The cyanide ion selective electrode responds according to the equation: E=constant –0.05916log[CN-] The electrode potential was –0.230 V when it was immersed in a 1.00x...

Question

The cyanide ion selective electrode responds according to the equation:

                                         E=constant –0.05916log[CN^-]

The electrode potential was –0.230 V when it was immersed in a 1.00x10^-3M solution of NaCN and -0.300V when placed in a solution of unknown CN^- concentration. What is the CN^- concentration of the unknown?

Answer 1

You are given the response equation, so this is a two-point problem: use the standard to find the unknown constant, then run the equation backwards on the unknown.

E = constant - 0.05916 log[CN-]

Step 1 - the calibration point

NaCN is a soluble salt that dissociates completely, so a 1.00 x 10^-3 M NaCN solution is 1.00 x 10^-3 M in CN-.

-0.230 = constant - 0.05916 log(1.00 x 10^-3)
-0.230 = constant - 0.05916(-3)
-0.230 = constant + 0.1775

constant = -0.4075 V

Step 2 - solve for the unknown

-0.300 = -0.4075 - 0.05916 log[CN-]

0.05916 log[CN-] = -0.4075 + 0.300 = -0.1075

log[CN-] = -1.817

[CN-] = 10^-1.817 = 1.5 x 10^-2 M (about 0.0153 M)

The faster way, once you trust it

The constant cancels if you subtract the two measurements:

E2 - E1 = -0.05916 ( log[CN-]2 - log[CN-]1 )

-0.300 - (-0.230) = -0.070 V, so the log changed by 0.070/0.05916 = +1.18 decades, and 1.00 x 10^-3 x 10^1.18 = 1.5 x 10^-2 M. Same answer, no constant needed.

Check the sign before you trust the number

Cyanide is an anion, and the response equation carries a minus sign, so a more concentrated solution gives a MORE negative potential. Your unknown read -0.300 V, more negative than the -0.230 V standard, so the unknown must be more concentrated than 10^-3 M - and 0.0153 M is. If you had gotten an answer below 10^-3 M, you would know a sign flipped somewhere.

That sign convention is the whole difference between a cation electrode and an anion electrode, and it is the most common place these problems go wrong. A pH electrode has +0.05916 in front of log[H+] (which is why pH and potential move together in the familiar way); a cyanide or fluoride electrode has -0.05916.