A battery relies on the oxidation of magnesium and the reduction of Cu2+. The initial concentrations of Mg2+ and Cu2+ are 1.0 * 10-4 M and 1.5 M, respectively, in 1.0-liter half-cells. a. What is the initial voltage of the battery?

Video transcript

hey everyone in this example we're told that the reduction of iron and the oxidation of zinc creates a theoretical battery. We need to calculate the initial voltage of the battery. If there are 1.3 molar of zinc two plus and 2.8 molar of iron two plus and a one liter half cell initially. So right now we're gonna take our two ions. And so for our zinc two plus catalon, we would form our product which would be solid sync by gaining two electrons. We also want to recognize that for our iron two plus cat ion, we would form a solid iron as a product by gaining two electrons. Now when we look up the cell potential reduction for the oxidation of solid zinc From our textbooks or online, we would see that we have a self potential value equal to negative 0.73V for the oxidation of zinc. When we look up the self potential value for the oxidation of solid iron, we would see that we have a self potential value equal to negative 0. volts in our textbooks or online. Now writing out our full reaction, we have zinc two plus reacting with solid zinc. Or sorry, that was iron two plus reacting with solid zinc to form solid iron and the zinc two plus cat ion. And so we should recognize that our iron went from a plus to charge to on the product side a net zero neutral charge, meaning we gained two electrons. And so because we gained electrons, we would say that this is therefore going to be a reduction. And so we would agree that because the iron went through a reduction, this voltage value occurs at our cathode, whereas in comparison, our zinc went from a net neutral charge on the reacting side to a net plus two charge on the product side meaning we lost electrons. And so this is therefore going to be an oxidation, meaning that we would recall that this voltage would occur at the node. And so now we can find our standard cell potential by taking our self potential of our cathode. And we recall that we should subtract this from the cell potential of our a note. And so what this would give us and we'll just actually do this below. So our cell potential, our standard cell potential will be equal to our self potential of our cathode. Which above we stated, occurs as negative 0.45V for our production of solid iron minus our self potential of our a node which above we stated, occurs at our oxidation of solid zinc, which has a value of negative 0.73 volts. And so what we're going to get here is a value equal to 0.28V. And so now we want to go ahead and calculate the voltage of our battery, which is going to give us a new value for our standard cell potential. Where we would calculate that by taking our standard cell potential And subtracting that from our Nerds equation constant, which we should recall is equal to a value of 0.0592V which is divided by our number of electrons transferred in our reduction and then multiplied by the log of Q. Where we should recall that Q represents our concentration of zinc two plus, divided by Our concentration of our Iron two plus. And so to calculate our voltage of our battery. So we're going to get that. This is equal to our standard cell potential, which above we calculated as 0.28 volts subtracted from our nursed equation constant, which has a value of 0.592 volts. And then when we look at our reduction, we would agree that we had a transfer of two electrons to form our solid iron on the product side. And so our value for end here is going to be too. So we would divide by two and then this is going to be multiplied by the log of our concentration of zinc two plus according to the prompt, which is a value of 1.3 molar. And then our concentration of iron two plus according to the prompt is given as 2.8 molar. So what we're going to get here when we plug this into our calculators is a value for the voltage of our battery equal to 0.29V. And so this here would be our final answer for the voltage of our battery. To complete this example as our final answer, I hope that everything I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.