The reaction that causes aqueous solutions of alkali metal carbonates to be basic is the hydrolysis of the carbonate ion (CO₃²⁻).

Here's how it works:

1. Dissolution: When an alkali metal carbonate (like sodium carbonate, Na₂CO₃) is dissolved in water, it dissociates into its ions:

```

Na₂CO₃(s) → 2Na⁺(aq) + CO₃²⁻(aq)

```

2. Hydrolysis: The carbonate ion (CO₃²⁻) reacts with water molecules in a reversible reaction:

```

CO₃²⁻(aq) + H₂O(l) ⇌ HCO₃⁻(aq) + OH⁻(aq)

```

3. Equilibrium: This reaction reaches equilibrium, but it favors the formation of bicarbonate ions (HCO₃⁻) and hydroxide ions (OH⁻). The hydroxide ions (OH⁻) are what make the solution basic.

In essence, the carbonate ion acts as a base by accepting a proton (H⁺) from water, generating hydroxide ions and making the solution alkaline.