Video Transcript
How long would it take to reduce
one mole of Ca2+ using a current of 19.8 amps? Assume the voltage is sufficient to
perform the reduction.
In this problem, calcium two plus
ions are reduced by the application of an electric current, which causes the calcium
two plus ions to gain two electrons to form solid calcium. We need to determine the amount of
time it will take to reduce the calcium ions using this equation, where 𝑄 is the
total charge, 𝐼 is the current, and 𝑡 is the time, measured in seconds. So we’re gonna solve for 𝑡. This problem gave us the current,
but we don’t have the total charge yet. So we’ll need to figure out how
much charge, that is, how many electrons, were needed to reduce the calcium two plus
ions.
If we look back at our reaction
equation, we can see that every one mole of calcium two plus ions reacts with two
moles of electrons. So two moles of electrons would be
required to reduce one mole of calcium two plus ions, like we have in this
problem. We need to determine the total
charge of these two moles of electrons, which we can do using this equation. We have two moles of electrons. And Faraday’s constant is
approximately equal to 96500 coulomb per mole of charge particles. The units of moles cancel. So the total charge is 193000
coulombs.
Now, we have everything we need to
solve for the time. We’ll first need to rearrange the
equation so we can isolate time, which we can do if we divide both sides of the
equation by the current, which gives us this. And let’s just flip that around
real quick so time is on the left-hand side. Now we can solve. The total charge is 193000
coulombs, and the current given in the problem is 19.8 amps. One amp is equivalent to one
coulomb per second. So the coulombs cancel, which gives
us about 9747.4747 seconds. That’s a very large amount of
seconds, so let’s convert that to hours. There are 3600 seconds in an
hour. So we can convert from seconds to
hours by dividing by 3600. This gives us about 2.70763
hours. Rounding to a sensible number of
digits gives us 2.71.
So it would take 2.71 hours to
reduce one mole of calcium two plus ions with a current of 19.8 amps.