1 (214)

Prévia do material em texto

206 6 CHEMICAL EQUILIBRIUM
�e cell reaction, which has ν = 1, is
AgCl(s) + 1
2H2(g) +OH
−(aq)→ Ag(s) +Cl−(aq)
Noting that aJ = 1 for pure solids, and that in this cell aH2 = 1 because the
hydrogen is at standard pressure, the Nernst equation for the cell is
Ecell = E−○cell −
RT
νF
lnQ = E−○cell −
RT
F
ln( aCl
−
aOH−
)
Writing the activities as a = γ±(b/b−○), the Nernst equation becomes
Ecell = E−○cell −
RT
F
ln( γ±(bCl−/b−○)
γ±(bOH−/b−○)
) = E−○cell −
RT
F
ln( bCl
−
bOH−
)
�e standard cell potential is split into contributions from the two electrodes
using [6D.3–224], E−○cell = E−○(R) − E−○(L)
Ecell = E−○(AgCl/Ag, Cl−) − E−○(H2O/H2 , OH−) −
RT
F
ln( bCl
−
bOH−
)
Hence
E−○(H2O/H2 , OH−) = E−○(AgCl/Ag, Cl−) − Ecell −
RT
F
ln( bCl
−
bOH−
)
�is equation is used with bCl− = 0.01125 mol kg−1, bOH− = 0.0100 mol kg−1,
and the values of Ecell and E−○(AgCl/Ag, Cl−) to calculate E−○(H2O/H2 , OH−)
at each temperature.�e relation derived earlier
pKw = −(F/RT ln 10)E−○(H2O/H2 , OH−)
is then used to calculate pKw.�e results are given in the following table.
θ/○C T/K Ecell/V E−○(AgCl/Ag, Cl−)/V E−○(H2O/H2 , OH−)/V pKw
20.0 293.15 1.047 74 0.225 02 −0.825 70 14.20
25.0 298.15 1.048 64 0.222 30 −0.829 37 14.02
30.0 303.15 1.049 42 0.219 59 −0.832 91 13.85
To �nd ∆rS−○ for the autoprotolysis, the relationship between E−○cell and temper-
ature [6C.6–222], dE−○cell/dT = ∆rS−○/νF is used. If ∆rS−○ is constant over the
temperature range this equation implies that a plot of E−○cell against T should
be a straight line of slope ∆rS−○/νF. In this case E−○cell for the autoprotolysis
reaction is equal to E−○(H2O/H2 , OH−) as explained earlier.�e plot is shown
in Fig. 6.4.
�e data fall on a good straight line, the equation of which is
E−○(H2O/H2 , OH−)/V = −7.229 × 10−4 × (T/K) − 0.6137