How many moles of oxygen are in a malachite sample containing [tex][tex]$2.3 \times 10^{25}$[/tex][/tex] atoms of hydrogen?

Malachite: [tex]Cu_2CO_3(OH)_2[/tex]

Internal ratio: [tex]\frac{2 \text{ mol H}}{5 \text{ mol O}}[/tex]

[?] moles O



Answer :

To determine how many moles of oxygen are in a malachite sample containing [tex]\(2.3 \times 10^{25}\)[/tex] atoms of hydrogen, we can follow a step-by-step process:

1. Identify the number of hydrogen atoms:

The sample contains [tex]\(2.3 \times 10^{25}\)[/tex] atoms of hydrogen.

2. Convert atoms of hydrogen to moles of hydrogen:

To convert the number of atoms to moles, we use Avogadro's number, which is [tex]\(6.022 \times 10^{23}\)[/tex] atoms per mole. The formula to convert atoms to moles is:

[tex]\[ \text{moles of hydrogen} = \frac{\text{number of atoms of hydrogen}}{\text{Avogadro's number}} \][/tex]

Plugging in the given values:

[tex]\[ \text{moles of hydrogen} = \frac{2.3 \times 10^{25}}{6.022 \times 10^{23}} = 38.19329126536035 \, \text{moles H} \][/tex]

3. Determine the internal ratio of hydrogen to oxygen in malachite:

The internal ratio of hydrogen to oxygen in malachite is given by:

[tex]\[ \frac{2 \text{ moles H}}{5 \text{ moles O}} \][/tex]

This means for every 2 moles of hydrogen, there are 5 moles of oxygen.

4. Calculate the moles of oxygen using the hydrogen to oxygen ratio:

To find the moles of oxygen, we need to multiply the moles of hydrogen by the ratio of oxygen to hydrogen:

[tex]\[ \text{moles of oxygen} = \text{moles of hydrogen} \times \frac{5 \text{ moles O}}{2 \text{ moles H}} \][/tex]

Given that we have 38.19329126536035 moles of hydrogen, we can calculate:

[tex]\[ \text{moles of oxygen} = 38.19329126536035 \times \frac{5}{2} = 95.48322816340088 \, \text{moles O} \][/tex]

Therefore, in a malachite sample containing [tex]\(2.3 \times 10^{25}\)[/tex] atoms of hydrogen, there are approximately [tex]\(95.48322816340088\)[/tex] moles of oxygen.