A rechargeable battery is constructed based on a concentration cell constructed of two Ag/Ag+ half-cells. The volume of each half-cell is 2.0 L, and the concentrations of Ag+ in the half-cells are 1.25 M and 1.0 * 10-3 M. c. Upon recharging, how long would it take to redissolve 1.00 * 102 g of silver at a charging current of 10.0 amps?

Video transcript

hey everyone in this example, we have a rechargeable battery made up of two gold two gold three plus half cells. We have the initial concentration of gold three plus in each half cell as 1. molars in 1.25 times 10 to the negative third power molars respectively. Each cell has a volume of 2.50 liters and we need to calculate the time it will take to re dissolve 1.25 times 10 to the second power grams of gold Charging at a current of 11.5 amps. So we need to write out our an ode reaction, which we should recall occurs as an oxidation reaction. So we would take our solid gold medal which will be formed by taking our Gold three plus carry on and gaining three electrons. So this would be our oxidation because we gained electrons on the product side of this reaction. And so we would agree that this occurs at our an ode. Now for our cathode reaction, we would agree that this would occur as a reduction reaction where we have our gold three plus cat ion Which loses three electrons to form we're sorry, which gains three electrons to form our solid gold medal. And so we would recognize that because we added the electrons on the reactant side, this would correspond to a reduction reaction which occurs at our cathode. And so we should recognize that we had the transfer in both of these reactions of three electrons. Now, according to the prompt, we have in 2.50 L. An initial concentration of the gold, three plus cat ion Equal to 1.50 Moller. And we should recall that polarity can be interpreted as moles per leader of our gold cat eye on. So we're going to convert from polarity. I'll show the map here below. We would convert from polarity. Two moles of electrons from moles of electrons. We're going to convert two columns from columns. We're going to convert two units of seconds. And then from second we're going to convert from units of minutes to finally ours as our final unit. To calculate the amount of time it will take to re dissolve our gold. So what we should recall next is that for one ampule we have one column per second. So according to the prompt we have 11.5 amps Which we can reinterpret as 11.5 columns per second. And so to start out our conversion, we're going to take The massive gold given to the prompt as 1.25 times 10 to the second power grams of gold. And we're going to convert from g of gold, two moles of gold. So we would recall that according to our periodic table for one mole of gold. We have a molar mass of 196.97 g of gold. Now we can cancel out grams of gold and we're going to convert from moles of our gold as a three plus catty on, two moles of electrons. And we would recall that because above we stated, we have the transfer of three electrons. We can say we have a transfer of three moles of electrons for one mole of the gold. Three plus catalon. Next we're going to multiply by our conversion factor. Where now that we've canceled that mold of gold, where can I convert from moles of electrons? Two columns by recalling our Faraday's constant, which we recall has a value of 96,485 columns for one mole of an electron. So now we're able to cancel out moles of our electrons. And just to make more room here. Sorry about that. So we have more room now and we're going to multiply by our next conversion factor where we're going to convert from columns two seconds. So we should recall that from the prompt. We have 11.5 amps which we're interpreting as 11. columns for one second. So now we're able to cancel out columns and for our next conversion factor. So I'm just going to make more room again, we are going to convert from units of seconds into minutes. And so we should recall that in 60 seconds, we have one minute. So we're able to cancel out seconds. And now from minutes we want to convert from minutes to hours. So we should recall that there are 60 minutes in one hour. And so we can cancel out minutes. We're left with ours as our final unit for time and what we're going to get here is a value equal to 4.44 hours. And so this here would be our final answer as the amount of time that it takes to re dissolve 1.25 times 10 to the second power grams of gold at the current 11. amps. So this is our final answer highlighted in yellow. If you have any questions, please leave them down below. Otherwise, I will see everyone in the next practice video.