Calculate the percentage mass of oxygen in sulfur dioxide, $SO_2$.
Answer (2)
The percentage mass of oxygen in sulfur dioxide (SO_2) is approximately 49.95%, calculated by finding the molar masses of sulfur and oxygen, the total mass of oxygen in the compound, and then calculating the percentage based on these values.
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Determine the molar masses of sulfur ( S ) and oxygen ( O ): M ( S ) ≈ 32.06 m o l g and M ( O ) ≈ 16.00 m o l g .
Calculate the molar mass of sulfur dioxide ( S O 2 ): M ( S O 2 ) = M ( S ) + 2 × M ( O ) = 64.06 m o l g .
Calculate the total mass of oxygen in S O 2 : 2 × M ( O ) = 32.00 m o l g .
Calculate the percentage mass of oxygen in S O 2 : 64.06 32.00 × 100% ≈ 49.95% .
Explanation
Understanding the Problem We are asked to calculate the percentage mass of oxygen in sulfur dioxide, which has the chemical formula S O 2 . This means we need to find what percentage of the total mass of the S O 2 molecule is made up of oxygen. To do this, we will use the molar masses of sulfur and oxygen.
Finding Molar Masses First, we need to find the molar mass of sulfur (S) and oxygen (O). From the periodic table, we have:
M ( S ) ≈ 32.06 m o l g M ( O ) ≈ 16.00 m o l g
Calculating Molar Mass of S O 2 Next, we calculate the molar mass of S O 2 . Since there is one sulfur atom and two oxygen atoms in the molecule, the molar mass of S O 2 is:
M ( S O 2 ) = M ( S ) + 2 × M ( O ) = 32.06 + 2 × 16.00 = 32.06 + 32.00 = 64.06 m o l g
Calculating Total Mass of Oxygen Now, we calculate the total mass of oxygen in one mole of S O 2 . Since there are two oxygen atoms, the total mass of oxygen is:
2 × M ( O ) = 2 × 16.00 = 32.00 m o l g
Calculating Percentage Mass To find the percentage mass of oxygen in S O 2 , we divide the total mass of oxygen by the molar mass of S O 2 and multiply by 100%:
M ( S O 2 ) 2 × M ( O ) × 100% = 64.06 32.00 × 100% ≈ 49.95%
Final Answer Therefore, the percentage mass of oxygen in sulfur dioxide ( S O 2 ) is approximately 49.95%.
Examples
Understanding the percentage composition of elements in chemical compounds is crucial in various fields. For instance, in environmental science, knowing the percentage of sulfur and oxygen in sulfur dioxide ( S O 2 ) helps in assessing its contribution to acid rain. In industrial chemistry, this knowledge aids in optimizing chemical reactions and ensuring product quality. Moreover, in materials science, the composition of compounds determines their properties and applications. Thus, calculating percentage mass is a fundamental skill with wide-ranging practical applications.
