Question

Determine the number of molecules of Cr2O3 that are formed when 1.34x10^3 grams of oxygencompletely reacts according to the following equation4Cr(s) + 3O₂(g) → 2Cr₂O₃(s)

Answer 1

Step 1 - "Reading" the chemical equation

The given chemical equation is:

$4Cr_{(s)}+3O_{2(g)}\rightarrow2Cr_2O_{3(s)}$

Let's read this equation. Remember: the numbers at the left of the substances represent the number of moles involved in this reaction.

Thus:

4 moles of Cr react with 3 moles of O2 to produce 2 moles of Cr2O3

As the exercise is specifically asking about the relation between O2 and Cr2O3, we can further simplify this statement to:

3 moles of O2 produce 2 moles of Cr2O3

This is a fixed relation we'll be using to solve the problem.

Step 2 - How many moles of C2O3 will be produced?

We know that 3 moles of O2 produce 2 moles of Cr2O3. Since the exercise gave us a mass of O2, 1.34x10^3 g, it is convenient to convert moles of O2 to mass.

In order to so, we need to multiply the number of moles by the molar mass (32 g/mol for O2):

$m_{O2}=3moles\times32g/mol=96g$

Therefore, 96g of O2 are required to produce 2 moles of Cr2O3. We can use this relation to predict how much C2O3 will be produced:

$\begin{gathered} if\text{ 96g of O2 produce ---- 2 moles of Cr2O3} \\ 1.34\times10^3\text{ would produce ---- x} \\ \\ x=\frac{2\times1340}{96}=27.9\text{ moles of Cr2O3} \end{gathered}$

Therefore, 27.9 moles of Cr2O3 would be produced.

Step 3 - Converting number of moles of Cr2O3 to number of molecules

One mole corresponds to 6.10^23 unities. Therefore, to convert the number of moles of Cr2O3 to number of molecules, we can set the following proportion:

$\begin{gathered} 1\text{ mole of Cr2O3 ----- 6}\times10^{23}\text{ molecules} \\ 27.9\text{ moles of Cr2O3 ---- x molecules} \\ \\ x=6\times27.9\times10^{23}=167.4\times10^{23}=1.67\times10^{25}\text{ molecules} \end{gathered}$

Answer: 1.67*10^25 molecules of Cr2O3 would be produced in this reaction.