Identifying an element from mass and atom count

Expert intro: Avogadro's number connects the 20 g sample to the atom count and reveals the element's molar mass.

Detailed walkthrough

What the data mean

The sample mass is 20 g, and the number of atoms is $4.95\times10^{23}$. To identify the element, convert atoms to moles using Avogadro's number and then find the molar mass.

Avogadro's number is

$6.022\times10^{23}\text{ atoms/mol}.$

So the number of moles in the sample is

$n=\frac{4.95\times10^{23}}{6.022\times10^{23}}\approx 0.822\text{ mol}.$

Find the molar mass

Molar mass equals mass divided by moles:

$M=\frac{20\text{ g}}{0.822\text{ mol}}\approx 24.3\text{ g/mol}.$

A molar mass of about 24.3 g/mol matches magnesium, whose atomic mass is approximately 24.305 g/mol. That makes the element Mg.

Why the scratch work leads to the same result

The expression in the prompt tries to set up a conversion between grams, moles, and atoms. The core idea is correct: use the relationship between grams and atoms to solve for the element's molar mass. If an element has molar mass $X$ g/mol, then

$20\text{ g}\times\frac{1\text{ mol}}{X\text{ g}}\times\frac{6.022\times10^{23}\text{ atoms}}{1\text{ mol}}=4.95\times10^{23}\text{ atoms}.$

Solving this gives

$X=\frac{20\times6.022\times10^{23}}{4.95\times10^{23}}\approx 24.3\text{ g/mol}.$

The value is not 0.01099302 amu; that result comes from a unit setup error. The atomic mass in amu and the molar mass in g/mol have the same numerical value for an element, so the answer should be a familiar periodic-table value.

How to identify the element

Once the molar mass is known, compare it to periodic table values. Magnesium is the closest match to 24.3 g/mol. Other nearby elements such as sodium at 23.0 and aluminum at 27.0 are farther away, so magnesium is the best identification.

Final answer

The element is $\boxed{\text{magnesium (Mg)}}$.

Common mistake

A frequent error is to divide the atom count by the mass directly without first converting to moles. That skips the meaning of Avogadro's number and produces the wrong unit. Another mistake is to treat the given atom count as if it were the number of moles. If you see atoms, moles must come first. A third issue is confusing amu with grams; although the numeric values match for atomic mass and molar mass, the units are different. In this problem, the correct path is atoms to moles to molar mass to element name.

💡 Pitfall guide

The step that usually causes trouble is the conversion from atoms to moles. If you try to force the 4.95 times 10 to the 23 atoms directly into a gram-based formula, the units will not cancel correctly and the final mass will look meaningless. Another trap is copying the scratch work line by line without checking what each quantity represents. The number 20 g is the sample mass, not the molar mass, so it cannot be plugged in as if it were the element's atomic mass. Also, do not round too early; keep enough digits in the intermediate mole calculation so that the final comparison to the periodic table stays accurate.

🔄 Real-world variant

If the sample had 32 g instead of 20 g but still contained 4.95 times 10 to the 23 atoms, the procedure would be the same. First compute moles from atoms: about 0.822 mol. Then the molar mass would be 32 divided by 0.822, or about 38.9 g/mol. That value would point to potassium if the atom count were adjusted accordingly, but with the same atom count it would mean the sample is not a pure element sample matching a standard atomic mass. If the atom count changed to 7.10 times 10 to the 23 atoms for a 20 g sample, the molar mass would be about 16.9 g/mol, which would suggest a different element such as fluorine or oxygen depending on the context. This variant shows how mass and atom count together determine identity.

🔍 Related terms

Avogadro's number, molar mass calculation, atoms to moles