What type of double displacement reactions yield carbonic acid as a product?

The reactions between an acid and a metal carbonate or a metal hydrogen carbonate are double displacement reactions that produce carbonic acid.

In a double displacement reaction, the cations change partners:

A⁺B⁻ + C⁺D⁻ → A⁺D⁻ + C⁺B⁻

To form H₂CO₃ as a product, the equation must be of the form:

2H⁺B⁻ + (C⁺)₂CO₃²⁻ → H₂CO₃ + 2C⁺B⁻

or

H⁺B⁻ + C⁺HCO₃⁻ → H₂CO₃ + C⁺B⁻

Typical examples are

2HCl + Na₂CO₃ → H₂CO₃ + 2NaCl

H₂SO₄ + CaCO₃ → H₂CO₃ + CaSO₄

HCl + NaHCO₃ → H₂CO₃ + NaCl

H₂SO₄ + Ca(HCO₃)₂ → H₂CO₃ + CaSO₄

The carbonic acid is unstable. It rapidly decomposes into water and carbon dioxide.

H₂CO₃ → H₂O + CO₂

Many baking powders are of a weak acid and a hydrogen carbonate salt such as NaHCO₃. They work by forming carbonic acid in a double displacement reaction. The bubbles of carbon dioxide expand in the moist batter and leaven the mixture.