a sample of H2SO4 has a mass of 15.0 grams. 1. calculate the number of moles of H2SO4 molecules in the sample. 2. What is the number of molecules of H2SO4 in the sample? 3. How many atoms are there in the sample? 4. Find the number of oxygen atoms in the sample.
The Correct Answer and Explanation is :
Given data:
- Mass of H₂SO₄ sample = 15.0 g
- Molar mass of H₂SO₄:
- H: 1.008 g/mol × 2 = 2.016 g/mol
- S: 32.065 g/mol
- O: 16.00 g/mol × 4 = 64.00 g/mol
- Total molar mass of H₂SO₄ = 98.08 g/mol
Step 1: Calculate the number of moles of H₂SO₄ molecules
[
\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{15.0 \text{ g}}{98.08 \text{ g/mol}}
]
[
= 0.153 \text{ moles of H₂SO₄}
]
Step 2: Find the number of molecules of H₂SO₄
Using Avogadro’s number (6.022 × 10²³ molecules/mol):
[
\text{Molecules} = \text{Moles} \times \text{Avogadro’s Number}
]
[
= 0.153 \times (6.022 \times 10^{23})
]
[
= 9.21 \times 10^{22} \text{ molecules of H₂SO₄}
]
Step 3: Find the total number of atoms in the sample
Each H₂SO₄ molecule contains:
- 2 H atoms
- 1 S atom
- 4 O atoms
- Total atoms per molecule = 2 + 1 + 4 = 7 atoms
Total atoms in the sample:
[
\text{Total atoms} = \text{Molecules} \times 7
]
[
= (9.21 \times 10^{22}) \times 7
]
[
= 6.45 \times 10^{23} \text{ atoms}
]
Step 4: Find the number of oxygen atoms
Each molecule of H₂SO₄ has 4 oxygen atoms, so:
[
\text{Total oxygen atoms} = \text{Molecules} \times 4
]
[
= (9.21 \times 10^{22}) \times 4
]
[
= 3.68 \times 10^{23} \text{ oxygen atoms}
]
Explanation (300 words)
Sulfuric acid (H₂SO₄) is a strong acid widely used in industries. In this problem, we calculated the number of moles, molecules, total atoms, and oxygen atoms in a 15.0 g sample of sulfuric acid.
First, to find the moles, we used the formula:
[
\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}
]
Since the molar mass of H₂SO₄ is 98.08 g/mol, dividing the sample’s mass (15.0 g) gives 0.153 moles of H₂SO₄.
Next, we determined the number of molecules using Avogadro’s number, which is 6.022 × 10²³ molecules/mol. By multiplying the moles by Avogadro’s number, we obtained 9.21 × 10²² molecules of H₂SO₄.
For the total number of atoms, we noted that each H₂SO₄ molecule has 7 atoms (2 hydrogen, 1 sulfur, and 4 oxygen). Multiplying the number of molecules by 7, we found 6.45 × 10²³ total atoms in the sample.
Finally, to determine the oxygen atoms, we noted that each H₂SO₄ molecule contains 4 oxygen atoms. Multiplying the number of molecules by 4 resulted in 3.68 × 10²³ oxygen atoms.
These calculations illustrate the atomic composition of sulfuric acid and are essential in chemistry for stoichiometric calculations, reaction balancing, and industrial applications.