  Thermodynamic uncertainty relations elucidate the intricate balance between
the precision of current and the thermodynamic costs or dissipation, marking a
recent and enthralling advancement at the confluence of statistical mechanics,
thermodynamics, and information theory. In this study, we derive a time-energy
uncertainty relation tailored for chemical reactions, expressed in terms of the
Gibbs free energy and chemical potential. This inequality holds true
irrespective of whether the total substance of chemical species is conserved
during the reaction. Furthermore, it supports the general thermodynamic
framework by ensuring the spontaneous decrease in Gibbs free energy. We present
two formulations of the thermodynamic uncertainty relation: one based on
chemical species concentrations and the other on molar fractions. The validity
of our inequalities is numerically demonstrated using model systems of the
Belousov-Zhabotinsky and Michaelis-Menten reactions. Our uncertainty relation
may find practical applications in measuring and optimizing thermodynamic
properties relevant to chemical reaction systems out of equilibrium.
