Answer
a. 1.0 mole
b. 10. moles
c. 5.0 moles
Work Step by Step
a. Find the conversion factors, and calculate the amount of $ O_2 $ moles
$ H_2 $ and $ O_2 $: $$ \frac{ 2 \space moles \space H_2 }{ 1 \space mole \space O_2 } \space and \space \frac{ 1 \space mole \space O_2 }{ 2 \space moles \space H_2 }$$$$ 2.0 \space moles \space H_2 \times \frac{ 1 \space mole \ O_2 }{ 2 \space moles \space H_2 } = 1.0 \space mole \space O_2 $$
b. Find the conversion factors, and calculate the amount of $ H_2 $ moles
$ O_2 $ and $ H_2 $: $$ \frac{ 1 \space mole \space O_2 }{ 2 \space moles \space H_2 } \space and \space \frac{ 2 \space moles \space H_2 }{ 1 \space mole \space O_2 }$$
$$ 5.0 \space moles \space O_2 \times \frac{ 2 \space moles \ H_2 }{ 1 \space mole \space O_2 } = 10. \space moles \space H_2 $$
c. Find the conversion factors, and calculate the amount of $ H_2O $ moles.
$ O_2 $ and $ H_2O $: $$ \frac{ 1 \space mole \space O_2 }{ 2 \space moles \space H_2O } \space and \space \frac{ 2 \space moles \space H_2O }{ 1 \space mole \space O_2 }$$
$$ 2.5 \space moles \space O_2 \times \frac{ 2 \space moles \ H_2O }{ 1 \space mole \space O_2 } = 5.0 \space moles \space H_2O $$