The frequency of collisions between the N₂ and H₂ molecules will decrease and the rate of reaction will also decrease.
Since the water is cooler than the gas mixture, heat will flow from the gas to the water.
The gas will cool down, so the average kinetic energy of the gas molecules will decrease.
The molecules will be moving more slowly, so there will be fewer collisions and fewer of these collisions will have enough energy to react.
The rate of reaction between H₂ and N₂ molecules at room temperature is exceedingly slow, but cooling the gas mixture will make the reaction even slower.