Nernst equation and equilibrium potential

Question

Solutions A and B are separated by a membrane that is permeable to Ca2+ and impermeable to Cl−.

Solution A contains 10 mM CaCl2 , and solution B contains 1 mM CaCl2.

Assuming that 2.3 RT/F = 60 mV, Ca2+ will be at electrochemical equilibrium when:

(A) solution A is +60 mV

(B) solution A is +30 mV

(C) solution A is −60 mV

(D) solution A is −30 mV

(E) solution A is +120 mV

(F) solution A is −120 mV

(G) the Ca2+ concentrations of the two solutions are equal

I eliminated A,B and E because of the +ve sign immediately, and G because it doesn't take into account the electrical potential factor. I also understand the general idea (that Ca2+ ions will cross the membrane but Cl- won't so it will stop when solution A is negative enough for the electrical gradient to be > concentration gradient) but I don't know what to do next.

$ EMF (millivolts) = \pm 61 * log \frac{C_{1}}{C_{2}}$

Using Nernst equation (reproduced from the version in my book), I got that the equilibrium potential is about -60 mV (I did -61log(10/1)) But the book's answer is D which makes me think I might have a huge misunderstanding in the principle itself.

Answer 1

The Nernst equation should be:

$\frac{RT}{zF}\ln\left(\frac{\mathrm{Out}}{\mathrm{In}}\right) = 2.3 \frac{RT}{zF}\log_{10}\left(\frac{\mathrm{Out}}{\mathrm{In}}\right)$

You substituted for 2.3 RT/F (approximately 60 or 61 mV: use 60 because your instructor asked you to), but forgot about z. Calcium is divalent (and positive) so for calcium z=2. Substitute this and you can see how you get your answer.

(Also note the "out/in" which is how you get negative numbers when z is positive and out < in )