If $\ce{1.84\times10^{-4}}$ moles of element A was completely reacted with element B to create $\ce{1.231\times 10^19}$ molecules of $\ce{(A3B2)_x}$ a hypothetical compound, what is the value of x?

I tried this:

$\pu{1 mol} = 6.02 \times 10^{23} ~\pu{molecules}$

$y~\pu{mol} = 1.231 \times 10^{19} ~\pu{molecules}$

$y = \pu{2.0449 \times 10^-5 mol}$

$\ce{(A_3B_2)_x} : 1.84\times10^{-4}+ {2\over 3}(1.84\times10^{-4})=3.067\times10^{-4}$

So it produces $3.067\times10^{-4}$ mol of the compound

and, $3.067 \times 10^{-4}~\pu{mol} \div 2.0449 \times 10^{-5}~\pu{mol} = 15$

And since 1 compound has 5 atoms, $15 \div 5 =3$

Therefore, $x$ is 3

I am not sure if I did this question correctly. Even if I did, is there a more efficient and organized way of solving this problem?

  • $\begingroup$ Can you describe what exactly you did below the first horizontal line? ("1 mol = 6.02×1023 molecules;x mol =1.231×1019 molecules;x = 2.0449×10−5 mol") what are you trying to do by that? $\endgroup$ – Gaurang Tandon Mar 7 '18 at 2:02
  • $\begingroup$ well, 1.84×10−4 is in moles, while 1.231×1019 is the actual number of molecules. So I'm trying to convert number molecules into moles $\endgroup$ – didgocks Mar 7 '18 at 2:44
  • $\begingroup$ @didgocks use different variables. “x mol = $\mathrm{1.231 x 10^{19}}$ and we also have $\ce{(A3B2)_x}$ “. $\endgroup$ – MollyCooL Mar 7 '18 at 4:55

At first you said that $x = \pu{2.0449\times10^−5 mol}$ and then later said $x=3$. It is clearly wrong even without going into the maths!

That said, I believe you are confusing the stoichiometry of the compound with the number of moles of the compound produced. The $x$ in $\ce{(A3B2)_x}$ is a part of the chemical formula for that compound, and not the moles of $\ce{(A3B2)}$ produced.

For example, $\ce{AlCl3}$ usually exists as a dimer in gas phase, so we write it as $\ce{Al2Cl6}$ or simply $\ce{(AlCl3)2}$ for clarity. You should hence realize that the $x$ in $\ce{(A3B2)_x}$ represents the number of $\ce{A3B2}$ molecules that have polymerized together to form a single molecule. And the question states that $\pu{1.231\times10^19}$ of such molecules was produced.

With the conceptual clarity attained, we'll now solve the numerical. Note that the question says that all the moles of elemental A were obtained in the compound. This implies:

$$ \begin{align} \text{moles of A in the compound} &= \text{original moles of elemental A}\\ \implies 3x\times(\text{moles of compound }\ce{A3B2})&=1.84\times10^{-4} \end{align} $$

Solving this, you'll get approximately $x=3$, which is the expected answer.


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