chemistry question, HELP

Question

The substance Fe₂ O₃ contains 2.325g of iron for every 1000g of oxygen.

How much iron and oxygen compound contains these elements in the ratio 2.616g of Fe to 1000g of oxygen.

What is the formula of this other compound?

Answer 1

Hi, Jessie,

To begin with, the "secret" to answering this (or any related question like this) is to recognize that molecules are formed by individual atoms independent of the atomic weight of those atoms. When given a question about the WEIGHT of any element, you have to first convert this to moles (or millimoles) to understand what the ratio is between different elements. Not that it matters too much, Jessie, but 1 mole is equal to 6.022 X 10E23 "units" (whether those units are atoms, molecules, ions or anything else). The IMPORTANT part is that 1 mole of any (atom, element) is exactly equal to the mass of that (atom, element) in grams. This is all we need to solve this problem!

To begin with (and to prove this idea about combining moles of things, not simply grams of things!), here is the first part of the question: Fe₂O₃ contains 2.325g of iron for every 1000g of oxygen. Is that true? Well, we know the following about those two elements: Fe, or iron, has an atomic weight of 55.85, and O, or oxygen (the element, not the gas!) has an atomic weight of 15.999. If we wanted to consider the ratio of the weights (masses, actually) of those two elements in Fe₂ O₃ we could arrange an equation that:

Fe₂/O₃ = (55.85 x 2)/(15.999 x 3), or 111.7/47.997. This means that the overall weight of iron to oxygen in this compound is 2.325 to 1.000, so for every 2.325 grams of iron/Fe, you would have 1.000 g of oxygen/O.

OK, so whoever provided you with this question has made a HUGE mistake by leaving out that decimal point(!!), because the ratio isn't 2.325 to 1000, but 2.325 to 1.000!! Either way, let's move on ...

To solve the ACTUAL problem, we can arrange the equation above only this time solving for Fe:

2.616g of Fe to 1000g of oxygen ( .... I'm going to change that to 1.000 g of oxygen, so let's see what we get here):

2.616/1.000 = x(55.85)/(15.997)

2.616 = x(55.85)/(15.997)

2.616 x 15.997 = x(55.85)

41.85/55.85 = x, or x = 0.75

So, the empirical formula is Fe_0.75 O₁, but THAT doesn't make sense (three quarters of an atom of iron for every atom of oxygen???).

We can fix this by maintaining the correct ratio simply by multiplying both "atoms" by four - this then becomes: Fe₃O₄ , and that compound (magnetite) will have a ratio of 2.616 g of iron for every 1.000 gram of oxygen. Check out it's structure here: https://byjus.com/chemistry/fe3o4-iron-oxide/#:~:text=Fe3O4%20occurs,as%20Magnetite%20or%20Magnetic%20oxide.

'Hope that helps,

Chris