Sulfur dioxide will react with water to form sulfurous acid (see balanced equation below).
SO2(g) + H20() → H2SO3()
What mass of sulfur dioxide is needed to prepare 27.86 g of H2SO3
(b? Molar mass: SO2: 64.06 g/mol
Molar mass: H2SO3: 82.08 g/mol
a. 21.74 g b.0.4348 g c. 35.69 g d. 0.3394 g e. 27.86 g
The Correct Answer and Explanation is :
To determine the mass of sulfur dioxide (SO₂) needed to prepare 27.86 g of sulfurous acid (H₂SO₃), we need to follow the steps of stoichiometric calculations. The chemical equation provided is:
[
\text{SO}_2(g) + \text{H}_2\text{O}(l) \rightarrow \text{H}_2\text{SO}_3(aq)
]
Step 1: Calculate moles of H₂SO₃
First, calculate the number of moles of H₂SO₃ that corresponds to 27.86 grams. We use the molar mass of H₂SO₃, which is given as 82.08 g/mol.
[
\text{moles of H}_2\text{SO}_3 = \frac{\text{mass of H}_2\text{SO}_3}{\text{molar mass of H}_2\text{SO}_3} = \frac{27.86 \, \text{g}}{82.08 \, \text{g/mol}} = 0.3394 \, \text{mol}
]
Step 2: Use stoichiometry to find moles of SO₂
From the balanced chemical equation, we can see that the mole ratio between SO₂ and H₂SO₃ is 1:1. This means that for every 1 mole of H₂SO₃ produced, 1 mole of SO₂ is consumed.
So, the moles of SO₂ needed will be the same as the moles of H₂SO₃:
[
\text{moles of SO}_2 = 0.3394 \, \text{mol}
]
Step 3: Calculate the mass of SO₂
Next, we convert the moles of SO₂ to grams. Using the molar mass of SO₂, which is 64.06 g/mol, we can find the mass of SO₂ required:
[
\text{mass of SO}_2 = \text{moles of SO}_2 \times \text{molar mass of SO}_2 = 0.3394 \, \text{mol} \times 64.06 \, \text{g/mol} = 21.74 \, \text{g}
]
Step 4: Conclusion
The correct answer is 21.74 g, which corresponds to option (a). Therefore, 21.74 grams of sulfur dioxide is needed to prepare 27.86 grams of sulfurous acid.
Summary
To summarize, we used the molar mass of H₂SO₃ to find the number of moles, then used stoichiometry to relate the moles of H₂SO₃ to the moles of SO₂, and finally converted moles of SO₂ to grams using its molar mass. This approach gives us the correct mass of SO₂ required to prepare the desired amount of H₂SO₃.