The temperature-dependent form of the extended Debye-Huckel equation is where ga

Question

The temperature-dependent form of the extended Debye-Huckel equation is where gamma is the activity coefficient, epsilon is the dielectric constant of water (a unit less quantity), T is the temperature (in units of K), z is the charge of the ion, mu is the ionic strength (in units of mol/L), and a is the ion size parameter (in units of pm). The temperature-dependence of the dielectric constant is given by the equation where the temperature is in units of Kelvin. What is the value of the activity coefficient of Pb^2+ at 50.00 degree C when the ionic strength is 0.071 M?

Explanation / Answer

Calculating dielectric constant:

E = 79.755 e (-4.6x 10-3) * (323.15 - 293.15)

E = 69.4744

The we calculate the activity coefficient:

log (gamma) = (-1.825 x 106) * (69.4744 * 323.15)-3/2 * 4 * sqrt (0.071M) / (1 + [(450pm*sqrt(0.071))/(2*(sqrt(69.4744*323.15)])

gamma = 10^((-1.825 x 106) * (69.4744 * 323.15)-3/2 * 4 * sqrt (0.071M) / (1 + [(450pm*sqrt(0.071))/(2*(sqrt(69.4744*323.15)])

gamma = 0.38637

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