Calculate the number of atoms in each sample.

Calculate the number of atoms in each sample. a. 14.955 g Cr b. 39.733 g S c. 12.899 g Pt d. 97.552 g Sn

The Correct Answer and Explanation is:

To calculate the number of atoms in each sample, we use the formula:Number of atoms=Mass of sample (g)Molar mass (g/mol)×Avogadro’s number\text{Number of atoms} = \frac{\text{Mass of sample (g)}}{\text{Molar mass (g/mol)}} \times \text{Avogadro’s number} Number of atoms=Molar mass (g/mol)Mass of sample (g)​×Avogadro’s number

Where:

• Molar mass is the atomic mass of the element (in grams per mole),
• Avogadro’s number is 6.022×1023 atoms/mol6.022 \times 10^{23} \, \text{atoms/mol}6.022×1023atoms/mol.

Let’s break it down for each sample:

a. 14.955 g Cr (Chromium)

The atomic mass of Chromium (Cr) is 52.00 g/mol.Number of atoms=14.955 g52.00 g/mol×6.022×1023 atoms/mol\text{Number of atoms} = \frac{14.955 \, \text{g}}{52.00 \, \text{g/mol}} \times 6.022 \times 10^{23} \, \text{atoms/mol}Number of atoms=52.00g/mol14.955g​×6.022×1023atoms/molNumber of atoms=14.95552.00×6.022×1023\text{Number of atoms} = \frac{14.955}{52.00} \times 6.022 \times 10^{23} Number of atoms=52.0014.955​×6.022×1023Number of atoms=0.287×6.022×1023\text{Number of atoms} = 0.287 \times 6.022 \times 10^{23}Number of atoms=0.287×6.022×1023Number of atoms≈1.73×1023 atoms\text{Number of atoms} \approx 1.73 \times 10^{23} \, \text{atoms}Number of atoms≈1.73×1023atoms

b. 39.733 g S (Sulfur)

The atomic mass of Sulfur (S) is 32.06 g/mol.Number of atoms=39.733 g32.06 g/mol×6.022×1023 atoms/mol\text{Number of atoms} = \frac{39.733 \, \text{g}}{32.06 \, \text{g/mol}} \times 6.022 \times 10^{23} \, \text{atoms/mol}Number of atoms=32.06g/mol39.733g​×6.022×1023atoms/molNumber of atoms=39.73332.06×6.022×1023\text{Number of atoms} = \frac{39.733}{32.06} \times 6.022 \times 10^{23}Number of atoms=32.0639.733​×6.022×1023Number of atoms=1.24×6.022×1023\text{Number of atoms} = 1.24 \times 6.022 \times 10^{23}Number of atoms=1.24×6.022×1023Number of atoms≈7.47×1023 atoms\text{Number of atoms} \approx 7.47 \times 10^{23} \, \text{atoms}Number of atoms≈7.47×1023atoms

c. 12.899 g Pt (Platinum)

The atomic mass of Platinum (Pt) is 195.08 g/mol.Number of atoms=12.899 g195.08 g/mol×6.022×1023 atoms/mol\text{Number of atoms} = \frac{12.899 \, \text{g}}{195.08 \, \text{g/mol}} \times 6.022 \times 10^{23} \, \text{atoms/mol}Number of atoms=195.08g/mol12.899g​×6.022×1023atoms/molNumber of atoms=12.899195.08×6.022×1023\text{Number of atoms} = \frac{12.899}{195.08} \times 6.022 \times 10^{23}Number of atoms=195.0812.899​×6.022×1023Number of atoms=0.0662×6.022×1023\text{Number of atoms} = 0.0662 \times 6.022 \times 10^{23}Number of atoms=0.0662×6.022×1023Number of atoms≈3.98×1022 atoms\text{Number of atoms} \approx 3.98 \times 10^{22} \, \text{atoms}Number of atoms≈3.98×1022atoms

d. 97.552 g Sn (Tin)

The atomic mass of Tin (Sn) is 118.71 g/mol.Number of atoms=97.552 g118.71 g/mol×6.022×1023 atoms/mol\text{Number of atoms} = \frac{97.552 \, \text{g}}{118.71 \, \text{g/mol}} \times 6.022 \times 10^{23} \, \text{atoms/mol}Number of atoms=118.71g/mol97.552g​×6.022×1023atoms/molNumber of atoms=97.552118.71×6.022×1023\text{Number of atoms} = \frac{97.552}{118.71} \times 6.022 \times 10^{23}Number of atoms=118.7197.552​×6.022×1023Number of atoms=0.823×6.022×1023\text{Number of atoms} = 0.823 \times 6.022 \times 10^{23}Number of atoms=0.823×6.022×1023Number of atoms≈4.96×1023 atoms\text{Number of atoms} \approx 4.96 \times 10^{23} \, \text{atoms}Number of atoms≈4.96×1023atoms

Summary of Results:

• a) 14.955 g Cr: 1.73×10231.73 \times 10^{23}1.73×1023 atoms
• b) 39.733 g S: 7.47×10237.47 \times 10^{23}7.47×1023 atoms
• c) 12.899 g Pt: 3.98×10223.98 \times 10^{22}3.98×1022 atoms
• d) 97.552 g Sn: 4.96×10234.96 \times 10^{23}4.96×1023 atoms

This calculation is based on the molar masses and the relationship between mass, moles, and atoms using Avogadro’s constant.