Answer :
- Calculate the molar mass of $H_2SO_4$: $(2 Imes 1.008) + (1 Imes 32.06) + (4 Imes 16.00) = 98.076 \text{ g/mol}$.
- Find the molar mass of S: $32.06 \text{ g/mol}$.
- Calculate the percent composition of S in $H_2SO_4$: $\frac{32.06}{98.076} \times 100 \approx 32.69\%$.
- The percent composition of sulfur in $H_2SO_4$ is approximately $\boxed{32.7 \%}$.
### Explanation
1. Understanding the Problem
We want to find the percent composition of sulfur (S) in sulfuric acid ($H_2SO_4$). This tells us what percentage of the total mass of sulfuric acid is made up of sulfur.
2. Calculating Molar Mass of Sulfuric Acid
First, we need to calculate the molar mass of sulfuric acid ($H_2SO_4$). We can do this by adding up the molar masses of all the atoms in the molecule. The molar mass of hydrogen (H) is approximately 1.008 g/mol, sulfur (S) is approximately 32.06 g/mol, and oxygen (O) is approximately 16.00 g/mol. So, the molar mass of $H_2SO_4$ is: $$(2 \times 1.008) + (1 \,\times 32.06) + (4 \times 16.00) = 2.016 + 32.06 + 64.00 = 98.076 \text{ g/mol}$$.
3. Finding Molar Mass of Sulfur
Next, we need to find the molar mass of sulfur (S), which is approximately 32.06 g/mol.
4. Calculating Percent Composition of Sulfur
Now, we can calculate the percent composition of sulfur in $H_2SO_4$ using the formula: $$\% \text{S} = \frac{\text{Molar mass of S}}{\text{Molar mass of } H_2SO_4} \times 100$$ Plugging in the values we found: $$\% \text{S} = \frac{32.06 \text{ g/mol}}{98.076 \text{ g/mol}} \times 100 \approx 32.69\% $$
5. Final Answer
Therefore, the percent composition of sulfur in $H_2SO_4$ 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 example, in environmental science, it helps in assessing the sulfur content in coal, which contributes to acid rain when burned. In agriculture, it's used to determine the sulfur content in fertilizers, ensuring plants receive the necessary nutrients for growth. In pharmaceuticals, it helps in determining the exact composition of drugs to ensure their safety and efficacy.
- Find the molar mass of S: $32.06 \text{ g/mol}$.
- Calculate the percent composition of S in $H_2SO_4$: $\frac{32.06}{98.076} \times 100 \approx 32.69\%$.
- The percent composition of sulfur in $H_2SO_4$ is approximately $\boxed{32.7 \%}$.
### Explanation
1. Understanding the Problem
We want to find the percent composition of sulfur (S) in sulfuric acid ($H_2SO_4$). This tells us what percentage of the total mass of sulfuric acid is made up of sulfur.
2. Calculating Molar Mass of Sulfuric Acid
First, we need to calculate the molar mass of sulfuric acid ($H_2SO_4$). We can do this by adding up the molar masses of all the atoms in the molecule. The molar mass of hydrogen (H) is approximately 1.008 g/mol, sulfur (S) is approximately 32.06 g/mol, and oxygen (O) is approximately 16.00 g/mol. So, the molar mass of $H_2SO_4$ is: $$(2 \times 1.008) + (1 \,\times 32.06) + (4 \times 16.00) = 2.016 + 32.06 + 64.00 = 98.076 \text{ g/mol}$$.
3. Finding Molar Mass of Sulfur
Next, we need to find the molar mass of sulfur (S), which is approximately 32.06 g/mol.
4. Calculating Percent Composition of Sulfur
Now, we can calculate the percent composition of sulfur in $H_2SO_4$ using the formula: $$\% \text{S} = \frac{\text{Molar mass of S}}{\text{Molar mass of } H_2SO_4} \times 100$$ Plugging in the values we found: $$\% \text{S} = \frac{32.06 \text{ g/mol}}{98.076 \text{ g/mol}} \times 100 \approx 32.69\% $$
5. Final Answer
Therefore, the percent composition of sulfur in $H_2SO_4$ 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 example, in environmental science, it helps in assessing the sulfur content in coal, which contributes to acid rain when burned. In agriculture, it's used to determine the sulfur content in fertilizers, ensuring plants receive the necessary nutrients for growth. In pharmaceuticals, it helps in determining the exact composition of drugs to ensure their safety and efficacy.
