Here's the balanced equation for the combustion of dimethyl ether (CH₃OCH₃) in air:

CH₃OCH₃ + 3O₂ → 2CO₂ + 3H₂O

Explanation:

* Reactants:

* Dimethyl ether (CH₃OCH₃) - the fuel.

* Oxygen (O₂) - from the air, the oxidant.

* Products:

* Carbon dioxide (CO₂)

* Water (H₂O)

Balancing the Equation:

1. Carbon (C): There are 2 carbon atoms on the left side and 2 on the right. Balanced.

2. Hydrogen (H): There are 6 hydrogen atoms on the left and 6 on the right. Balanced.

3. Oxygen (O): There are 3 oxygen atoms on the left and 7 on the right. We need to adjust the coefficients:

* Place a coefficient of 3 in front of O₂ on the left side (3 x 2 = 6 oxygen atoms).

* Now the oxygen atoms are balanced: 3 on the left + 4 on the right = 7.

This results in the balanced equation: CH₃OCH₃ + 3O₂ → 2CO₂ + 3H₂O