Accepted answer
Answer included
How many atoms are in 2.19 moles of lithium
For an elemental substance such as lithium, the “entities” counted by moles are individual atoms. The conversion from moles to atoms uses Avogadro’s number as a fixed conversion factor.
Conversion principle: \(1\ \text{mol}\) of any element contains \(N_A = 6.022 \times 10^{23}\) atoms.
Given information and formula
| Quantity | Symbol | Value | Units |
|---|---|---|---|
| Amount of lithium | \(n\) | \(2.19\) | \(\text{mol}\) |
| Avogadro’s number | \(N_A\) | \(6.022 \times 10^{23}\) | \(\text{atoms/mol}\) |
The relationship between amount of substance and particle count is:
\[ N = n \cdot N_A \]Step-by-step calculation
- Substitute the given amount and Avogadro’s number: \[ N = (2.19\ \text{mol}) \cdot \left(6.022 \times 10^{23}\ \frac{\text{atoms}}{\text{mol}}\right) \]
- Cancel units and multiply the numbers: \[ N = (2.19 \times 6.022)\times 10^{23}\ \text{atoms} \] \[ N = 13.18818 \times 10^{23}\ \text{atoms} = 1.318818 \times 10^{24}\ \text{atoms} \]
- Apply significant figures: \(2.19\) has 3 significant figures, so the final atom count is reported to 3 significant figures: \[ N = 1.32 \times 10^{24}\ \text{atoms} \]
Result: \(2.19\ \text{mol}\) of lithium contains \(\boxed{1.32 \times 10^{24}}\) lithium atoms.
Visualization: mole-to-atoms conversion flow
Quick check (reasonableness)
- \(2\ \text{mol}\) corresponds to about \(2 \times 10^{24}\) atoms, so \(2.19\ \text{mol}\) should be slightly above \(2 \times 10^{24}\), consistent with \(1.32 \times 10^{24}\) only after recognizing that the base is \(6.022 \times 10^{23}\) per mole, not \(10^{24}\) per mole.
- The magnitude is correct because \(6.022 \times 10^{23}\) is close to \(10^{24}\), and multiplying by a number near 2 produces a result near \(10^{24}\).
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