1. Balanced Chemical Equation:

First, we need the balanced chemical equation for the reaction of methane (CH₄) with chlorine (Cl₂) to produce dichloromethane (CH₂Cl₂):

CH₄ + 2Cl₂ → CH₂Cl₂ + 2HCl

2. Mole Ratios:

The equation tells us that 1 mole of methane reacts to produce 1 mole of dichloromethane.

3. Convert Mass of Methane to Moles:

* Molar mass of methane (CH₄) = 12.01 g/mol (C) + 4 * 1.01 g/mol (H) = 16.05 g/mol

* Mass of methane = 1.54 kg = 1540 g

* Moles of methane = 1540 g / 16.05 g/mol = 95.96 mol

4. Calculate Theoretical Yield of Dichloromethane:

* Since the mole ratio is 1:1, the theoretical yield of dichloromethane is also 95.96 mol.

5. Calculate Actual Yield of Dichloromethane:

* Percent yield = (actual yield / theoretical yield) * 100%

* Actual yield = (Percent yield / 100%) * Theoretical yield

* Actual yield = (48.2 / 100) * 95.96 mol = 46.26 mol

6. Convert Moles of Dichloromethane to Grams:

* Molar mass of dichloromethane (CH₂Cl₂) = 12.01 g/mol (C) + 2 * 1.01 g/mol (H) + 2 * 35.45 g/mol (Cl) = 84.93 g/mol

* Mass of dichloromethane = 46.26 mol * 84.93 g/mol = 3935 g

Therefore, 3935 grams of dichloromethane result from the reaction of 1.54 kg of methane with a yield of 48.2%.