Balanced equation : 2C₂H₆ (g) + 7O₂ (g) ⟶ 4CO₂ (g) + 6H₂O (ℓ)
Further explanation
Alkanes are saturated hydrocarbons that have single bonds in chains
General formula for alkanes :

Hydrocarbon combustion reactions (specifically alkanes)

So that the burning of ethane with air (oxygen):

2C₂H₆ (g) + 7O₂ (g) ⟶ 4CO₂ (g) + 6H₂O (ℓ)
or we can use mathematical equations to solve equilibrium chemical equations by giving the coefficients for each compound involved in the reaction
C₂H₆ (g) + aO₂ (g) ⟶ bCO₂ (g) + cH₂O (ℓ)
C : left 2, right b ⇒ b=2
H: left 6, right 2c⇒ 2c=6⇒ c= 3
O : left 2a, right 2b+c⇒ 2a=2b+c⇒2a=2.2+3⇒2a=7⇒a=7/2