To solve the problem of finding how many moles of pennies have a mass equal to the mass of the Moon, we will follow these steps:
1. Determine the mass of the Moon in grams.
The mass of the Moon is given in kilograms [tex]\((7.35 \times 10^{22} \text{ kg})\)[/tex].
We need to convert this mass into grams because the mass of the penny is given in grams.
Recall that [tex]\(1 \text{ kg} = 1000 \text{ g}\)[/tex].
[tex]\[
\text{Mass of the Moon in grams} = 7.35 \times 10^{22} \text{ kg} \times 1000 \frac{\text{g}}{\text{kg}}
\][/tex]
[tex]\[
\text{Mass of the Moon in grams} = 7.35 \times 10^{25} \text{ g}
\][/tex]
2. Determine the number of moles of pennies.
We know that:
- The mass of a single penny is [tex]\(2.50 \text{ g}\)[/tex].
- The mass of the Moon in grams is [tex]\(7.35 \times 10^{25} \text{ g}\)[/tex].
We calculate the number of moles of pennies by dividing the mass of the Moon by the mass of a penny.
[tex]\[
\text{Number of moles of pennies} = \frac{\text{Mass of the Moon in grams}}{\text{Mass of a penny in grams}}
\][/tex]
[tex]\[
\text{Number of moles of pennies} = \frac{7.35 \times 10^{25} \text{ g}}{2.50 \text{ g}}
\][/tex]
[tex]\[
\text{Number of moles of pennies} = 2.94 \times 10^{25}
\][/tex]
So, the number of moles of pennies that have a mass equal to the mass of the Moon is [tex]\(2.94 \times 10^{25}\)[/tex].
