The standard potential for the following galvanic cell is 0.40 V: (Europium, Eu, is one of the lanthanide elements.) Use the data in Table 19.1 to calculate the standard reduction potential for Eu3+/Eu2+ half-cell.

Video transcript

Hello. And this prom. We're told the golden Excel containing magnesium and Siri um has a standard cell potential of 0.870 volts were asked to provide the standard reduction potential for the Syrian half cell. Let's begin by looking at the shorthand notation that we've been provided. So recall that what's provided on the left hand side. This is the anodes is separated by a double vertical line which represents our cell bridge. And then on the other side we have our cathode we call. Then that oxidation occurs at the anodes. So our oxidation half reaction will have magnesium metal being oxidized for magnesium mines. And the reduction half reaction which is taking place at the cathode. We will have Syrian four being reduced To form Siri um three. Our overall reaction. Then the number of electrons that are being lost has equal number of electrons being gained. So multiply through by two. Then combining everything. We have magnesium metal Acting with two moles of Syrian four or magnesium mines And two moles of Serum three. Our number of electrons that are lost is equal the number of electrons that are gained. So those cancel we're told that the standard cell potential for this Overall reaction is 0.870. We are trying to find the standard reduction potential for this Syrian half cell. We can find standard oxidation potential for this half. So it's equal magnitude but opposite and sign the standard reduction potential. We take our oxidation half reaction and write it in reverse. You then get our magnesium ions being reduced to form magnesium metal. This half reaction has a standard reduction potential Of -2.37V. And so our standard oxidation potential will be equal magnitude but opposite science would be equal to a positive 2.37V. Knowing this, we can now find the standard reduction potential. So our standard reduction potential, we'll take our standard cell potential and subtract off the standard oxidation potential 0.870V -2.37V. And this works out to negative 1.50V. Keep in mind that even though we multiply through this reaction by two, our standard reduction potential is an intensive property. So it's independent of the quantity of reacting to products. And multiplying by two does not impact the value for the standard reduction potential. So the standard reduction potential for the Syrian half cell is negative 1.50 volts. And this corresponds to answer B. Thanks for watching. Hope this helps