Before revision:  Previous works in the literature showed that the original stochastic system can be approximated with a reduced limiting system, as the scaling parameter N tends to infinity. In general scaling regimes, the convergence to the limiting system can be studied by using the law of large numbers and the relative compactness in a measure space.
After revision:  Previous works in the literature showed that the original stochastic system can be approximated using an associated reduced system. In this paper, we establish an error bound for this approximation. We consider general chemical kinetics and allow for higher order reactions, which generalizes existing results in the literature. Our approach is based on a direct analysis of the convergence to the limiting system can be studied by using the law of large numbers and the relative compactness in a measure space.