Calculate ΔG at 25°C for the precipitation of lead(II) chloride from mixing 100. mL of 0.025 M lead(II) nitrate solution with 100. mL of 0.15 M sodium chloride solution. The ΔG° for the reaction at 25°C = −27.36 kJ/mol. (Hint: write out reaction equation – also, consider total solution volume)
To calculate ΔG at 25°C for the precipitation of lead(II) chloride, we can use the equation:
ΔG = ΔG° + RTln(Q)
Where:
ΔG is the change in Gibbs free energy
ΔG° is the standard Gibbs free energy change
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
Q is the reaction quotient
First, let's write out the balanced chemical equation for the precipitation reaction:
Pb(NO3)2(aq) + 2NaCl(aq) → PbCl2(s) + 2NaNO3(aq)
Next, let's calculate the concentration of the reactants in the mixture solution. Since we have 100. mL of 0.025 M lead(II) nitrate solution and 100. mL of 0.15 M sodium chloride solution, we need to find the total volume of the solution and use it to calculate the concentrations.
Total volume of the solution = 100. mL + 100. mL = 200. mL = 0.2 L
Concentration of lead(II) nitrate solution (C1) = 0.025 M
Concentration of sodium chloride solution (C2) = 0.15 M
Now, we can calculate the reaction quotient (Q) for the precipitation reaction using the concentrations of the reactants:
Q = [PbCl2] / ([Pb(NO3)2] * [NaCl]^2)
Since the lead(II) nitrate and sodium chloride are in a 1:2 ratio, and assuming complete dissociation in solution, we have:
[Pb(NO3)2] = (0.025 M) * (0.2 L) = 0.005 mol
[NaCl] = (0.15 M) * (0.2 L) = 0.03 mol
[PbCl2] = unknown
Plugging these values into the equation for Q, we get:
Q = [PbCl2] / (0.005 mol * (0.03 mol)^2)
Now, let's substitute the known variables into the equation for ΔG:
R = 8.314 J/(mol·K)
T = 25°C = 25 + 273 = 298 K (Kelvin)
ΔG = ΔG° + RTln(Q)
Substituting the values, we get:
ΔG = -27.36 kJ/mol + (8.314 J/(mol·K) * 298 K) * ln(Q)
Finally, we need to convert kJ to J:
ΔG = -27.36 kJ/mol * 1000 J / 1 kJ + (8.314 J/(mol·K) * 298 K) * ln(Q)
Thus, we have outlined the method to calculate ΔG at 25°C for the precipitation of lead(II) chloride. The specific value of ΔG will depend on the calculated Q for the reaction.