Certainly! Let's determine which of the given substances contains the greatest number of particles by performing a detailed, step-by-step comparison.
1. Understanding the Task:
- We want to compare 4 grams of each substance (Lithium, Chlorine gas, Hydrogen gas, and Water) to determine which has the greatest number of particles.
2. Concepts to Consider:
- Number of moles: This is calculated by dividing the mass of the substance by its molar (atomic/molecular) mass.
- Number of particles: One mole of any substance contains Avogadro's number of particles, which is approximately [tex]\(6.022 \times 10^{23}\)[/tex] particles/mole.
3. Calculations for Each Substance:
a) Lithium ([tex]$Li$[/tex]):
- Given mass: 4 grams
- Atomic mass of Lithium: 7 g/mol
- Number of moles [tex]\(= \frac{4 \text{ grams}}{7 \text{ g/mol}} \approx 0.5714 \text{ moles}\)[/tex]
- Number of particles [tex]\(= 0.5714 \text{ moles} \times 6.022 \times 10^{23} \text{ particles/mole} \approx 3.441 \times 10^{23}\)[/tex] particles
b) Chlorine gas [tex]\(Cl_2\)[/tex]:
- Given mass: 4 grams
- Molecular mass of [tex]\(Cl_2 = 2 \times 35.5 = 71 \text{ g/mol}\)[/tex]
- Number of moles [tex]\(= \frac{4 \text{ grams}}{71 \text{ g/mol}} \approx 0.0563 \text{ moles}\)[/tex]
- Number of particles [tex]\(= 0.0563 \text{ moles} \times 6.022 \times 10^{23} \text{ particles/mole} \approx 3.393 \times 10^{22}\)[/tex] particles
c) Hydrogen gas [tex]\(H_2\)[/tex]:
- Given mass: 4 grams
- Molecular mass of [tex]\(H_2 = 2 \times 1 = 2 \text{ g/mol}\)[/tex]
- Number of moles [tex]\(= \frac{4 \text{ grams}}{2 \text{ g/mol}} = 2 \text{ moles}\)[/tex]
- Number of particles [tex]\(= 2 \text{ moles} \times 6.022 \times 10^{23} \text{ particles/mole} = 1.204 \times 10^{24}\)[/tex] particles
d) Water ([tex]\(H_2O\)[/tex]):
- Given mass: 4 grams
- Molecular mass of [tex]\(H_2O = 2 \times 1 + 16 = 18 \text{ g/mol}\)[/tex]
- Number of moles [tex]\(= \frac{4 \text{ grams}}{18 \text{ g/mol}} \approx 0.2222 \text{ moles}\)[/tex]
- Number of particles [tex]\(= 0.2222 \text{ moles} \times 6.022 \times 10^{23} \text{ particles/mole} \approx 1.338 \times 10^{23}\)[/tex] particles
4. Comparison of Particles:
- Lithium: [tex]\( \approx 3.441 \times 10^{23}\)[/tex] particles
- Chlorine gas: [tex]\( \approx 3.393 \times 10^{22}\)[/tex] particles
- Hydrogen gas: [tex]\( \approx 1.204 \times 10^{24}\)[/tex] particles
- Water: [tex]\( \approx 1.338 \times 10^{23}\)[/tex] particles
From the calculations, we can observe that the substance with the greatest number of particles is Hydrogen gas ([tex]\(H_2\)[/tex]) with approximately [tex]\(1.204 \times 10^{24}\)[/tex] particles.
Conclusion:
The answer to the question "Which of the following contains the greatest number of particles?" is:
c) 4 g of hydrogen gas [tex]\(\left( H_2 \right)\)[/tex].
