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Answer :
To find the mass in grams of [tex]\(4.59 \times 10^{22}\)[/tex] molecules of water, we follow these steps:
1. Understand the concept:
- Water (H[tex]\(_2\)[/tex]O) has a known molar mass of approximately 18.015 grams per mole.
- Avogadro's number, [tex]\(6.022 \times 10^{23}\)[/tex], tells us how many molecules are in a mole.
2. Find the number of moles:
- We calculate the number of moles of water molecules using Avogadro's number.
- Divide the number of molecules by Avogadro's number:
[tex]\[
\text{moles of water} = \frac{4.59 \times 10^{22}}{6.022 \times 10^{23}}
\][/tex]
3. Compute the mass:
- Once we have the number of moles, we find the mass in grams. This is done by multiplying the number of moles by the molar mass of water:
[tex]\[
\text{mass in grams} = \text{moles of water} \times 18.015
\][/tex]
After performing these calculations, you will find that the mass of [tex]\(4.59 \times 10^{22}\)[/tex] molecules of water is approximately 1.37 grams.
Thus, the answer is 1.37 grams.
1. Understand the concept:
- Water (H[tex]\(_2\)[/tex]O) has a known molar mass of approximately 18.015 grams per mole.
- Avogadro's number, [tex]\(6.022 \times 10^{23}\)[/tex], tells us how many molecules are in a mole.
2. Find the number of moles:
- We calculate the number of moles of water molecules using Avogadro's number.
- Divide the number of molecules by Avogadro's number:
[tex]\[
\text{moles of water} = \frac{4.59 \times 10^{22}}{6.022 \times 10^{23}}
\][/tex]
3. Compute the mass:
- Once we have the number of moles, we find the mass in grams. This is done by multiplying the number of moles by the molar mass of water:
[tex]\[
\text{mass in grams} = \text{moles of water} \times 18.015
\][/tex]
After performing these calculations, you will find that the mass of [tex]\(4.59 \times 10^{22}\)[/tex] molecules of water is approximately 1.37 grams.
Thus, the answer is 1.37 grams.
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