The Brønsted-Lowry model defines acids and bases in terms of protons, where acids are proton donors, and bases are proton acceptors. In contrast, the Lewis model defines acids and bases in terms of electron pairs, where Lewis acids are electron-pair acceptors, and Lewis bases are electron-pair donors.   

In a Brønsted acid, like acetic acid, the hydrogen can also act as a Lewis acid because it has an empty orbital to accept electrons donated from a base, like water, acting as a Lewis base.

The advantage of the Lewis model is that it allows scientists to classify a greater number of compounds as acids—including the ones that do not have ionizable protons. For example, boron trifluoride cannot be classified as an acid by the Brønsted-Lowry model because it does not contain hydrogen.

However, boron trifluoride possesses an incomplete octet with an empty orbital that can accept an electron pair from a Lewis base, such as ammonia, and, therefore, can act as a Lewis acid.

The resultant product formed by such Lewis acid-base reactions is called a Lewis acid-base adduct.

Some molecules, like carbon dioxide, can rearrange their electrons to act as a Lewis acid.

For example, in the reaction between water and carbon dioxide, an electron-pair moves from the carbon-oxygen pi bond to the terminal oxygen of the carbon dioxide.

The resultant empty orbital on the carbon atom allows it to accept the electron pair from a water molecule and act as a Lewis acid. As the water molecule donates the electron pair, it acts as a Lewis base.

In further rearrangement, a proton is transferred from the water oxygen to the terminal oxygen of the carbon dioxide, resulting in the formation of the carbonic acid adduct.

Small metal cations, like Al(III), can reacquire electron pairs and act as Lewis acids. For example, Al(III) accepts lone pairs of electrons from water and forms hexaaquaaluminum ions. Here, water molecules donate electron pairs and act as a Lewis base.