A catalyst includes a zeolite, wherein the zeolite has: a CHA framework; a particle size less than or equal to 100 nanometers; and a silica to alumina mole ratio in the range of about 50:1 to about 150:1. The catalyst can include a metal dopant. The catalyst can be used for purifying a product by flowing a reactant across the catalyst to form the product; and condensing or separating the product. The product can be an olefin or alkenes with an increased carbon chain. The catalyst can be used for selective catalytic reduction of nitrogen oxide or a gas to liquid reaction. A method of producing the catalyst can include selecting the concentration of a crystal growth inhibitor based on the ratio of the silica precursor and an alumina precursor such that the zeolite crystals have a mean particle size less than or equal to 100 nanometers.