Video Transcript
Calculate the mass of zinc that forms when a current of 0.2 amps is passed through a
cell for 45 minutes. Take the molar mass of zinc to be 65.4 grams per mole and one faraday of charge to be
9.65 times 10 to the four coulombs. Give your answer in units of grams and to three decimal places.
In this problem, a current in a cell causes zinc two plus ions to be reduced to form
solid zinc. We’ll be able to solve this problem if we can determine how many electrons reacted to
form zinc metal in the cell. We can use this formula to calculate the total charge, where 𝑄 is the total charge,
𝐼 is the current, and 𝑡 is the time, measured in seconds. From there, we can determine the amount of electrons delivered to the cell and then
figure out the mass of zinc that was formed.
This problem gave us the current, 0.2 amps. And the problem says the current passed through the cell for 45 minutes. But we need to express this time in seconds to plug it into our equation. There are 60 seconds in one minute, so we can convert from minutes to seconds if we
multiply by 60. That gives us 2700 seconds. We can go ahead and plug that into our problem. One amp is equivalent to one coulomb per second. We can substitute those units in. So now, the seconds will cancel. The total charge is 540 coulombs.
Now, we need to know how many electrons this total charge is equivalent to so we can
calculate the amount of zinc that was formed. We can figure that out using this formula, which tells us the charge is equal to the
amount of charged particles multiplied by Faraday’s constant. We want to solve for the amount, so we’ll need to rearrange this equation to isolate
𝑛. We can do that if we divide both sides of the equation by 𝐹, which gives us this
equation. Let’s quickly swap that equation around so that 𝑛 is on the left-hand side.
Now, we can plug in the charge we calculated for 𝑄. And we’ll plug in Faraday’s constant for 𝐹, which was given in the problem to be
9.65 times 10 to the four coulombs of charge per mole of charged particles. The units of coulombs cancel, and we get about 0.0055958 moles of electrons.
Now, we need to figure out how much zinc is formed when this amount of electrons
react with zinc ions. From our reaction equation, we can see that every two moles of electrons form one
mole of solid zinc. So, the amount of zinc is half the amount of electrons. So, we need to calculate half of 0.0055958, which is about 0.0027979 moles.
Now, the last thing we need to do is convert this amount of zinc into a mass of
zinc. We can do that by multiplying the amount of zinc by the molar mass of zinc. Let’s plug in the amount we just calculated. And the molar mass was given in the problem; it’s 65.4 grams per mole. The units of moles cancel, and we get about 0.182984 grams. The problem told us to report our answer to three decimal places. So, we can round to 0.183 grams. So, the mass of zinc formed when a current of 0.2 amps is passed through a cell for
45 minutes is 0.183 grams.
