How does increasing the amount of water effect an ammonium nitrate endothermic reaction?

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It sounds like you're asking about the heat absorbed by ammonium nitrate when ammonium nitrate dissolves endothermically in water. This means that it absorbs heat from the surroundings, in this case water, causing the water temperature to go down. The amount of heat absorbed by the ammonium nitrate depends on the amount dissolving. The heat of solution of ammonium nitrate is +25.41 kJ/mol.

The amount of heat absorbed by the ammonium nitrate will equal the amount released by the water in which is it's dissolved, so varying the amount of water won't affect the total amount of heat it loses assuming there's still enough water for all of the ammonium nitrate to dissolve.

What will vary, however, is the temperature change of the water. The heat gained or lost by water is q=mc `Delta` T, where m is the mass of the water,  `Delta` T is the temperature change and c is the specific heat of water, a constant that tells us how much heat is required to raise the temperature of water by one degree celsius. In the case we're considering, the temperature changes, so:

 `Delta` T = q/mc 

From this form of the equation we can see that the temperature change of water will decrease if the amount of water used to dissolve a given amount of ammonium nitrate is increased, and since the temperature change is negative the final temperature of the solution will be higher if more water is used. The same amount of heat is being lost by more molecules.

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