The amount of 1 mole of a gas at STP is calculated to be 22.4L. We first calculate the amount of oxygen gas in moles.
oxygen gas in moles = 7.5 L / (22.4 L/mol) = 0.335 moles O2
Then, we calculate the moles of H2O produced based on the given balanced chemical reaction.
(0.335 moles O2)(2 moles H2O/ 1 mole O2) = 0.67 moles H2O
Then, converting again the calculated moles to volume,
volume of water = (0.67 moles) x (22.4 L/mole) = 15 L of H2O
Thus, the amount of gaseous water produced is 15 L.