Question

what is the minimum mass of oxygen gas necessary to produce 200. g of sulfuric acid in the following reaction?
2so₂ + o₂ + 2 h₂o → 2h₂so₄
62.6 g
52.6 g
42.6 g
32.6 g
none of the above

Explanation:

Step1: Calculate molar mass of \(H_2SO_4\)

Molar mass of \(H_2SO_4\) = \(2\times1 + 32 + 4\times16\) = \(2 + 32 + 64\) = \(98\space g/mol\)

Step2: Moles of \(H_2SO_4\)

Moles of \(H_2SO_4\) = \(\frac{mass}{molar\space mass}\) = \(\frac{200\space g}{98\space g/mol}\) ≈ \(2.0408\space mol\)

Step3: Mole ratio from reaction

From reaction \(2SO_2 + O_2 + 2H_2O
ightarrow 2H_2SO_4\), mole ratio of \(O_2\) to \(H_2SO_4\) is \(1:2\)
So moles of \(O_2\) = \(\frac{1}{2}\times\) moles of \(H_2SO_4\) = \(\frac{1}{2}\times2.0408\space mol\) ≈ \(1.0204\space mol\)

Step4: Mass of \(O_2\)

Molar mass of \(O_2\) = \(32\space g/mol\)
Mass of \(O_2\) = moles \(\times\) molar mass = \(1.0204\space mol\times32\space g/mol\) ≈ \(32.65\space g\) ≈ \(32.6\space g\)

Answer:

32.6 g