Calculate the percentage mass of sulfur in sulfur dioxide, $SO_2$.
Answer (2)
To find the percentage mass of sulfur in sulfur dioxide (SO₂), we first determined the molar mass of SO₂, which is 64.06 u. By using the atomic mass of sulfur (32.06 u), we calculated that the percentage mass of sulfur in SO₂ is approximately 50.05%. Therefore, sulfur constitutes about 50.05% of the mass of sulfur dioxide.
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Determine the relative atomic masses of sulfur (S) and oxygen (O).
Calculate the molar mass of S O 2 by summing the masses of its constituent atoms: M o l a r ma ss o f S O 2 = 32.06 + 2 ( 16.00 ) = 64.06 u .
Compute the percentage mass of sulfur in S O 2 using the formula: P erce n t a g e ma ss o f S = 64.06 32.06 × 100 .
The percentage mass of sulfur in S O 2 is approximately 50.05% .
Explanation
Understanding the Problem Let's break down how to calculate the percentage mass of sulfur in sulfur dioxide ( S O 2 ). This involves understanding the chemical formula and the atomic masses of the elements involved.
Identifying Atomic Masses First, we need to know the relative atomic masses of sulfur (S) and oxygen (O). From the periodic table:
The relative atomic mass of sulfur (S) is approximately 32.06 u.
The relative atomic mass of oxygen (O) is approximately 16.00 u.
Calculating Molar Mass of S O 2 Next, we calculate the molar mass of sulfur dioxide ( S O 2 ). Since the formula has one sulfur atom and two oxygen atoms, we calculate it as follows:
M o l a r , ma ss , o f , S O 2 = ( 1 t im es M o l a r , ma ss , o f , S ) + ( 2 t im es M o l a r , ma ss , o f , O ) M o l a r , ma ss , o f , S O 2 = ( 1 t im es 32.06 , u ) + ( 2 t im es 16.00 , u ) M o l a r , ma ss , o f , S O 2 = 32.06 , u + 32.00 , u M o l a r , ma ss , o f , S O 2 = 64.06 , u
Calculating Percentage Mass of Sulfur Now, we calculate the percentage mass of sulfur in S O 2 . This is the ratio of the mass of sulfur to the molar mass of S O 2 , multiplied by 100:
P erce n t a g e , ma ss , o f , S , in , S O 2 = f r a c M a ss , o f , S M o l a r , ma ss , o f , S O 2 t im es 100 P erce n t a g e , ma ss , o f , S , in , S O 2 = f r a c 32.06 , u 64.06 , u t im es 100 P erce n t a g e , ma ss , o f , S , in , S O 2 = 0.500468 t im es 100 P erce n t a g e , ma ss , o f , S , in , S O 2 = 50.0468 Rounding to two decimal places, we get 50.05%.
Final Answer Therefore, the percentage mass of sulfur in sulfur dioxide ( S O 2 ) is approximately 50.05%.
Examples
Understanding percentage composition is crucial in various fields. For instance, in environmental science, knowing the percentage of sulfur in sulfur dioxide helps assess air quality and pollution levels. In chemistry, it's essential for stoichiometric calculations and understanding compound properties. Moreover, in industrial processes, such as manufacturing sulfuric acid, knowing the precise composition ensures efficient and controlled reactions, leading to optimized production and reduced waste. This concept helps in quantifying the elemental makeup of compounds, enabling better analysis and application in real-world scenarios.
