Calculate The Number Of Atoms In Each Sample: 1.59 G
A. 14.955 G Cr
B. 39.733 G S
C. 12.899 G Pt
D. 97.552 G Sn
E. 163.215g Oz (Think About This One Before You Start)
The Correct Answer and Explanation is :
To calculate the number of atoms in each sample, we use the mole concept and Avogadro’s number.
Steps to Calculate:
- Find the atomic mass of the element from the periodic table.
- Convert grams to moles using the formula:
[
\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}
] - Convert moles to atoms using Avogadro’s number:
[
\text{Atoms} = \text{Moles} \times (6.022 \times 10^{23} \text{ atoms/mol})
]
Now, let’s compute each:
A. Chromium (Cr)
- Atomic Mass = 51.996 g/mol
- Moles = ( \frac{14.955}{51.996} = 0.2876 ) mol
- Atoms = ( 0.2876 \times 6.022 \times 10^{23} )
- = 1.73 × 10²³ atoms
B. Sulfur (S)
- Atomic Mass = 32.065 g/mol
- Moles = ( \frac{39.733}{32.065} = 1.24 ) mol
- Atoms = ( 1.24 \times 6.022 \times 10^{23} )
- = 7.47 × 10²³ atoms
C. Platinum (Pt)
- Atomic Mass = 195.084 g/mol
- Moles = ( \frac{12.899}{195.084} = 0.0662 ) mol
- Atoms = ( 0.0662 \times 6.022 \times 10^{23} )
- = 3.98 × 10²² atoms
D. Tin (Sn)
- Atomic Mass = 118.710 g/mol
- Moles = ( \frac{97.552}{118.710} = 0.8218 ) mol
- Atoms = ( 0.8218 \times 6.022 \times 10^{23} )
- = 4.95 × 10²³ atoms
E. Oz (Think First!)
- “Oz” commonly refers to ounces (not an element).
- If it meant Oxygen (O), we need to clarify if it’s O (atom) or O₂ (molecule).
- Assuming O (atomic oxygen):
- Atomic Mass = 16.00 g/mol
- Moles = ( \frac{163.215}{16.00} = 10.20 ) mol
- Atoms = ( 10.20 \times 6.022 \times 10^{23} )
- = 6.14 × 10²⁴ atoms
Explanation (300 words)
The calculation of the number of atoms in a sample involves converting mass to moles and then using Avogadro’s number. The molar mass (or atomic mass) is taken from the periodic table in grams per mole (g/mol). This helps determine how many moles are present in the given mass.
Moles represent the quantity of a substance that contains 6.022 × 10²³ particles (atoms, molecules, or ions). This is known as Avogadro’s constant. By multiplying the number of moles by Avogadro’s number, we obtain the total number of atoms.
For example, in the case of Sulfur (S), with a given mass of 39.733 g and an atomic mass of 32.065 g/mol, we first convert the mass to moles:
[
Moles = \frac{39.733}{32.065} = 1.24 \text{ moles}
]
Multiplying this by Avogadro’s number gives:
[
1.24 \times 6.022 \times 10^{23} = 7.47 \times 10^{23} \text{ atoms}
]
A tricky part in this question is “Oz” in part E. If it refers to ounces (not an element), then the problem is misleading. However, if it means oxygen (O), we must clarify whether it refers to atomic oxygen (O) or molecular oxygen (O₂). If we assume atomic oxygen, we follow the same process using 16.00 g/mol as the atomic mass.
Understanding these conversions is essential in chemistry as it allows scientists to calculate substance amounts in chemical reactions and everyday applications like pharmaceuticals and materials science.