A 0.355 mol sample of a metal has a mass of 24.75 g. What is the mass of one atom of the element?

Question

A 0.355 mol sample of a metal has a mass of 24.75 g.  What is the mass of one atom of the element?

BlackTom AI · Accepted Answer

First, I will restate the problem in my own words: we have a 0.355 mol sample of a metal with a total mass of 24.75 g, and we need to find the mass of a single atom of that element.

Option A: 2.38 × 10–26 g. This value is far too small for the mass of a single atom. To check, the mass per atom is roughly the molar mass divided by Avogadro’s number. Even if the molar mass were on the order of a few tens of g/mol, dividing by 6.02e23 yields something on the order of 1e-23 to 1e-22 g per atom, not 1e–26 g. Therefore, this option underestimates the mass per atom.

Option B: 8.64 × 10^21 g. This is an absurdly large number for a single atom’s mass. A single atom weighs roughly 10–23 to 10–22 grams, so a value around 10^21 g would imply an astronomically massive atom, which is physically impossible. This option is incorrect by several orders of magnitude.

Option C: 69.7 g. This is on the order of grams per atom, which is completely unreasonable for a single atom. The mass of one atom is far, far less than a gram. This option cannot be correct.

Option D: 4.20 × 10^25 g. Similar to option B, this is an astronomically large mass for a single atom. Atoms weigh about 10–23 g each; 4.20 × 10^25 g would correspond to an enormous number of atoms, not a single atom. This option is incorrect.

Option E: 1.16 × 10–22 g. This value lies in the expected range for the mass of a single atom. To justify: the sample mass is 24.75 g for 0.355 mol, so the molar mass is 24.75 g / 0.355 mol ≈ 69.7 g/mol. The mass of one atom is therefore (69.7 g/mol) / (6.022 × 10^23 atoms/mol) ≈ 1.16 × 10–22 g per atom. This matches the order of magnitude typically seen for atomic masses, making it the physically reasonable choice.

Overall, options A, B, C, and D present values that are either too small, too large, or simply unrealistic for atomic scale masses. Option E aligns with the standard relation between molar mass and mass per atom, using the given amount of substance and Avogadro’s number to arrive at the correct scale for a single atom.

A 0.355 mol sample of a metal has a mass of 24.75 g. What is the mass of one atom of the element?单项选择题

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