Electrolysis of a metal nitrate solution M(NO3)2(aq) for 325 min with a constant current of 20.0 A gives 111 g of the metal. Identify the metal ion M2+.

Video transcript

Hello. Everyone in this video, we're being told that we have an acquis metal nitrate solution. So of this formula Right over here, it was subjected to trellises using a current of 25 amps. So the 408 g of this metal is produced in 400 minutes. What is the identity of the metal ion? Which is M three plus. So for the reaction here, we know that the M three plus, which is acquis reacts with three electrons to yield our neutral metal in its solid state. We're gonna go ahead and calculate the molds of our medals of capital M some units to go ahead and recognizes that one amp is equal to one column per second. And of course we also have our Fair Days constant, Which is equal to 96,485 columns per mole of electron. This L over Alright, there we go. So again, we're tackling for the moles of our metal. So Capital M here, starting off with the 400 minutes of production time that we have, We're gonna go ahead and convert this in two seconds. So we know that for every one minute we have one seconds going from seconds into columns. And that conversion factor is for every 25.0 columns, we have one second going from columns into moles of electrons raising Faraday's constant here. So that is for every 96,485 columns. We have one mole of electrons. And now just using our equation that we have and read above. We know that for everyone mole of our M three plus. So the metal cast iron, we need three moles of electrons. And then using the motor mole ratio here, we know that for every one mole, our M3 plus we can yield one mole of our neutral metal. And we can see that we do get the units of moles of our mental. And just to make sure we can go ahead and cancel our units here. So we see that the myths is canceled. The seconds are canceled, columns are canceled, moles of electrons are canceled and most importantly the moles of N three plus is canceled, which does leave us the units being in molds of our metal. So once we put everything into the calculator, we see that the moles of our neutral metal here is equal to 2. moles of our capital M metal. So one thing to keep in mind is that my molar mass of em then is equal to. So the mass that were given again is 408 g of this metal. We know that units of molar masses go to the grams per mole. So using the grams that were given and the recently calculated value of moles, that is 2. moles of R M. This will give me the numerical value to be 196.8294. of course the unit is just g per mole. Which does mean that we have our molar mass. So referring to our pR table and looking at this calculated molar mass. Whatever elemental mass matches this one is going to be the metal ion. So we're gonna see here that from our fair table, the one that best matches the 196.8294 is going to be our gold element, which is a. You. So again gold, which has the mental symbol of a. U. This means that my metal ion is going to be our AU. Three plus. So this right here is going to be my final answer for this problem.