A common approach to inducing selective mechanochemical transformations relies on embedding the target molecules (called mechanophores) within elastomeric polymer networks. Mechanical properties of such elastomers can also be modulated through the mechanochemical response of the constituent polymer chains. The inherent randomness in the molecular structure of such materials leads to heterogeneity of the local forces exerted on individual mechanophores. Here we use coarse-grained simulations to study the force distributions within random elastomeric networks and show that those distributions are close to exponential regardless of the applied macroscopic load, entanglement effects, or network parameters. Exponential form of the distribution allows one to completely characterize the mechanophore kinetics in terms of the mean value of the force. At the same time, heterogeneity of the local force affects the kinetics qualitatively: While a narrow force distribution around the mean would lead to exponential kinetics, exponential force distribution results in highly nonexponential kinetics, with a fast kinetic phase involving highly loaded molecules, followed by a slow phase dominated by unloaded molecules.