Question

A 3.0 g sample of an element contains 3.474 1022 atoms. identify the element.

Answer 1

The element with the molar mass closest to 52.0 g/mol for a 3.0 g sample containing 3.474 × 1022 atoms is chromium (Cr).

Step-by-step explanation:

To identify the element based on the given sample mass and number of atoms, we can calculate the element's molar mass (atomic weight) using Avogadro's number (6.02 × 1023 atoms/mol). The molar mass in grams per mole is found by dividing the sample mass by the number of moles, which is calculated from the given number of atoms.

The steps are as follows:

1. Calculate the number of moles of the element using the given number of atoms and Avogadro's number: Moles = Number of atoms / Avogadro's number.
2. Determine the molar mass (in g/mol) by dividing the sample mass by the number of moles calculated in step 1.
3. Compare the calculated molar mass with the known molar masses of elements to identify the element.

Let's apply these steps:

1. Number of moles = 3.474 × 1022 atoms / 6.02 × 1023 atoms/mol = 0.0577 mol

2. Molar Mass = 3.0 g / 0.0577 mol = 52.0 g/mol

The molar mass closest to 52.0 g/mol among common elements is that of chromium (Cr), which has an atomic mass of approximately 52 amu.