Calculate values of for the following sparingly soluble solutes.
Calculate value of Ksp for AgI (delta Gf(Ag^+)=77.11 kj mol^-1 , delta Gf(I^-) =-51.57 kJ mol^-1, delta Gf(AgI) =-66.19 kJ mol^-1).
AgI ==> Ag^+ + I^-
dGf rxn = (n*dGf products) - (n*dGf reacrtants)
Then dG = dGfrxn -RTlnKsp
dG = 0
R is 8.314.
Solve for Ksp.
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To calculate the value of Ksp for AgI (Silver Iodide), you need to use the standard Gibbs free energy change (ΔGf) for each species involved in the reaction.
The formula for calculating Ksp is as follows:
Ksp = [Ag+][I-]
Given the values of ΔGf for Ag+, I-, and AgI, you can use the equation:
ΔGf(AgI) = ΔGf(Ag+) + ΔGf(I-)
Rearranging the equation, we have:
ΔGf(Ag+) = ΔGf(AgI) - ΔGf(I-)
Plugging in the given values:
ΔGf(Ag+) = -66.19 kJ mol^-1 - (-51.57 kJ mol^-1)
ΔGf(Ag+) = -14.62 kJ mol^-1
Now, using the equation:
Ksp = [Ag+][I-]
You can plug in the value of ΔGf(Ag+) and solve for Ksp.
However, it's important to note that the values given for ΔGf are in kilojoules (kJ), but Ksp is usually calculated using concentrations (mol/L) rather than Gibbs energy. To convert the values, you need to use the equation:
ΔG = -RTlnK
where R is the gas constant (8.314 J/mol·K) and T is the temperature in Kelvin.
Convert the given values from kJ/mol to J/mol:
ΔGf(Ag+) = -14.62 kJ mol^-1 * 1000 J/kJ
ΔGf(Ag+) = -14,620 J/mol
Now, you need to know the temperature (T) to calculate Ksp accurately.
Assuming the temperature is 298 K (25°C), you can calculate Ksp using the equation:
Ksp = e^(-ΔG/RT)
Substituting the values:
Ksp = e^(-(-14,620 J/mol) / (8.314 J/mol·K * 298 K))
Now you can solve the equation using a scientific calculator or by using a computer program or online calculator.