Studies of chemical reactions by a single pair of atoms in a well defined quantum state constitute a corner stone in quantum chemistry. Yet, the number of demonstrated techniques which enable observation and control of a single chemical reaction is handful. Here we propose and demonstrate a new technique to study chemical reactions between an ultracold neutral atom and a cold ion using quantum logic. We experimentally study the release of hyperfine energy in a reaction between an ultracold rubidium atom and isotopes of singly ionized strontium for which we do not have experimental control. We detect the reaction outcome and measure the reaction rate of the chemistry ion by reading the motional state of a logic ion via quantum logic, in a single shot. Our work opens new avenues and extends the toolbox of studying chemical reactions, with existing experimental tools, for all atomic and molecular ions in which direct laser cooling and state detection are unavailable.