Since the components in a mixture are NOT chemically bound, you cannot use chemical methods to separate them lest you’ll counter-intuitively mix them chemically to form compounds. Rather physical methods are used to separate the components.
Explanation:
Air is made of a mixture of gases like Nitrogen, Oxygen and Carbon dioxide and particles like dust particles and water vapor. It is a homogeneous mixture because the components are well mixed up proportionately through out the mixture. The different components air can be separated using their different densities or melting and boiling points.
Magma cools and crystallizes to form igneous rock. Igneous rock undergoes weathering (or breakdown) to form sediment. The sediment is transported and deposited somewhere (such as at the beach or in a delta, or in the deep sea). The deposited sediment undergoes lithification (the processes that turn it into a rock).