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Consider the production of 100 kg of sodium metal using a current of 50,000 A, assuming a 100% yield.(a) How long will it take to produce the 100 kg of sodium metal?(b) What volume of chlorine at $25^{\circ} \mathrm{C}$ and 1.00 atm forms?

a. 2.33 hoursb. 53145.37 $\mathrm{L}$

Chemistry 101

Chapter 18

Representative Metals, Metalloids, and Nonmetals

Nonmetals Chemistry

Carleton College

Rice University

Brown University

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here we're making 100 kilograms of sodium using a current of 50,000 and piers. So in order to answer this question, we have to first think about what the reaction looks like for the formation of sodium. And that typically happens from the electrolysis of either molten sodium chloride or a prism. Clara, when you run a current through this again, this is electrolysis. We conform, um, elemental sodium and chlorine gas. We need a balanced chemical reaction for that, and then consider the half reaction Um, that forms the sodium. So in the starting chloride we have and plus the addition of an electron. That's where this current comes from. It provides electrons. Alas, for the reduction of sodium form. So did zero. So we have sodium coming from certain chloride. We have the electrons coming from the current. How does this help us figure out what? How long it takes the form of sodium? For that, we need to remember that, and fears are a unit of charge per second. So an impure is, in fact, one Coolum for every second. So our current tell us is how fast we're delivering charge, and we know that one Electron has charge of 1.62 one for you. Six go to 10 cents on the negative. 19 Cool abs. This is known as the elementary charge. So if we're delivering 50,000 calls for seconds, we can figure out how many electrons per second that is. This is cool enough for everyone. Second, if we divide that by the charge for every one electron, then we can figure out that we are delivering 3.1 to warn times 10 to the 23rd electrons for every second. Now that seems like an outrageously large number of electrons. That is true because we're working with very, very tiny particles. So in chemistry, we used avocados number to make the very large number of very tiny particles were accessible. So instead of dealing with electrons per second, individual electrons for second, let's deal with moles of electrons per second. So one more of electrons is equal to six point to several dodgersnumber some sense of the 23rd individual electrons. And when I performed this conversion, I find that I'm working with you're a 0.518 moles of electrons in every second. Remember where half reaction was so we're adding this many electrons per second. We're making huge assumption that every time I deliver on electron, I formed sodium ion. Shoot him, Adam. So let's run with that and figure out how long it would take to make 100 kilograms of sodium. So if their relationship right now isn't mold, we need to convert our 100 kilograms of this in a different color for 100 kilograms of sodium into molds of sodium. So first we're going to change this quantity, cramps and then use the molar mass of sodium, 22.99 grams of sodium everyone more psyllium to find that this is a total of 4000 350 mo. Of sodium. So we're making a total of 4350 miles sodium, and we're making about half a mold of second. How long will that take? Should be on the order of two hours a little bit more than two hours. Let's calculate the exact value by dividing our 4350 move bye rate, which is in every one second. I form money. Oh, can't leave and find that this is approximately 8397 seconds. That's not a very useful number. So we're gonna divide 302,600 because there are 3600 seconds in one hour. And this is where I get two hours, 2.33 hours, about two hours and 20 minutes again making huge assumption that every time that I deliver on electron, I am forming 1 30 Madame, that is the work. Uh, next were asked how much chlorine gas will be produced. Turn conditions to remember that this reaction also results in information of chlorine gas. Can you use this reaction for part B? And I found above that I made 4350 mold sodium and I'm gonna use that to find volume of chlorine gas. Ah, the relationship that we used that we take advantage of to convert quantities and moles too. Properties of gases. Just volume is the ideal Gasol lab. PB equals on Artie. I am solving for volume of chlorine. And for that I first need the number of moles of Cory. So I noticed that there is a 2 to 1 ratio between sodium quarry, so for every one more. Corinne, have two moles. So, Dion So I'm working with about 21 2100 75 Moles of Cory. We're going back to our ideal gas equation. I have pressure of number of malls are the constant temperature Now I confined the volumes on the salt for that first and then plug in the values that they know. This is 2175 more chlorine. The ideal gas, Constance. But is it applicable here? 0.8 to 1. The units are leader atmospheres for every move. Kelvin, remember that unusual gas equation? I have to use units of Kelemen, so the 25 degrees Celsius is actually 298 degrees. Kelvin. So that is the value that I was present in this equation. You divide all of that with the 1.0 atmospheres given in the problem so that I can finish first check with units. Well, he left with the gets of leaders. And if I put this into calculator, I will get a number like 53,200 in 9.7. The whole bunch of decibels, um, looks like your original problem. The figures that we were given 100 kilograms 50,000 years each had with one significant for a year. It's a little outrageous, especially given the huge assumptions that we made in this process, to think that I have this many digits of significance. So at most I could report 53,000 liters or have something more accurately like 50,000 leaders. Um, but whether you say 50 or 53,000 I would not include any more significant digits.

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