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 unitless quantity), T is the temperature fin units of K), z is the charge of the ion, mu is the ionic strength (in units of mol/L), and alpha is the ion size parameter (in units of pm). The temperature-dependence of the dielectric constant is given by the equation epsilon = 79.755 e^(-4.6 Times 10^-5) (T - 293.25) where the temperature is in units of Kelvin. What is the value of the activity coefficient of Pb^2+ at 40.00 degree C when the ionic strength is 0.038 M?

Explanation / Answer

dielectric constant of water using the above formula is

dielectric constant = 79.755*e^((-4.6*10^-3)*(273+40-293.15)))

=72.79

let the activity coefficient be x.so,

ln(x)/ln(10) = (-1.825*10^6)*(313*72.79)^-1.5 * (2)^2*(0.038)^0.5/(1+(84*0.038^0.5/(2*(72.79*313)^0.5))

=0.405

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