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ENTHALPY AND HESS’S LAW

Since chemical reactions involve the breaking and making of bonds, energy changes generally accompany reactions. To initiate a reaction, an activation energy, Ea, must first be supplied for the reactants to reach an activated complex, whether or not the reaction is spontaneous. When a reaction occurs, a change in enthalpy, that is, heat content, also known as the heat of reaction, AHrx, occurs. This is the amount of heat exchanged—either liberated or absorbed—with the surroundings under constant external pressure. Recall Figure 1.1 on exothermic and endothermic reactions for clarification. It may be measured experimentally (directly) or calculated theoretically (indirectly), and expressed in either kilojoules (kJ) or kilocalories (kcal).

The enthalpy change, known as the standard heat of formation, AHf, is defined as the heat of reaction for a product derived only from its elements, the superscript o meaning measured under standard conditions (usually at STP). See Table 2.4 for thermodynamic values of common substances.

Table 2.4. Thermodynamic constants for the changes of formation in enthalpy, entropy, and Gibbs free energy at STP

Aluminum

AHf (kJ/mol)

AGf (kJ/mol)

So (J/mol K)

Al (s)

0

0

28.3

AICI3 (s)

-704.2

-628.8

110.7

AI2O3 (s)

-1,675.7

-1,582.3

50.9

Al(OH)3 (s)

-1,277.0

Barium

AHf (kJ/mol)

AGof (kJ/mol)

So (J/mol K)

Ba (s)

0

0

67.0

BaCl2 (s)

-858.6

-810.4

123.7

ВаСОз (s)

-1,219.0

-1,139.0

112.0

BaO (s)

-553.5

-525.1

70.4

Ba(OH)2 (s)

-946.0

BaSO4 (s)

-1,473.2

-1,362.2

132.2

Beryllium

AHof (kJ/mol)

AGof (kJ/mol)

So (J/mol K)

Be (s)

0

0

9.5

BeO (s)

-599.0

-569.0

14.0

Be(OH)2 (s)

-902.5

-815.0

51.9

Bromine

AHof (kJ/mol)

AGof (kJ/mol)

So (J/mol K)

Br (g)

111.9

82.4

175.0

Br2 (l)

0

0

152.2

Br2 (g)

30.9

3.1

245.5

Br2 (aq)

-3.0

4.0

130.0

Br- (aq)

-121.0

-175.0

82.0

BrF3 (g)

-255.6

-229.4

292.5

HBr (g)

-36.3

-53.5

198.7

Cadmium

AH°/ (kJ/mol)

AG0/ (kJ/mol)

So (J/mol K)

Cd (s)

0

0

52.0

CdO (s)

-258.0

-228.0

55.0

Cd(OH)2 (s)

-561.0

-474.0

96.0

CdS (s)

-162.0

-156.0

65.0

CdSO4 (s)

-935.0

-823.0

123.0

Calcium

AH0/ (kJ/mol)

AGo/ (kJ/mol)

So (J/mol K)

Ca (s)

0

0

41.4

Ca (g)

178.2

144.3

158.9

Ca2+ (g)

1,925.9

CaC2 (s)

-59.8

-64.9

70.0

CaCO3 (s, calcite)

-1,206.9

-1,128.8

92.9

CaCl2 (s)

-795.8

-748.1

104.6

CaF2 (s)

-1,219.6

-1,167.3

68.9

CaH2 (s)

-186.2

-147.2

42.0

CaO (s)

-635.1

-604.0

39.8

CaS (s)

-482.4

-477.4

56.5

Ca(OH)2 (s)

-986.1

-898.5

83.4

Ca(OH)2 (aq)

-1,002.8

-868.1

-74.5

Ca3(PO4)2 (s)

-4,126.0

-3,890.0

241.0

CaSO4 (s)

-1,434.1

-1,321.8

106.7

CaSiO3 (s)

-1,630.0

-1,550.0

84.0

Carbon

AHo/ (kJ/mol)

AGo/ (kJ/mol)

So (J/mol K)

C (s, graphite)

0

0

5.7

C (s, diamond)

1.9

2.9

2.4

  • 5.7
  • 2.4
  • (Continued)

Carbon

AH/ (kJ/mol)

AG0/ (kJ/mol)

A° (J/mol K)

C (g)

716.7

671.3

158.1

CCL, (l)

-135.4

-65.2

216.4

CCI4 (g)

-102.9

-60.6

309.9

CHCI3 (l)

-134.5

-73.7

201.7

CHCI3 (g)

-103.1

-70.3

295.7

CH4 (g)

-74.8

-50.7

186.3

CH3OH (g)

-200.7

-162.0

239.8

CH3OH (l)

-238.7

-166.3

126.8

H2CO (g)

-116.0

-110.0

219.0

HCOOH (g)

-363.0

-351.0

249.0

HCN (g)

135.1

125.0

202.0

C2H2 (g)

226.7

209.2

200.9

C2H4 (g)

52.3

68.2

219.6

CH3CHO (g, acetaldehyde)

-166.0

-129.0

250.0

C2H4O (g, ethylene oxide)

-53.0

-13.0

242.0

CH3CH2OH (l)

-277.7

-174.8

160.7

CH3CH2OH (g)

-235.1

-168.5

282.7

CH3COOH (l)

-484.0

-389.0

160.0

C2H6 (g)

-84.7

-32.8

229.6

C3H6 (g)

20.9

62.7

266.9

C3H8 (g)

-103.8

-23.5

269.9

CH2=CHCN (l)

152.0

190.0

274.0

C6H6 (l)

49.0

124.5

172.8

C6H12O6 (s)

-1,275.0

-911.0

212.0

CO (g)

-110.5

-137.2

197.7

Carbon

AHf (kJ/mol)

AGof (kJ/mol)

So (J/mol K)

CO2 (g)

-393.5

-394.4

213.7

CS2 (g)

117.4

67.1

237.8

COCl2 (g)

-218.8

-204.6

283.5

Chlorine

AH°/ (kJ/mol)

AGof (kJ/mol)

So (J/mol K)

Cl (g)

121.7

105.7

165.2

CI2 (g)

0

0

223.1

CI2 (aq)

-23.0

7.0

121.0

Cl- (aq)

-167.0

-131.0

57.0

Cl- (g)

-233.1

HCl (g)

-92.3

-95.3

186.9

HCl (aq)

-167.2

-131.2

56.5

Chromium

AHof (kJ/mol)

AGof (kJ/mol)

So (J/mol K)

Cr (s)

0

0

23.8

Cr2Os (s)

-1,139.7

-1,058.1

81.2

CrOs (s)

-579.0

-502.0

72.0

CrCls (s)

-556.5

-486.1

123.0

Copper

AHof (kJ/mol)

AGof (kJ/mol)

So (J/mol K)

Cu (s)

0

0

33.2

CuCl2 (s)

-220.1

-175.7

108.1

CuCOs (s)

-595.0

-518.0

88.0

Cu2O (s)

-170.0

-148.0

93.0

CuO (s)

-157.3

-129.7

42.6

Cu(OH)2 (s)

-450.0

-372.0

108.0

CuS (s)

-49.0

-49.0

67.0

Fluorine

AH°/ (kJ/mol)

AGof (kJ/mol)

So (J/mol K)

F2 (g)

0

0

202.8

F (g)

79.0

61.9

158.8

F- (g)

-255.4

F- (aq)

-332.6

-278.8

-13.8

HF (g)

-271.1

-273.2

173.8

HF (aq)

-332.6

-278.8

88.7

Hydrogen

AH°/ (kJ/mol)

AGof (kJ/mol)

So (J/mol K)

H2 (g)

0

0

130.7

H (g)

218.0

203.2

114.7

H+ (g)

1,536.2

H+ (aq)

0

OH- (aq)

-230.0

-157.0

-11.0

H2O (l)

-285.8

-237.1

69.9

H2O (g)

-241.8

-228.6

188.8

H2O2 (l)

-187.8

-120.4

109.6

Iodine

AHof (kJ/mol)

AGof (kJ/mol)

So (J/mol K)

I2 (s)

0

0

116.1

I2 (g)

62.4

19.3

260.7

I2 (aq)

23.0

16.0

137

I (g)

106.8

70.3

180.8

I- (g)

-197.0

I- (aq)

-55.0

-52.0

106.0

ICl (g)

17.8

-5.5

247.6

(Continued)

Iron

AH/ (kJ/mol)

AG0/ (kJ/mol)

So (J/mol K)

Fe (s)

0

0

27.8

FesC (s)

21.0

15.0

108.0

FeCl2 (s)

-341.8

-302.3

118.0

FeCls (s)

-399.5

-333.9

142.3

Feo.950 (s) (wustite)

-264.0

-240.0

59.0

FeO (s)

-272.0

Fe304 (s, magnetite)

-1,118.4

-1,015.4

146.4

Fe203 (s, hematite)

-824.2

-742.2

87.4

FeS (s)

-95.0

-97.0

67.0

FeS2 (s, pyrite)

-178.2

-166.9

52.9

FeS04 (s)

-929.0

-825.0

121.0

Fe(CO)5 (l)

-774.0

-705.3

338.1

Lead

AH0/ (kJ/mol)

AG0/ (kJ/mol)

So (J/mol K)

Pb (s)

0

0

64.8

PbCl2 (s)

-359.4

-314.1

136.0

Pb0 (s, yellow)

-217.3

-187.9

68.7

Pb02 (s)

-277.0

-217.0

69.0

PbS (s)

-100.4

-98.7

91.2

PbS04 (s)

-920.0

-813.0

149.0

Magnesium

AHo/ (kJ/mol)

AG0/ (kJ/mol)

So (J/mol K)

Mg (s)

0

0

32.7

MgCl2 (s)

-641.3

-591.8

89.6

MgC03 (s)

-1,095.8

-1,012.1

65.7

Mg0 (s)

-601.7

-569.4

26.9

  • 65.7
  • 26.9
  • (Continued)

Magnesium

AH0/ (kJ/mol)

AG0/ (kJ/mol)

S0 (J/mol K)

Mg(OH)2 (s)

-924.5

-833.5

63.2

MgS (s)

-346.0

-341.8

50.3

Manganese

AH0/ (kJ/mol)

AG0/ (kJ/mol)

So (J/mol K)

Mn (s)

0

0

32.0

MnO (s)

-385.0

-363.0

60.0

МП3О4 (s)

-1,387.0

-1,280.0

149.0

M2O3 (s)

-971.0

-893.0

110.0

MnO2 (s)

-521.0

-466.0

53.0

MnO4- (aq)

-543.0

-449.0

190.0

Mercury

AHo/ (kJ/mol)

AG0/ (kJ/mol)

So (J/mol K)

Hg (l)

0

0

75.9

HgCl2 (s)

-224.3

-178.6

146.0

Hg2Cl2(s)

-265.4

-210.7

191.7

HgO (s, red)

-90.8

-58.5

70.3

HgS (s, red)

-58.2

-50.6

82.4

Nickel

AHo/ (kJ/mol)

AG0/ (kJ/mol)

So (J/mol K)

Ni (s)

0

0

29.9

NiCl2 (s)

-305.3

-259.0

97.7

NiO (s)

-239.7

-211.7

38.0

Ni(OH)2 (s)

-538.0

-453.0

79.0

NiS (s)

-93.0

-90.0

53.0

Nitrogen

AH/ (kJ/mol)

AG0/ (kJ/mol)

So (J/mol K)

N2 (g)

0

0

191.6

N (g)

472.7

455.6

153.3

NH3 (g)

-46.1

-16.5

192.5

NH3 (aq)

-80.0

-27.0

111.0

NH4+ (aq)

-132.0

-79.0

113.0

NO (g)

90.3

86.6

210.8

NOCl (g)

51.7

66.1

261.8

NO2 (g)

33.9

51.3

240.1

N2O (g)

82.1

104.2

219.9

N2O4 (g)

9.2

97.9

304.3

N2O4 (l)

-19.5

97.0

209.0

N2O5 (s)

-42.0

134.0

178.0

N2H4 (l)

50.6

149.3

121.2

N2H3CH3 (l)

54.0

180.0

166.0

HNO3 (aq)

-207.4

-111.3

146.4

HNO3 (l)

-174.1

-80.7

155.6

HNO3 (g)

-135.1

-74.7

266.4

NH4ClO4 (s)

-295.0

-89.0

186.0

NH4Cl (s)

-314.4

-202.9

94.6

NH4Cl (aq)

-299.7

-210.5

169.9

NH4NO3 (s)

-365.6

-183.9

151.1

NH4NO3 (aq)

-339.9

-190.6

259.8

Oxygen

AH0/ (kJ/mol)

AGo/ (kJ/mol)

So (J/mol K)

O2 (g)

0

0

205.1

O (g)

249.2

231.7

161.1

O3 (g)

142.7

163.2

238.9

Phosphorus

AH°/ (kJ/mol)

AGof (kJ/mol)

So (J/mol K)

P (s, white)

0

0

164.4

P (s, red)

-70.4

-48.4

91.2

P (s, black)

-39.0

-33.0

23.0

P (g)

314.6

278.3

163.2

P4 (s, white)

0

0

41.1

P4 (s, red)

-17.6

-12.1

22.8

P4 (g)

59.0

24.0

280.0

PF5 (g)

-1,578.0

-1,509.0

296.0

PH3 (g)

5.4

13.4

210.2

PCI3 (g)

-287.0

-267.8

311.8

H3PO4 (l)

-1,279.0

-1,119.1

110.5

H3PO4 (aq)

-1,288.0

-1,143.0

158.0

P4O10 (s)

-2,984.0

-2,697.7

228.9

Potassium

AHf (kJ/mol)

AGof (kJ/mol)

So (J/mol K)

K (s)

0

0

64.2

KCl (s)

-436.7

-409.1

82.6

KClO3 (s)

-397.7

-296.3

143.1

KClO4 (s)

-433.0

-304.0

151.0

KI (s)

-327.9

-324.9

106.3

K2O (s)

-361.0

-322.0

98.0

K2O2 (s)

-496.0

-430.0

113.0

KO2 (s)

-283.0

-238.0

117.0

KOH (s)

-424.8

-379.1

78.9

KOH (aq)

-482.4

-440.5

91.6

(Continued)

Silicon

AH°/ (kJ/mol)

AGo/ (kJ/mol)

So (J/mol K)

Si (s)

0

0

18.3

SiBr4 (l)

-457.3

-443.9

277.8

SiC (s)

-65.3

-62.8

16.6

SiCl4 (g)

-657.0

-617.0

330.7

SiH4 (g)

34.3

56.9

204.6

SiF4 (g)

-1,614.9

-1,572.7

282.5

SiO2 (s, quartz)

-910.9

-856.6

41.8

Silver

AH0/ (kJ/mol)

AGo/ (kJ/mol)

So (J/mol K)

Ag (s)

0

0

42.6

Ag+ (aq)

105.0

77.0

73.0

AgBr (s)

-100.0

-97.0

107.0

AgCN (s)

146.0

164.0

84.0

AgCl (s)

-127.1

-109.8

96.2

Ag2CrO4 (s)

-712.0

-622.0

217.0

AgI (s)

-62.0

-66.0

115.0

Ag2O (s)

-31.1

-11.2

121.3

AgNO3 (s)

-124.4

-33.4

140.9

Ag2S (s)

-32.0

-40.0

146.0

Sodium

AHof (kJ/mol)

AGo/ (kJ/mol)

So (J/mol K)

Na (s)

0

0

51.2

Na (g)

107.3

76.8

153.7

Na+ (g)

609.4

Na+ (aq)

-240.0

-262.0

59.0

NaBr (s)

-361.0

-349.0

86.8

(Continued)

Sodium

AH0/ (kJ/mol)

AG0/ (kJ/mol)

So (J/mol K)

Na2CO3 (s)

-1,130.7

-1,044.4

135.0

NaHCOs (s)

-948.0

-852.0

102.0

NaCl (s)

-411.2

-384.1

72.1

NaCl (g)

-176.7

-196.7

229.8

NaCl (aq)

-407.3

-393.1

115.5

NaH (s)

-56.0

-33.0

40.0

Nal (s)

-288.0

-282.0

91.0

NaNO2 (s)

-359.0

NaNO3 (s)

-467.0

-366.0

116.0

Na2O (s)

-416.0

-377.0

73.0

Na2O2 (s)

-515.0

-451.0

95.0

NaOH (s)

-425.6

-379.5

64.5

NaOH (aq)

-470.1

-419.2

48.1

Sulfur

AH0/ (kJ/mol)

AGo/ (kJ/mol)

So (J/mol K)

S (s, rhombic)

0

0

31.8

S (s, monoclinic)

0.3

0.1

33.0

S (g)

278.8

238.3

167.8

S2- (aq)

33.0

86.0

-15.0

S8 (g)

102.0

50.0

431.0

S2Cl2 (g)

-18.4

-31.8

331.5

SF6 (g)

-1,209.0

-1,105.3

291.8

H2S (g)

-20.6

-33.6

205.8

SO2 (g)

-296.8

-300.2

248.2

SO3 (g)

-395.7

-371.1

256.8

SOCl2 (g)

-212.5

-198.3

309.8

SO42- (aq)

-909.0

-745.0

20.0

H2SO4 (l)

-814.0

-690.0

156.9

H2SO4 (aq)

-909.3

-744.5

20.1

Tin

AHf (kJ/mol)

AG0/ (kJ/mol)

So (J/mol K)

Sn (s, white)

0

0

51.6

Sn (s, gray)

-2.1

0.1

44.1

SnCL, (l)

-511.3

-440.1

258.6

SnCl4 (g)

-471.5

-432.2

365.8

SnO (s)

-285.0

-257.0

56.0

SnO2 (s)

-580.7

-519.6

52.3

Sn(OH)2 (s)

-561.0

-492.0

155.0

Titanium

AH0/ (kJ/mol)

AG0/ (kJ/mol)

So (J/mol K)

Ti (s)

0

0

30.6

TiCl4 (l)

-804.2

-737.2

252.3

TiCl4 (g)

-763.2

-726.7

354.9

TiO2 (s)

-939.7

-884.5

49.9

Uranium

AHo/ (kJ/mol)

AG0/ (kJ/mol)

So (J/mol K)

U (s)

0

0

50.0

UF6 (s)

-2,137.0

-2,008.0

228.0

UF6 (g)

-2,113.0

-2,029.0

380.0

UO2 (s)

-1,084.0

-1,029.0

78.0

U3O8 (s)

-3,575.0

-3,393.0

282.0

UO3 (s)

-1,230.0

-1,150.0

99.0

Xenon

AH°f (kJ/mol)

AG°f (kJ/mol)

So (J/mol K)

Xe (g)

0

0

170.0

XeF2 (g)

-108.0

-48.0

254.0

XeF4 (s)

-251.0

-121.0

146.0

XeF6 (g)

-294.0

XeO3 (s)

402.0

Zinc

AH°f (kJ/mol)

AG0f (kJ/mol)

So (J/mol K)

Zn (s)

0

0

41.6

ZnCl2 (s)

-415.1

-369.4

111.5

ZnO (s)

-348.3

-318.3

43.6

Zn(OH)2 (s)

-642.0

ZnS (s, wurtzite)

-193.0

ZnS (s, zinc blende)

-206.0

-201.3

57.7

ZnSO4 (s)

-983.0

-874.0

120.0

Regardless of the reaction, Hess’s law states that the enthalpy change of a chemical reaction is the same regardless of the chemical path taken from reactants to products. If the reaction of interest is the sum of several other reactions, the individual heats of reaction must be added algebraically. In other words,

Note that this same principle also applies to the calculation of the Gibbs free energy change for chemical reactions.

Example 2.21

The standard heats of formation, bHf, for NO2 and N2O4 are as follows: EHf [NO2] = 33.9 kJ/mol and EHf [N2O4] = -19.5 kJ/mol. Predict by calculation the heat of reaction, AHrx, for the following reaction at standard conditions.

Solution Use Hess’s law.

Note that the negative sign means that the reaction is exothermic.

Example 2.22

Given the following reactions and data for ДЯ°:

Compute AHrx° for the following reaction:

Solution

First, recognize that, if the first given reaction (I) is reversed and added to the second reaction (II), the desired reaction is obtained, because the 2NO2 terms will be on opposite sides of the reaction and will therefore cancel. To do this, the sign of AHo(I) must be changed from positive to negative, so the value becomes -87.30 kJ. Then, the two ДЯ° values must be added together. Thus:

Another way to solve this problem is to use Hess’s law and set the solution up as follows:

The problem with this approach is that, although AHf [O2] = 0 and the value for KHf [N2O4] is given in Example 2.22, the value for KHf [NO] is unknown.

 
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