To determine the mass of sulfur dioxide (SO₂) produced by burning 16 grams of sulfur (S) in excess oxygen, we'll follow these steps:
### Step 1: Determine the moles of sulfur (S)
Given the mass of sulfur and its atomic mass, we first calculate the number of moles of sulfur.
- Mass of sulfur (S): 16 grams
- Atomic mass of sulfur (S): 32 grams/mol
The formula for moles is:
[tex]\[ \text{Moles of sulfur} = \frac{\text{Mass of sulfur}}{\text{Atomic mass of sulfur}} \][/tex]
Substituting the values:
[tex]\[ \text{Moles of sulfur} = \frac{16\, \text{g}}{32\, \text{g/mol}} \][/tex]
[tex]\[ \text{Moles of sulfur} = 0.5\, \text{moles} \][/tex]
### Step 2: Use the stoichiometry of the reaction
The balanced chemical equation for the reaction is:
[tex]\[ S + O_2 \rightarrow SO_2 \][/tex]
This indicates that 1 mole of sulfur reacts with 1 mole of oxygen to produce 1 mole of sulfur dioxide (SO₂).
Therefore, 0.5 moles of sulfur will produce 0.5 moles of sulfur dioxide.
### Step 3: Calculate the molar mass of sulfur dioxide (SO₂)
To determine the mass of sulfur dioxide produced, we need its molar mass.
- Atomic mass of sulfur (S): 32 g/mol
- Atomic mass of oxygen (O): 16 g/mol
Sulfur dioxide (SO₂) consists of 1 sulfur atom and 2 oxygen atoms. Therefore, its molar mass is calculated as follows:
[tex]\[ \text{Molar mass of SO₂} = 32\, \text{g/mol} + 2 \times 16\, \text{g/mol} \][/tex]
[tex]\[ \text{Molar mass of SO₂} = 32\, \text{g/mol} + 32\, \text{g/mol} \][/tex]
[tex]\[ \text{Molar mass of SO₂} = 64\, \text{g/mol} \][/tex]
### Step 4: Calculate the mass of sulfur dioxide produced
Finally, we use the number of moles of sulfur dioxide and its molar mass to find the mass of sulfur dioxide produced.
[tex]\[ \text{Mass of SO₂} = \text{Moles of SO₂} \times \text{Molar mass of SO₂} \][/tex]
Substituting the values:
[tex]\[ \text{Mass of SO₂} = 0.5\, \text{moles} \times 64\, \text{g/mol} \][/tex]
[tex]\[ \text{Mass of SO₂} = 32\, \text{g} \][/tex]
Thus, the mass of sulfur dioxide produced by burning 16 grams of sulfur in excess oxygen is 32 grams.
### Explanation of Average Atomic Mass
The term "average atomic mass" accounts for the fact that many elements exist as mixtures of isotopes, each with different masses. The average atomic mass is the weighted average of these isotopic masses based on their natural abundance. For example, sulfur has several isotopes, but for many calculations, particularly at a high school or general chemistry level, the average atomic mass given (32 g/mol for sulfur) is sufficient and is commonly used in stoichiometric calculations.
