Sure, I can guide you through understanding the molar mass calculation for an element when given certain data.
Here's the step-by-step explanation:
1. Given Data:
- The number of particles: \(6.02 \times 10^{23}\) particles.
- The mass of the element: 100 grams.
2. Avogadro's Number:
Avogadro's number (\(N_A\)) is a known constant which is the number of particles in one mole of a substance. The value of Avogadro's number is \(6.02214076 \times 10^{23}\) particles per mole.
3. Molar Mass Calculation:
To find the molar mass (M) of the unknown element, we use the formula:
[tex]\[
\text{Molar Mass} = \frac{\text{Mass of the Element (g)}}{\frac{\text{Number of Particles}}{N_A}}
\][/tex]
4. Substitute the Given Values:
- Mass of the element: 100 g.
- Number of particles: \(6.02 \times 10^{23}\).
- Avogadro's Number: \(6.02214076 \times 10^{23}\).
Plugging in the values, we get:
[tex]\[
\text{Molar Mass} = \frac{100 \text{ g}}{\frac{6.02 \times 10^{23} \text{ particles}}{6.02214076 \times 10^{23} \text{ particles/mole}}}
\][/tex]
5. Simplify the Calculation:
Simplify the denominator by calculating the ratio of the number of particles to Avogadro's number:
[tex]\[
\frac{6.02 \times 10^{23}}{6.02214076 \times 10^{23}} \approx 0.999643
\][/tex]
So, the molar mass calculation becomes:
[tex]\[
\text{Molar Mass} = \frac{100 \text{ g}}{0.999643}
\][/tex]
6. Calculate the Molar Mass:
Performing the division:
[tex]\[
\text{Molar Mass} \approx 100.0355607973422 \text{ g/mol}
\][/tex]
To summarize, given [tex]\(6.02 \times 10^{23}\)[/tex] particles of the element and a mass of 100 grams, the molar mass of the element is approximately 100.0355607973422 grams per mole. This molar mass helps identify the element in question.
