Answer
$rate=-\frac{1}{2}\frac{\Delta[H_{2}O]}{\Delta t}=\frac{1}{2}\frac{[H_{2}]}{\Delta t}=\frac{\Delta[O_{2}]}{\Delta t}$
Work Step by Step
Consider the chemical equation: aA + bB -> cC + dD
The rate expression would be:
$rate=-\frac{1}{a}\frac{\Delta[A]}{\Delta t}=-\frac{1}{b}\frac{[B]}{\Delta t}=\frac{1}{c}\frac{\Delta[C]}{\Delta t}=\frac{1}{d}\frac{\Delta[D]}{\Delta t}$
There are negative signs before A and B because their change in concentration ($\Delta [X]$) would be negative as their amount decreases over time.
Therefore, the rate for this reaction should be: $rate=-\frac{1}{2}\frac{\Delta[H_{2}O]}{\Delta t}=\frac{1}{2}\frac{[H_{2}]}{\Delta t}=\frac{\Delta[O_{2}]}{\Delta t}$
