a solution formed by mixing 50ml of 10.0 M NaX with 50ml of 2.0x10^3M CuNO3.Assume that Cu(l) forms complexions with X asn follows
Cu^+ + X^- = CuX K1=1x 10^2
CuX + X^- = CuX2^- K2=1 x10^4
CuX2^- + X^- =CuX3^2- K3= 1x10^3
with overall reaction
Cu^+ +3X^- = CuX3^2- K=1X 10^9
Calculate the following concetrations at equilibrium
a)CuX3^2- b)CuX2^- c)Cu^+
To calculate the concentrations at equilibrium, we need to consider the equilibrium expressions for each step and then solve the system of equations.
Let's define the following variables:
[CuX] = concentration of CuX
[CuX2^-] = concentration of CuX2^-
[CuX3^2-] = concentration of CuX3^2-
a) CuX3^2-
The equation for this step is Cu^+ + 3X^- = CuX3^2-
Using the equilibrium constant K = 1 x 10^9, we can write the equilibrium expression as:
[CuX3^2-] = [Cu^+][X^-]^3 / K
b) CuX2^-
The equation for this step is CuX + X^- = CuX2^-
Using the equilibrium constant K2 = 1 x 10^4, we can write the equilibrium expression as:
[CuX2^-] = [CuX][X^-] / K2
c) Cu^+
The equation for this step is Cu^+ + X^- = CuX
Using the equilibrium constant K1 = 1 x 10^2, we can write the equilibrium expression as:
[Cu^+] = [X^-][CuX] / K1
Now, let's calculate the concentrations using the given initial concentrations.
In the solution, we have:
Volume of NaX solution = 50 mL
Concentration of NaX solution = 10.0 M
Volume of CuNO3 solution = 50 mL
Concentration of CuNO3 solution = 2.0 x 10^3 M
We need to convert the volumes to liters:
Volume of NaX solution = 50 mL = 0.050 L
Volume of CuNO3 solution = 50 mL = 0.050 L
First, calculate the moles of each species involved:
moles of X^- = concentration of NaX solution x volume of NaX solution = 10.0 M x 0.050 L = 0.50 moles
moles of Cu^+ = concentration of NaX solution x volume of NaX solution = 10.0 M x 0.050 L = 0.50 moles
Next, calculate the moles of CuNO3:
moles of CuNO3 = concentration of CuNO3 solution x volume of CuNO3 solution = 2.0 x 10^3 M x 0.050 L = 100 moles
Now, let's set up the equilibrium expression for [CuX3^2-]:
[CuX3^2-] = [Cu^+][X^-]^3 / K
Substituting the values:
[CuX3^2-] = (0.50 moles)(0.50 moles)^3 / (1 x 10^9) = 0.125 x 10^-9 moles/L
Similarly, for [CuX2^-]:
[CuX2^-] = [CuX][X^-] / K2
Substituting the values:
[CuX2^-] = (0.50 moles)(0.50 moles) / (1 x 10^4) = 0.25 x 10^-4 moles/L
And for [Cu^+]:
[Cu^+] = [X^-][CuX] / K1
Substituting the values:
[Cu^+] = (0.50 moles)(0.50 moles) / (1 x 10^2) = 0.25 x 10^-2 moles/L
Therefore, the concentrations at equilibrium are:
a) [CuX3^2-] = 0.125 x 10^-9 moles/L
b) [CuX2^-] = 0.25 x 10^-4 moles/L
c) [Cu^+] = 0.25 x 10^-2 moles/L