4. A Beer’s Law plot was prepared for the reaction A(aq) + B(aq)
AB(aq), plotting absorption over AB(aq) concentration. The linear equation for this plot was y = 78.3x.
A solution was prepared by mixing 10.0mL of 0.100M A with 5.00mL of 0.100M B and adding enough water to bring the total volume to 50.0 mL. The absorption of this solution was measured as 0.646.
Given this information, calculate the following:
a) The initial concentrations of each reactant.
b) The equilibrium concentration
of AB
c) The equilibrium concentrations of each reactant
d) The equilibrium constant with respect to concentration
To solve this problem, we can use the Beer's Law and stoichiometry to determine the concentrations of reactants and products.
a) The initial concentrations of each reactant:
We are given the initial volumes and molarities of A and B:
Volume of A solution (Va) = 10.0 mL
Molarity of A solution (Ma) = 0.100 M
Volume of B solution (Vb) = 5.00 mL
Molarity of B solution (Mb) = 0.100 M
To determine the initial concentrations, we need to convert the volumes to liters:
Va = 10.0 mL = 10.0 mL * (1 L / 1000 mL) = 0.0100 L
Vb = 5.00 mL = 5.00 mL * (1 L / 1000 mL) = 0.00500 L
The initial concentration (Ca0) of A can be calculated using the formula:
Ca0 = Ma * Va
Ca0 = 0.100 M * 0.0100 L = 0.00100 mol/L
Similarly, the initial concentration (Cb0) of B can be calculated:
Cb0 = Mb * Vb
Cb0 = 0.100 M * 0.00500 L = 0.000500 mol/L
Therefore, the initial concentrations of A and B are 0.00100 mol/L and 0.000500 mol/L, respectively.
b) The equilibrium concentration of AB:
The reaction A(aq) + B(aq) -> AB(aq) is a 1:1 stoichiometric reaction. So, the equilibrium concentration of AB will be the same as the concentrations of reactants A and B at equilibrium.
c) The equilibrium concentrations of each reactant:
Since the reaction is a 1:1 stoichiometric reaction, at equilibrium, the concentrations of reactants A and B will be equal to the equilibrium concentration of AB.
d) The equilibrium constant with respect to concentration:
To calculate the equilibrium constant (Kc), we need the equilibrium concentrations. However, since the reaction is in the form A(aq) + B(aq) -> AB(aq), the equilibrium constant can be calculated using the absorption measurements.
Given that the absorption of the solution is 0.646 and the linear equation for the Beer's Law plot is y = 78.3x, we can use the equation to find the concentration (x) of AB at equilibrium:
y = 78.3x
0.646 = 78.3x
x = 0.646 / 78.3
x = 0.00825 mol/L
Therefore, the equilibrium concentration of AB is 0.00825 mol/L.
Since the reaction is in the form A(aq) + B(aq) -> AB(aq), the equilibrium constant (Kc) is given by:
Kc = [AB] / ([A] * [B])
Kc = 0.00825 / (0.00100 * 0.000500)
Kc = 16.5 mol/L²
Hence, the equilibrium constant with respect to concentration (Kc) is 16.5 mol/L².