Question

A 20.0-g sample of an element contains 1.37 × 10²³ atoms.

Identify the element.
-OK
-Te
-Sr
-Cu

Answer 1

The element in a 20.0-g sample with 1.37 × 10²³ atoms is identified by calculating the number of moles in the sample and comparing the computed molar mass to the molar masses of the given elements, which indicates the sample is likely copper (Cu).

Step-by-step explanation:

To identify the element of a 20.0-g sample that contains 1.37 × 10²³ atoms, we will use Avogadro's number and the concept of molar mass. Avogadro's number tells us that one mole of any substance contains 6.022 × 10²³ atoms. Therefore, by comparing the given number of atoms to Avogadro's number, we can calculate the number of moles of the element in the sample. We then use the molar mass of each potentially given element to identify which one corresponds to the sample's mass for that number of moles.

First, we calculate the moles of the sample:

1.37 × 10²³ atoms × (1 mol / 6.022 × 10²³ atoms) = approximately 0.227 moles.

Looking at the molar masses provided from the reference information, we divide the sample mass by the number of moles to find the molar mass that matches:

• 20.0 g / 0.227 moles = 88.11 g/mol

Comparing this with the molar masses given:

• Sulfur (S) = 32.1 g/mol
• Silicon (Si) = 28.1 g/mol
• Lead (Pb) = 207 g/mol
• Tin (Sn) = 118.7 g/mol
• Copper (Cu) = 63.5 g/mol

The molar mass closest to 88.11 g/mol from the options provided is Copper (Cu). Therefore, the element in the sample is likely copper (Cu).

Answer 2

To identify the element, we calculate the atomic mass using the sample's mass and the provided number of atoms. The calculation shows that copper (Cu), with a molar mass of 63.5 g/mol, matches the properties of the sample.

Step-by-step explanation:

To identify the element from the given options based on the atomic mass and the number of atoms present in a 20.0-g sample, we must first understand that one mole of any element contains an Avogadro's number of atoms, which is 6.022 × 1023 atoms.

The given number of atoms in the sample is 1.37 × 1023, which is approximately one-quarter of Avogadro's number. Therefore, we are looking for an element whose atomic mass is approximately four times the mass of the given sample, because one mole of that element would have four times the mass.

Calculating the molar mass for the given sample: 20.0 g/(1.37 × 1023 atoms) × (6.022 × 1023 atoms/mol) = 63.5 g/mol. By comparing this calculated molar mass with the options provided, we find that copper (Cu) has a molar mass of 63.5 g/mol and therefore is the element in the sample.