1. Balanced Equation:

The balanced chemical equation for the reaction is:

2 H₂S + 3 O₂ → 2 SO₂ + 2 H₂O

2. Mole Ratios:

From the balanced equation, we see the following mole ratios:

* 2 moles of H₂S react with 3 moles of O₂ to produce 2 moles of SO₂.

3. Ideal Gas Law:

We'll use the ideal gas law to relate volume and moles:

* PV = nRT

* Where:

* P = pressure (assumed constant)

* V = volume

* n = number of moles

* R = ideal gas constant

* T = temperature (assumed constant)

Since pressure and temperature are constant, we can simplify this to:

* V₁ / n₁ = V₂ / n₂ (where V and n represent the volume and moles of any of the gases involved)

4. Calculation:

* Step 1: Find moles of SO₂:

* Assume standard temperature and pressure (STP: 0°C and 1 atm)

* At STP, 1 mole of any gas occupies 22.4 L.

* Therefore, 14.2 L of SO₂ corresponds to (14.2 L / 22.4 L/mol) = 0.634 moles of SO₂.

* Step 2: Calculate moles of H₂S and O₂:

* From the mole ratios in the balanced equation:

* Moles of H₂S = (0.634 moles SO₂) * (2 moles H₂S / 2 moles SO₂) = 0.634 moles H₂S

* Moles of O₂ = (0.634 moles SO₂) * (3 moles O₂ / 2 moles SO₂) = 0.951 moles O₂

* Step 3: Convert moles to volume (at STP):

* Volume of H₂S = (0.634 moles H₂S) * (22.4 L/mol) = 14.2 L H₂S

* Volume of O₂ = (0.951 moles O₂) * (22.4 L/mol) = 21.3 L O₂

Answer:

You need 14.2 L of H₂S gas and 21.3 L of oxygen gas to produce 14.2 L of sulfur dioxide at standard temperature and pressure (STP).