We report experiments on emerging coherence through weak global coupling of populations of electrochemical oscillators with heterogeneities. The experiments are done with an array of nickel electrodes undergoing electrodissolution in sulfuric acid. The experiments verify theories of Winfree and Kuramoto that predict that global coupling of a set of smooth limit cycle oscillators with different frequencies produces a phase transition in which some of the elements synchronize. Both the critical point and the predicted dependence of order on coupling are seen in the experiments. We extend the studies to relaxation oscillators and characterize the quantitative similarities and differences between the two types of systems. Numerical simulations using a coupled form of a nickel electrodissolution model support the experimental findings.