The balanced chemical equation for the reaction of methane (CH4) with fluorine (F2) to produce hydrogen fluoride (HF) and fluoroform (CHF3) is:

CH4 + 4F2 → 4HF + CHF3

Here's how to balance the equation:

1. Count the atoms on each side:

* Reactants: 1 C, 4 H, 8 F

* Products: 1 C, 1 H, 7 F

2. Balance the carbon atoms: Both sides have 1 carbon atom, so this is already balanced.

3. Balance the hydrogen atoms: The reactants have 4 hydrogen atoms, and the products only have 1. To balance, add a coefficient of 4 in front of HF:

* CH4 + 4F2 → 4HF + CHF3

4. Balance the fluorine atoms: The reactants have 8 fluorine atoms, and the products now have 7. Add a coefficient of 4 in front of F2:

* CH4 + 4F2 → 4HF + CHF3

Now the equation is balanced, as both sides have 1 carbon, 4 hydrogen, and 8 fluorine atoms.