ ® + D =

o

2 22 (3): 2S(g) 2O (g) 2SO (g) –593.6 kJ H´ + ® D =


Plan Your Strategy





2 2H (g) ( ) o

2 2 O (g) 2H O –571.6 kJH+ ® D =) ) )

2 2 2H S(g) 2H (g)® 2S(g) + o 41.2 kJHD =

2S(g) o

2 2 2O (g) 2SO (g) –593.6 kJ H+ ® D =

( ) o

2 2 2 2 2H S(g) 3O (g) 2SO (g) 2H O –1124.0 kJH+ ® + D =))) )

Check Your Solution







48. The reaction to convert SO2(g) to SO3(g) is a two-step process:

Step 1: SO2(g) + 299 kJ S(s) + O2(g) Step 2: S(s) + O2(g) + 1

2O2(g) SO3(g)

The enthalpy diagram below is a graphical representation of the process. Use this

diagram to determine the enthalpy change for step 2.

What Is Required?

You need to determine the enthalpy change for one step in a reaction sequence.

What Is Given?

You have a graphical representation of the two steps in the sequence and the overall

reaction.

Plan Your Strategy

Apply Hess’s law. The overall reaction is determined by adding the equations in steps

1 and 2 together, with species that are common to both sides being cancelled.


2(1): SO (g) S(s)® 2 + O (g) o

1 299 kJHD = +

(2): S(s) 2O (g)+ o

2 3 2

1O (g) SO (g) kJ

2H x+ ® D =

o

2 2 3 3

1 SO (g) O (g) SO (g) –96.0 kJ

2H+ ® D =

Plan Your Strategy Act on Your Strategy

The enthalpy change for the overall

reaction is the sum of the ∆Ho values

of each step. Set up an equation and

solve for x to determine the enthalpy

change for step 2.

1 2 3

( 299 kJ) ( kJ) ( 96 kJ)( kJ) ( 96 kJ) ( 299 kJ)

397

H H H

xx

x

° ° °D +D = D+ + = -

= - - += -

The enthalpy change for step 2 is –397 kJ.

Check Your Solution

The algebraic solution, ∆H2 = ∆H3 – ∆H1, corresponds to the mathematical depiction

of the reaction.


49. Ethene, C2H4(g), is used in the manufacture of many polymers. If ethene could be

formed from the elements carbon and hydrogen, the equation would be as follows:

2C(s) + 2H2(g) C2H4(g)

Use Hess’s law and the equations given below to determine the molar enthalpy of

formation for C2H4(g).

(1) C(s) + O2(g) CO2(g) ∆Ho = –393.5 kJ

(2) H2(g) + 1

2O2(g) H2O(ℓ) ∆H

o = –285.8 kJ

(3) C2H4(g) + 3O2(g) 2CO2(g) + 2H2O(ℓ) ∆Ho = –1411.2 kJ

What Is Required?


reactions.

What Is Given?




Plan Your Strategy



Manipulate the equations by first multiplying the coefficients of each of (1) and (2)

by 2. The, reverse (3).


Act on Your Strategy o

2 22 (1) : 2C(s) 2O (g) 2CO (g) 787.0 kJH´ + ® D = -

( ) o

2 2 22 (2): 2H (g) O (g) 2H O 571.6 kJH´ + ® D = - ))) )

( ) ( ) o

2 2 2 4 21 (3): 2CO (g) 2H O C H g 3O (g) 1411.2 kJ H- ´ + ® + D =2 2 22 2 2)) C H) C HC)2 2 22 2 22 2 2)


Plan Your Strategy





2 2C(s) 2O (g)+ 22CO (g)® o 787.0 kJHD = -

2 2 2H (g) O (g)+ ( )22H O® ) o 571.6 kJHD = -

( ) ( ) o

2 2 2 4 21 (3): 2CO (g) 2H O C H g 3O (g) 1411.2 kJ H- ´ + ® + D =2 2 22 2 2)) C H) C HC)2 2 22 2 22 2 2)

o

2 2 2 f 2C(s) 2H (g) C H (g) 52.6 kJ H+ ® D =

Check Your Solution







50. From the following equations, determine the molar enthalpy of formation for

HNO2(aq), as shown below in the overall equation:

1

2H2(g) +

1

2N2(g) + O2(g) HNO2(aq)

(1) NH4NO2(aq) N2(g) + 2H2O(ℓ) ∆Ho = –320.1 kJ

(2) NH3(aq) + HNO2(aq) NH4NO2(aq) ∆Ho = –37.7 kJ

(3) 2NH3(aq) N2(g) + 3H2(g) ∆Ho = +169.9 kJ

(4) H2(g) + 1

2O2(g) H2O(ℓ) ∆H

o = –285.8 kJ

What Is Required?

You need to determine the enthalpy change of a reaction by using four other reactions.

What Is Given?


You are given four equations and their corresponding enthalpy changes that can be


Plan Your Strategy



Manipulate the equations by first reversing each of (1) and (2). Then, multiply the

coefficients of (3) by 1

2and multiply the coefficients of (4) by 2.


Act on Your Strategy o

2 2 4 21 (1): N (g) 2H O( ) NH NO (aq) 320.1 kJH- ´ + ® D = +2 2 42 2 4) NH N) NH N) N2 2 42 2 42 2 4

o

4 2 3 21 (2): NH NO (aq) NH (aq) HNO (aq) 37.7 kJH- ´ ® + D = +

o

3 2 2

1 1 3(3): NH (aq) N (g) H (g) 84.95 kJ

2 2 2H´ ® + D = +

o

2 2 22 (4): 2H (g) O (g) 2H O( ) –571.6 kJH´ + ® D =( ) ( )( )


Plan Your Strategy





2 N (g) 2 2H O( ) + ( ) 4 2 NH NO (aq)® o 320.1 kJHD = +

4 2 NH NO (aq) 3NH (aq)® o

2 HNO (aq) 37.7 kJH+ D = +

3 NH (aq) 2

1N (g)

2® 2

3 H (g)

2+ o 84.95 kJHD = +

2 2H (g) 2 2O (g) 2H O( )+ ® ( ) o –571.6 kJHD =

o

2 2 2 2 f

1 1H (g) N (g) O (g) HNO (g) –128.8 kJ

2 2H+ + ® D =

Check Your Solution






using hess’s law to determine enthalpy...

Documents