Certainly! Let's break down the solution step-by-step:
1. Understand the chemical formula: The chemical formula of malachite is [tex]\( Cu_2CO_3(OH)_2 \)[/tex]. This implies that each molecule of malachite contains 2 copper (Cu) atoms.
2. Know the given information:
- We have 3.5 moles of malachite.
- Avogadro's number is [tex]\( 6.022 \times 10^{23} \)[/tex] atoms per mole. This value tells us how many units (atoms, molecules, etc.) are in one mole of a substance.
3. Determine the total number of copper atoms:
- For every mole of malachite, there are [tex]\( 6.022 \times 10^{23} \)[/tex] molecules.
- Since each molecule of malachite contains 2 copper atoms, the number of copper atoms per mole of malachite is [tex]\( 2 \times 6.022 \times 10^{23} \)[/tex].
- Therefore, for 3.5 moles of malachite:
[tex]\[
\text{Number of copper atoms} = 3.5 \times (2 \times 6.022 \times 10^{23})
\][/tex]
4. Perform the multiplication:
[tex]\[
3.5 \times 2 = 7
\][/tex]
Thus, we have:
[tex]\[
7 \times 6.022 \times 10^{23}
\][/tex]
5. Combine the numbers:
[tex]\[
7 \times 6.022 = 42.154 \times 10^{23}
\][/tex]
6. Express the result in scientific notation:
- We convert [tex]\( 42.154 \times 10^{23} \)[/tex] to scientific notation. This is done by expressing it as:
[tex]\[
4.22 \times 10^{24}
\][/tex]
So, the number of copper atoms in 3.5 moles of malachite is [tex]\( 4.22 \times 10^{24} \)[/tex] atoms.
### Final Answer:
- The coefficient in the green blank should be 4.22.
- The exponent in the yellow blank should be 24.
Therefore, the final formatted answer is:
[tex]\[
\boxed{4.22} \times 10^{\boxed{24}} \text{ atoms } Cu
\][/tex]
