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Multiple Choice
Calculate the activity coefficient of H+ using the extended Debye-Huckel equation for a solution comprised of H+ and I –. Given that H+ has a size of 9.00 x 10-10 m and the molar concentration of the solution is 0.075. log γ = − 0.51 z 2√µ / 1 + (α √µ / 305)
A
0.917
B
0.982
C
0.837
D
1.49
Verified step by step guidance
1
Identify the parameters needed for the extended Debye-Huckel equation: the charge of the ion (z), the ionic strength of the solution (µ), and the effective diameter of the ion (α). For H+, z = +1 and α = 9.00 x 10^-10 m.
Calculate the ionic strength (µ) of the solution. Since the solution is comprised of H+ and I-, and both have a charge of ±1, the ionic strength can be calculated using the formula: µ = 0.5 * Σ(c_i * z_i^2), where c_i is the concentration of each ion and z_i is the charge of each ion.
Substitute the values into the extended Debye-Huckel equation: log γ = −0.51 * z^2 * √µ / (1 + (α * √µ / 305)). Here, z = 1, and α is given as 9.00 x 10^-10 m.
Simplify the expression by calculating the term (α * √µ / 305) and then the entire denominator (1 + (α * √µ / 305)).
Calculate the value of log γ using the simplified expression and then find the activity coefficient (γ) by taking the antilog (10^log γ).