To determine which expression correctly gives the number of particles in 2.0 grams of Neon (Ne), let’s break down the problem step-by-step.
1. Identify the Molar Mass of Neon (Ne):
- The molar mass of Neon (Ne) is 20.18 grams per mole (g/mol).
2. Determine Avogadro's Number:
- Avogadro's number is [tex]\( 6.0 \times 10^{23} \)[/tex] particles per mole.
3. Given Mass of Neon:
- The mass of Neon in question is 2.0 grams (g).
4. Calculate the Number of Moles:
- To find the number of moles in 2.0 grams of Neon, use the formula:
[tex]\[
\text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}}
\][/tex]
Substituting the values, we get:
[tex]\[
\text{Number of moles} = \frac{2.0 \, \text{g}}{20.18 \, \text{g/mol}}
\][/tex]
5. Calculate the Number of Particles:
- Once we have the number of moles, we can find the number of particles using Avogadro's number:
[tex]\[
\text{Number of particles} = \text{Number of moles} \times \text{Avogadro's number}
\][/tex]
Substituting the values, we get:
[tex]\[
\text{Number of particles} = \left( \frac{2.0 \, \text{g}}{20.18 \, \text{g/mol}} \right) \times (6.0 \times 10^{23} \, \text{particles/mol})
\][/tex]
6. Identifying the Correct Expression:
- From above, we see that the expression correctly matches option (C):
[tex]\[
\frac{2.0 \, \text{g}}{20.18 \, \text{g/mol}} \times (6.0 \times 10^{23} \, \text{particles/mol})
\][/tex]
Thus, option (C) correctly represents the number of particles in 2.0 grams of Neon. The number of particles is approximately [tex]\( 5.9464816650148655 \times 10^{22} \)[/tex] particles.
