Find the Concentration of Cu2+ in Unknown Solution

[jesuslovesu]

Homework Statement

What is the concentration of the unknown Cu2+ solution?
The reaction is Zn(s) + Cu2+(aq) -> Zn2+(aq) + Cu(s).
The concentration of Zn2+ is 0.05 M

Homework Equations

The Attempt at a Solution

I'm coming up with about 2 different answers, and I'm not sure which is correct.
Using a graph of (Emf vs log Cu2+) I obtained the line y = -1.0967 - 0.02x and I'm not sure how to figure out the unknown copper concentration.

Method 1 (I'm leaning towards this method):
-1.08 V is the voltage obtained from the unknown.
-1.08 V = -1.0967 - 0.02x
x = -.835
10^x = 10^-.835

[Cu2+] = .146 M

Method 2:
I'm assuming E0 is the y intercept and -0.0592/2logQ is the slope, not positive if that is correct.
E = E0 - 0.0592/2logQ
Q = [Zn2+]/[Cu+2]
-1.08 = -1.0967 - 0.0592/2 log Q
[Cu+2] = .183 M

Which is the correct method to use for finding the copper concentration?

 

[Borek]

For both metals you have E = E0 + 0.0296 log [Me+2]

Just compare and put correct E0 values in, you will get one equation with one unknown.

 

[Blueshift5]

I would recommend using Method 2 to find the concentration of Cu2+ in the unknown solution. This method uses the Nernst equation, which takes into account the standard electrode potential and the activity coefficients of the ions. It is a more accurate and reliable method compared to Method 1, which uses a graph and assumes a linear relationship between emf and log [Cu2+]. Additionally, Method 2 uses the correct formula for calculating the reaction quotient, [Zn2+]/[Cu2+], which is crucial in determining the concentration of Cu2+.