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Experimentally how it is proved that chemical equilibrium is dynamic in nature?

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$$H_2(g) + I_2(g) \rightleftharpoons 2HI (g)$$
In the above equilibrium, on adding radioactive isotope of iodine, there is no change in relative concentrations of hydrogen, iodine and hydrogen iodide. This shows that the reaction is taking place in both the directions at the same rate. The formation of radioactive reaction is taking place in forward direction but the same concentrations shows same rate of reaction in both the directions. Thus, chemical equilibrium is a dynamic equilibrium.

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