The reaction you described is actually a displacement reaction, where magnesium bromide (MgBr₂) reacts with hydrochloric acid (HCl) to produce magnesium chloride (MgCl₂) and hydrobromic acid (HBr).

Here's the balanced chemical equation:

MgBr₂ (aq) + 2 HCl (aq) → MgCl₂ (aq) + 2 HBr (aq)

Here's the breakdown:

* MgBr₂: Magnesium bromide, a soluble ionic compound.

* HCl: Hydrochloric acid, a strong acid.

* MgCl₂: Magnesium chloride, another soluble ionic compound.

* HBr: Hydrobromic acid, a strong acid.

The equation is balanced because the number of atoms of each element on both sides of the equation is the same:

* Mg: 1 on each side

* Br: 2 on each side

* H: 2 on each side

* Cl: 2 on each side

Important Note: The reaction is not a simple acid-base reaction, as it might seem initially. While both HCl and HBr are acids, the key driving force is the higher reactivity of chlorine compared to bromine. This leads to the displacement of bromide ions from magnesium bromide by chloride ions from hydrochloric acid.