To determine the mass of [tex]\(2.30 \times 10^{24}\)[/tex] particles of water ([tex]\(H_2O\)[/tex]), we'll follow a step-by-step process involving Avogadro's number and the molar mass of water.
1. Understand the given data:
- Number of water particles, [tex]\(N = 2.30 \times 10^{24}\)[/tex].
2. Use Avogadro's number:
- Avogadro's number, [tex]\(N_A\)[/tex], is [tex]\(6.022 \times 10^{23}\)[/tex]. This represents the number of particles in one mole of a substance.
3. Calculate the number of moles:
- The number of moles [tex]\(n\)[/tex] is given by the ratio of the number of particles to Avogadro's number:
[tex]\[
n = \frac{N}{N_A}
\][/tex]
Substituting the given values:
[tex]\[
n = \frac{2.30 \times 10^{24}}{6.022 \times 10^{23}}
\][/tex]
[tex]\[
n \approx 3.82 \text{ moles}
\][/tex]
4. Determine the molar mass of water:
- Water ([tex]\(H_2O\)[/tex]) has a molar mass calculated from its constituent atoms: 2 Hydrogen atoms and 1 Oxygen atom.
- Atomic masses: Hydrogen [tex]\(\approx 1 \, \text{g/mol}\)[/tex], Oxygen [tex]\(\approx 16 \, \text{g/mol}\)[/tex].
- Molar mass of water:
[tex]\[
\text{Molar mass of } H_2O = 2 \times 1 + 16 = 18 \, \text{g/mol}
\][/tex]
5. Calculate the mass of water:
- The mass [tex]\(m\)[/tex] in grams is the product of the number of moles and the molar mass of water:
[tex]\[
m = n \times \text{Molar mass of } H_2O
\][/tex]
Substituting the calculated number of moles and the molar mass of water:
[tex]\[
m \approx 3.82 \text{ moles} \times 18 \, \text{g/mol}
\][/tex]
[tex]\[
m \approx 68.75 \, \text{grams}
\][/tex]
Conclusively, the mass of [tex]\(2.30 \times 10^{24}\)[/tex] particles of water is approximately 68.75 grams.
