An unknown metal M is electrolyzed. It took 74.1 s for a current of 2.00 A to plate out 0.107 g

step 1 So we have metal M, right? Metal M. And this metal nitrate, when you write metal nitrate, this i

An unknown metal M is electrolyzed. It took 74.1 s for a...

Key Concepts

Determination of Atomic Weight

By combining the mass of the metal deposited with the calculated moles (based on the electron transfer stoichiometry), one can determine the atomic weight of the metal. This method is particularly useful in analytical chemistry for identifying an unknown metal based on its electrochemical deposition.

Stoichiometry of Electrochemical Reactions

In electrolysis, the reduction reaction at the cathode often involves the transfer of a specific number of electrons per metal ion. Recognizing the stoichiometric relationship—how many electrons are needed to reduce one ion of the metal—allows one to calculate the moles of the metal deposited from the moles of electrons transferred.

Conversion of Charge from Current and Time

This concept involves using the relationship Q = I × t, where Q is the charge in coulombs, I is the current in amperes, and t is the time in seconds. It forms the bridge between the macroscopic electrical parameters and the microscopic amount of charge that drives the chemical reaction.

Faraday's Laws of Electrolysis

These laws relate the amount of substance deposited at an electrode to the total electric charge passed through the electrolyte. Specifically, the mass of the substance deposited is directly proportional to the quantity of electricity, which means that knowing the current and the time gives the total charge, and then the mass can be linked back to the number of moles of electrons involved in the reaction.

Transcript

00:02 So we have metal m, right? metal m.

00:11 And this metal nitrate, when you write metal nitrate, this is what rather, metal nitrate will look like this.

00:22 Metal nitrate.

00:25 Metal nitrate.

00:30 That means that this three here tells us that this metal has the capability of losing three electrons.

00:38 Okay? in electrolysis, okay, plus the electrons, all right? so in this case, this metal was electrolyzed with current of 2 ampiers in the in 74 .1 seconds and current was 2 .0 amperors, okay, and then i were given that mass that was deposited was 0.

01:17 107 grams okay so we need to find it we need to find a formula mass for this we need to find this metal first after forming in the ram of course and we know that most of this particular substance by electron is equal to mass of that was deposited okay over the relative atomic mass and then we know that charge is equals to current by time okay this is crucial in this step because we have current and we have time so you are substituting and the current here is two ampers month by time which is 74 .1 seconds time should be in seconds this gives us around 148 .2 columns or ampere seconds okay so this is our current but according to farad is low we know that one moreover our pi electron gives us 96 ,000 and 6 ,000 485 columns of charge so how many moles will you know 148 how many more once will be 148 .2 columns give us so when you cross matplied this we're going to get around 148 columns and i'm at by the one mole or per electron divided by 96 485 columns.

03:03 Okay, so these columns will cancel off and we get around, and we get around 1 .53, but by 10 to power three, three moles, okay? but this is for the three electrons that we are seeing here, three electrons.

03:28 So when you want to get per per mole, we divide by three.

03:33 And this gives us around five, 5 .12, mudplied by 10 to power negative 4 moles, okay? moles.

03:51 So this is the total number of moles for this particular metal that were electrolyzed.

04:00 Okay...

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