What's the percent composition of sulfur in [tex]$H _2 SO _4$[/tex]?
A) [tex]$2.1 \%$[/tex]
B) [tex]$32.7 \%$[/tex]
C) [tex]$65.2 \%$[/tex]
D) [tex]$98.1 \%$[/tex]
Answer (1)
Calculate the molar mass of H 2 S O 4 : ( 2 × 1.008 ) + ( 1 × 32.06 ) + ( 4 × 16.00 ) = 98.076 g/mol .
Determine the mass of sulfur in one mole of H 2 S O 4 : 32.06 g/mol .
Divide the mass of sulfur by the molar mass of H 2 S O 4 and multiply by 100: 98.076 32.06 × 100 ≈ 32.69% .
The percent composition of sulfur in H 2 S O 4 is approximately 32.7% .
Explanation
Problem Analysis We want to find the percentage of sulfur (S) in sulfuric acid ( H 2 S O 4 ). To do this, we need to calculate the molar mass of H 2 S O 4 , then find the mass of sulfur in one mole of H 2 S O 4 , and finally divide the mass of sulfur by the molar mass of H 2 S O 4 and multiply by 100.
Calculating Molar Mass of Sulfuric Acid First, we calculate the molar mass of H 2 S O 4 . The molar masses of each element are approximately:
Hydrogen (H): 1.008 g/mol
Sulfur (S): 32.06 g/mol
Oxygen (O): 16.00 g/mol
So, the molar mass of H 2 S O 4 is:
( 2 × 1.008 ) + ( 1 × 32.06 ) + ( 4 × 16.00 ) = 2.016 + 32.06 + 64.00 = 98.076 g/mol
Determining Mass of Sulfur Next, we find the mass of sulfur in one mole of H 2 S O 4 . There is one sulfur atom in each molecule of H 2 S O 4 , so the mass of sulfur is simply its molar mass, which is 32.06 g/mol.
Calculating Percent Composition Now, we divide the mass of sulfur by the molar mass of H 2 S O 4 and multiply by 100 to find the percent composition of sulfur:
98.076 g/mol 32.06 g/mol × 100 ≈ 32.69%
Final Answer Therefore, the percent composition of sulfur in H 2 S O 4 is approximately 32.69%. Looking at the answer choices, the closest answer is 32.7%.
Examples
Understanding percent composition is crucial in various fields. For instance, in agriculture, knowing the sulfur content in fertilizers helps farmers optimize plant growth, as sulfur is an essential nutrient. Similarly, in environmental science, determining the sulfur content in pollutants like sulfur dioxide ( S O 2 ) aids in assessing air quality and its impact on ecosystems. In chemical manufacturing, precise knowledge of elemental composition ensures the quality and consistency of products, such as sulfuric acid used in various industrial processes. This concept helps in accurately formulating compounds for specific applications.
