Question

how many moles are contained in 9.54 × 10²³ atoms of platinum? include the units, but do not write the chemical formula. round the answer to 3 significant figures.
answer:

Explanation:

Step1: Recall Avogadro's number

Avogadro's number is \( 6.022 \times 10^{23} \) atoms/mol, which relates the number of atoms to moles: \( \text{moles} = \frac{\text{number of atoms}}{\text{Avogadro's number}} \)

Step2: Substitute values

Given number of atoms \( = 9.54 \times 10^{23} \), Avogadro's number \( = 6.022 \times 10^{23} \) atoms/mol.
\( \text{moles} = \frac{9.54 \times 10^{23}}{6.022 \times 10^{23}} \)

Step3: Calculate and round

Simplify: \( \frac{9.54}{6.022} \approx 1.584 \). Round to 3 significant figures: \( 1.58 \) (wait, recalculate: \( 9.54 \div 6.022 \approx 1.584 \), 3 sig figs: 1.58? Wait, 9.54 has 3, 6.022 has 4. So 9.54/6.022 ≈ 1.584, rounded to 3 sig figs is 1.58? Wait no, 9.54 ÷ 6.022: let's do exact division. 9.54 / 6.022 ≈ 1.584, so 1.58 when rounded to 3 significant figures? Wait, 1.584: the third significant figure is 8, next digit is 4, which is less than 5, so we keep 8. Wait, no: 1.584, first sig fig 1, second 5, third 8, fourth 4. So round to 3: 1.58. Wait, but let's check again: 9.54e23 / 6.022e23 = 9.54/6.022 ≈ 1.584, so 1.58 moles? Wait, no, maybe I miscalculated. Wait 6.0221.58 = 6.0221.5 + 6.022*0.08 = 9.033 + 0.48176 = 9.51476, which is close to 9.54. So 1.58 is correct? Wait, 9.54 - 9.51476 = 0.02524. So 0.02524/6.022 ≈ 0.0042, so total ≈ 1.58 + 0.0042 ≈ 1.5842, so 1.58 when rounded to 3 sig figs. Wait, but maybe I made a mistake. Wait, 9.54 / 6.022: let's use calculator steps. 9.54 ÷ 6.022. Let's divide numerator and denominator by 1e23: 9.54/6.022 ≈ 1.584. So 3 sig figs: 1.58. Wait, but 1.584 rounded to 3 sig figs is 1.58 (since the fourth digit is 4, which is less than 5, so we don't round up the third digit). Wait, no: 1.584, the third significant figure is 8, the next digit is 4, so we keep 8. So 1.58. Wait, but let's check with more precise calculation: 9.54 ÷ 6.022 = 1.5841913... So 3 significant figures: 1.58.

Wait, but maybe I messed up. Wait, Avogadro's number is 6.022×10²³, so the calculation is correct. So the moles are approximately 1.58 moles? Wait, no, wait 9.54e23 divided by 6.022e23: the exponents cancel, so 9.54/6.022 ≈ 1.584, so 1.58 when rounded to 3 significant figures.

Wait, but let's check again: 6.022 1.58 = 6.0221.5 + 6.022*0.08 = 9.033 + 0.48176 = 9.51476, which is 9.51e23, but we have 9.54e23. The difference is 0.02524e23, so 0.02524/6.022 ≈ 0.0042, so total is 1.58 + 0.0042 ≈ 1.5842, so 1.58 when rounded to 3 sig figs. Yes.

Answer:

1.58 moles