A sample of sulfur dioxide, SO2(g), has a mass of 56.6 g. How many molecules are in this sample?

Question

A sample of sulfur dioxide, SO2(g), has a mass of 56.6 g.  How many molecules are in this sample?

BlackTom AI · Accepted Answer

Question restatement: A sample of sulfur dioxide, SO2(g), has a mass of 56.6 g. How many molecules are in this sample?

Option A: 0.883 molecules
- This is far too small. To convert grams to molecules, you must first convert to moles using the molar mass, then multiply by Avogadro’s number. A result less than one molecule is impossible for a macroscopic mass in this context, indicating a misapplication of unit conversions.

Option B: 6.02 × 10–21 molecules
- This value resembles a fraction of a mole scaled by Avogadro’s number but is off by several orders of magnitude. The calculation would require an extraordinarily tiny number of moles, which is inconsistent with 56.6 g of a compound with molar mass around 64 g/mol. In short, the exponent is incorrect for a sample of this mass.

Option C: 3.41 × 10^25 molecules
- To assess plausibility, convert grams to moles: Molar mass of SO2 ≈ 32.07 (S) + 2×16.00 (O) ≈ 64.07 g/mol. Moles = 56.6 g ÷ 64.07 g/mol ≈ 0.885 mol. Multiply by Avogadro’s number (6.02×10^23): 0.885 × 6.02×10^23 ≈ 5.33×10^23 molecules. This is far from 3.41×10^25, which would correspond to about 56.6 g × (6.02×10^23) / 0.0224 L for a gas at STP or some other mismatched setup. Therefore this option is not correct for a straightforward gram-to-molecule calculation.

Option D: 1.42 × 10–24 molecules
- This is an astronomically small number of molecules, incompatible with a 56.6 g sample. It would imply an almost inconceivably tiny amount of substance, inconsistent with the mole-based conversion process from grams to molecules.

Option E: 5.32 × 10^23 molecules
- This aligns with the standard conversion: first find moles = 56.6 g ÷ 64.07 g/mol ≈ 0.885 mol. Then multiply by Avogadro’s number: 0.885 mol × 6.02×10^23 molecules/mol ≈ 5.33×10^23 molecules. This is a correct magnitude and order of growth for the number of molecules in a 56.6 g sample of SO2 at the stated molar mass. Minor differences in significant figures (0.885 vs 0.884 or 0.885×6.02×10^23) yield the result around 5.3×10^23, which matches the provided option closely.

Summary of reasoning across options:
- Options A, B, D, and E each represent different orders of magnitude that either underestimate or overestimate the number of molecules for a 56.6 g sample, given the ~64 g/mol molar mass of SO2. The key steps are converting grams to moles via the molar mass, then converting moles to molecules by Avogadro’s number. The only option that matches that standard calculation is the one near 5.3×10^23 molecules; deviations in the options reflect common calculation or unit-handling slips, such as misplacing decimal points or misapplying exponents.

A sample of sulfur dioxide, SO2(g), has a mass of 56.6 g. How many molecules are in this sample?Single choice

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