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.
