In some applications nickel–cadmium batteries have been replaced by nickel–zinc batteries. The overall cell reaction for this relatively new battery is: 2 H2O1l2 + 2 NiO1OH21s2 + Zn1s2 ¡ 2 Ni1OH221s2 + Zn1OH221s2 (d) Would you expect the specific energy density of a nickel–zinc battery to be higher or lower than that of a nickel–cadmium battery?

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welcome back everyone. Nickel iron batteries have less impact on the environment because nickel iron batteries don't contain cadmium, which is considered a hazardous material, were given the overall reaction for the nickel iron cell as two moles of nickel oxide hydroxide solid reacting with two moles of liquid water, one mole of iron solid to produce two moles of nickel to hydroxide solid and one mole of iron to hydroxide solid, which would be higher the specific energy density of a nickel iron battery or the specific energy density of a nickel cadmium battery. Our first step is to recall what specific energy density is defined as and it's going to be the measure of how much energy a battery has in proportion to its weight. Next, we should recognize that were given to the redox reactions involved, based on our overall reaction, given in the prompt where one of these redox reactions is based on our cadmium or nickel cadmium battery. Were also given the cell potentials for each of these reactions. Now we need to recognize which of these reactions is occurring as an oxidation or reduction because we see that we have a more positive self potential value as 10.49 volts here for this first reaction, we're going to recognize this reaction as occurring as a reduction, meaning it's going to occur at the cathode electrode of our voltaic cell. So we have this as our cathode. So now we know which of these reactions is occurring at our cathode. We need to figure out between these two which occurs at the anodes. And because looking at our overall reaction, we see that we have iron on our reactant side. That means iron is going to be releasing electrons to form our iron to hydroxide. And so these electrons are actually really on our product side. So this reaction should be flipped, meaning that this is occurring as an oxidation because electrons are on the product side and because this is occurring as an oxidation, we should recognize that this tells us that this reaction occurs that are an ode. And so we would also assume the same for this reaction here because we would assume that in place of iron solid, we would have cadmium solid for the cadmium nickel cadmium battery. And that would mean the cadmium solid would also be releasing two electrons as a product. So this will also occur as an oxidation, which tells us that this is also occurring at the anodes. So next we need to figure out what the standard cell potential which were college represented as not sell is for this overall reaction, we should recall that we can calculate this by taking the standard cell potential of our cathode subtracted from the standard cell potential of our node. And we're going to find the standard cell potential for each are nickel iron battery and our nickel cadmium battery. So beginning with the standard cell potential. And sorry, this is not standard cell potential of our nickel cadmium battery. We're going to take the cell potential of our cathode, which we determined is positive 0.49 volts subtracted from the cell potential of our node which we are using for the nickel cadmium battery as negative 0.81 volts. So because we have minus negative, we're really gonna have 0.49 volts subtract or added rather to 0.81 volts. And this sum is going to give us our standard cell potential for the nickel cadmium battery equal to 1.37 volts. Now finding the standard cell potential for our nickel iron battery, We begin with the self potential of our cathode, which again, we determined as .49V subtracted from the standard cell potential of our Nickel Iron Battery being negative .88V. Which again is going to give us .49 now added 2.88, which will give us a standard cell potential for the nickel iron battery equal to 1.37 volts. And just to make a correction, this should be 1.30 volts as the standard cell potential for our nickel cadmium battery. If we do 0.49 plus 0.81 volts. So now that we have our standard cell potential for these two batteries, we now want to figure out the proportion of the nickel iron battery and the energy that it operates at in comparison to our nickel cadmium battery. So we're going to take that standard cell potential that we just calculated. So we're gonna take this 1.37V. And we're going to divide this from our standard cell potential of our nickel cadmium battery, which we just calculated to be 1.30V. And this proportion is going to give us a decimal of 1.05, which we will multiply by 100%. And this is going to give us 105%, which tells us that therefore our nickel iron battery has an energy capacity. That is 105 of the nickel cadmium battery. And now we want to look at the proportion of our nickel iron battery to the in terms of its weight to the nickel cadmium battery. So we want to recall from our periodic table that iron Has a molar mass of 55.845 g per mole. And making note of our molar mass of cadmium on the periodic table, we see that it has a molar mass of 112.411 g per mole. And so we're going to take 55.845g and divide that by 112.4 11 g. And we're gonna say per mole. And this proportion is going to give us, let's also actually include the multiplication by 100. So times 100%. This is going to give us a result of 49.68%. So what this result is going to tell us is that we have a smaller proportion in the energy density as well as a larger mass associated with our nickel cadmium battery, whereas our nickel iron battery has a larger energy density and a lower mass percent in comparison to our nickel cadmium battery. And so our nickel iron battery is going to have a longer battery runtime in relation to its smaller battery size. So we're going to confirm that therefore the nickel iron battery has a higher specific energy density. So this is going to be our final answer to complete this example as the battery that will have a higher specific energy density and thus a longer battery runtime in relation to its size. So I hope everything I reviewed was helpful if you have any questions, leave them down below and I will see everyone in the next practice video.

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Key Concepts

Specific Energy Density

Electrochemical Reactions

Battery Chemistry