How long would it take for 1.50 mol of water at 100.0 ? c to be converted completely into steam if heat were added at a constant rate of 25.0 j/s ?

The molar latent heat of vaporization of a substance is the amount of energy necessary to transform one mole of a substance from a liquid to a gas at constant temperature. In the case of water, this is 40,650 J/mol. Assuming no energy is lost, the total amount of energy required will be:

Q = 1.5 * 40,650
Q = 60,975 J

The time taken will be:
60,975/25 s

The vaporization will take 2,439 seconds.