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204 6 CHEMICAL EQUILIBRIUM
Hence ∆fH−○(Cl− , aq) = ∆rH−○ + ∆fH−○(AgCl, s)
= (−40.0... kJmol−1) + (−127.07 kJmol−1) = −167.1 kJmol−1
Finally, noting from Section 3C.2(b) on page 94 that S−○m(H+ , aq) = 0, the
standard reaction entropy is
∆rS−○ = S−○m(Ag, s) + S−○m(Cl− , aq) − S−○m(AgCl, s) − 1
2 S
−○
m(H2 , g)
Hence
S−○m(Cl− , aq) = ∆rS−○ + S−○m(AgCl, s) + 1
2 S
−○
m(H2 , g) − S−○m(Ag, s)
= (−62.2... J K−1mol−1) + (96.2 JK−1mol−1)
+ 1
2 × (130.684 JK−1mol−1) − (42.55 JK−1mol−1)
= 56.8 JK−1mol−1
Solutions to integrated activities
I6.2 (a) �e ionic strength is given by [5F.29–188], I = 1
2 (b+z
2
+ + b−z2−) /b−○ , where
z+ and z− are the charges on the ions. For the CuSO4 compartment,
z+ = 2, z− = −2, and b+ = b− = bCuSO4 :
I = 1
2 (b+z
2
+ + b−z2−) /b−○ = 1
2 [bCuSO4 × (+2)2 + bCuSO4 × (−2)2] /b−○
= 4(bCuSO4/b−○) = 4 ×
1.00 × 10−3 mol kg−1
1 mol kg−1
= 4.00 × 10−3
Because the charges are the same forZnSO4 it follows that I = 4(bZnSO4/b−○)
= 1.20 × 10−2 .
(b) According to the Debye–Hückel limiting law (Section 5F.4(b) on page
187), themean activity coe�cient is given by [5F.27–188], log γ± = −A∣z+z−∣I1/2,
where A = 0.509 for aqueous solutions at 25 ○C. For the CuSO4 solution
log γ±,CuSO4 = −(0.509) × ∣(2) × (−2)∣ × (4.00 × 10−3)1/2 = −0.128...
Hence γ±,CuSO4 = 10−0.128... = 0.743... = 0.743 . For the ZnSO4 solution
log γ±,ZnSO4 = −(0.509) × ∣(2) × (−2)∣ × (1.20 × 10−2)1/2 = −0.223...
Hence γ±,ZnSO4 = 10−0.223... = 0.598... = 0.598 .
(c) Noting that pure solids have aJ = 1 and writing the activities of ions in
solution as a = γ±(b/b−○), the reaction quotient for the reaction
Zn(s) +Cu2+(aq)→ Zn2+(aq) +Cu(s)
is given by
Q = aZn
2+
aCu2+
= γ±,ZnSO4(bZn2+/b−○)
γ±,CuSO4(bCu2+/b−○)
= γ±,ZnSO4
γ±,CuSO4
× bZn
2+
bCu2+
= 0.598...
0.743...
× 3.00 × 10
−3 mol kg−1
1.00 × 10−3 mol kg−1
= 2.41... = 2.41