CALCULATING THE STANDARD ENTROPY OF REACTION Calculate the standard entropy of reaction at 25 °C for the Haber synthesis of ammonia: N2(g) + 3 H2(g) → 2 NH3(g)

Question

CALCULATING THE STANDARD ENTROPY OF REACTION

Calculate the standard entropy of reaction at 25 °C for the Haber synthesis of ammonia:

[latex]N_{2}(g) + 3 H_{2}(g) → 2 NH_{3}(g)[/latex]

STRATEGY
To calculate ΔS° for the reaction, subtract the standard molar entropies of all the reactants from the standard molar entropies of all the products. Look up the S° values in Table 16.1 or Appendix B, and remember to multiply the value for each substance by its coefficient in the balanced chemical equation.

TABLE 16.1 Standard Molar Entropies for Some Common Substances at 25 °C

Substance Formula S°[J/K · mol)]

Gases

Acetylene [latex]C_{2}H_{2}[/latex] 200.8

Ammonia [latex]NH_{3}[/latex] 192.3

Carbon dioxide [latex]CO_{2}[/latex] 213.6

Carbon monoxide CO 197.6

Ethylene [latex]C_{2}H_{4}[/latex] 219.5

Hydrogen [latex]H_{2}[/latex] 130.6

Methane [latex]CH_{4}[/latex] 186.2

Nitrogen [latex]N_{2}[/latex] 191.5

Nitrogen dioxide [latex]NO_{2}[/latex] 240.0

Dinitrogen tetroxide [latex]N_{2}O_{4}[/latex] 304.3

Oxygen [latex]O_{2}[/latex] 205.0

Liquids

Acetic acid [latex]CH_{3}CO_{2}H[/latex] 160

Ethanol [latex]CH_{3}CH_{2}OH[/latex] 161

Methanol [latex]CH_{3}OH[/latex] 127

Water [latex]H_{2}O[/latex] 69.9

Solids

Calcium carbonate [latex]CaCO_{3}[/latex] 91.7

Calcium oxide CaO 38.1

Diamond C 2.4

Graphite C 5.7

Iron Fe 27.3

Iron(III) oxide [latex]Fe_{2}O_{3}[/latex] 87.4

Accepted Answer

ΔS° = 2 [latex]S°(NH_{3}) - [S°(N_{2}) + 3 S°(H_{2})][/latex]

= [latex](2 mol)\left(192.3 \frac{J}{K · mol}\right) - \left[(1 mol)\left(191.5 \frac{J}{K · mol}\right) + (3 mol)\left(130.6 \frac{J}{K · mol}\right)\right][/latex]

= -198.7 J/K

BALLPARK CHECK
As predicted in Worked Example 16.1c, ΔS° should be negative because the reaction decreases the number of gaseous molecules from 4 mol to 2 mol.

Question 16.3: CALCULATING THE STANDARD ENTROPY OF REACTION Calculate the s...

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