The sodium–sulfur battery has molybdenum electrodes with anode and cathode compartments separated by b-alumina, a ceramic through which sodium ions can pass. Because the battery operates at temperatures above 300 °C, all the reactants and products are present in a molten solution. The cell voltage is about 2.0 V. (b) How many kilograms of sodium are consumed when a 25 kW sodium–sulfur battery produces current for 32 min?

Video transcript

Hello Everyone in this video. We're given the cell reaction Right over here, we're being asked to calculate the mass of nickel produced in kilograms. If a 12.3 kilowatts, sodium per nickel chloride battery producing a current in a span of 45 minutes. So let's first recognize the overall reaction that we have here. So the overall reaction is where our N I C L two The solution. And then we're gonna go ahead and add two moles of RNA solution. This is an equilibrium with our products of N I so nickel, which is a solution here and two moles of R N A C L. Again, that is our solution and breaking apart into the half reactions. We have R N I C L two which yields two or R N I two plus canyon are metal candy in here and two moles of cl minus. We also then have our nickel two plus wrecked ng with two electrons to give us our neutral one mole of nickel. So we can see here that two electrons are being transferred. All right. So, some units to keep in mind is that for every one watt that we have? This is one columns times one volt per second. So one What per one volt is equal to one column per second. Alright, starting off with the 12.3 kW that were given in this problem. We're gonna go ahead and convert this into watts first. So for every one kilowatt We have 10 to the third watts. So this yield 12,300 watts. I'm gonna go and scroll down for more space here. So The 1, 2300 watts. We have for every 2.58V. Again, this value is given, this is then equal to 4767. watts per volt. Which is also then equal to 4767. columns per second. So we know that the molder mass Of Nickel according to our pr table is 58.6394 units being g per mole. I'm gonna go ahead and scroll down for more space here. So then for my mass Of Nickel. So we're gonna go ahead. Start our dimensional analysis here first. Starting off with the 45 minutes that we're being told. We have Ready to go ahead and convert this into seconds. So for every one minute that we have, we have 60 seconds and then we're gonna go ahead and use what we saw for bright and green on top. So for every one second that we have, We have 4,767. lumps. And then we know for every 96485 columns, we have one mole of electron continuing our dimension analysis, we know that from half reactions that every one mole of r N I two plus we have two moles of electrons. And then finally we know that for every one mole of nickel. Two plus we get one mole of our neutral nickel. Again, our the meta analysis continues. And this is finally just using the molar mass. So we're going from moles of our neutral nickel here into grams. So that's 58.6394 g of nickel. All right. Just to make sure we can go ahead and go through the whole dimension analysis equation here and seeing if all the units to cancel properly, which most likely does mean that our calculations also correct. So our minutes here will cancel. Second will cancel will cancel moles, electrons will cancel moles of N I two plus will cancel and moles of N I are neutral nickel will also cancel. So once I put everything into my calculator, we see that we get the mass of nickel to equal to 3911.55 g. We actually want the units here instead of g to be in kg. Who this suggests a direct conversion which can be done very easily. I'll move this down from more space here, But we know that for every one kg we have 10 to the three or 1000 g. So then you can see there are units of grams were canceled. Leaving us with the final value of the massive nickel to equal to 3.91 kg. So this right here is going to be my final answer for this problem.