How many sodium atoms are there in a 30.2 g sample of Na3AlF6?

Question

BlackTom AI · Accepted Answer

We start by identifying the key data in the problem and then step through the conversions carefully.
Option 1: 2.89 × 10^22 atoms. This value is off by roughly an order of magnitude compared to the correct result and is likely obtained by miscalculating either the number of formula units or the number of Na atoms per unit. A common pitfall would be treating the sample as containing 1 Na per formula unit or misplacing the exponential factor, which would yield a result far from the correct 10^23 scale.
Option 2: 2.60 × 10^23 atoms. This is the correct magnitude and matches the correct reasoning: first compute the molar mass of Na3AlF6 (3×22.99 + 26.98 + 6×18.998 ≈ 209.95 g/mol). Then moles in 30.2 g: 30.2 g ÷ 209.95 g/mol ≈ 0.1440 mol. Multiply by Avogadro’s number to get formula units: 0.1440 mol × 6.022×10^23 ≈ 8.67×10^22 formula units. Each formula unit contains 3 Na atoms, so Na atoms ≈ 3 × 8.67×10^22 ≈ 2.60×10^23 atoms. This aligns with the provided option.
Option 3: 8.66 × 10^22 atoms. This value corresponds to the number of Na3AlF6 formula units, not the number of Na atoms. Since each formula unit contains 3 sodium atoms, you would multiply by 3 to get the correct Na count, which would give about 2.60×10^23 atoms, not 8.66×10^22. The confusion here is treating formula units as Na atoms directly.
Option 4: 0.432 atoms. This is completely implausible for a macroscopic sample; any real sample containing many grams contains on the order of 10^23 atoms. This value suggests a gross miscalculation, perhaps mixing up molar amounts with discrete counts or misplacing exponentials.
Option 5: 5.20 × 10^23 atoms. This result is roughly double the correct value, indicating a likely error such as using an incorrect molar mass or forgetting the factor of 3 Na atoms per formula unit, or a misapplication of Avogadro’s number. The correct count is about 2.60×10^23, not 5.20×10^23.

How many sodium atoms are there in a 30.2 g sample of Na3AlF6?

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