Answer
(a) $\Delta n_{gas} = $ 3
(b) $\Delta n_{gas} = $ -1
(c) $\Delta n_{gas} = $ 3
Work Step by Step
(a) The only gas in this reaction is $O_2$ in the products, with 3 molecules:
$n_{gas \space products} = 3$
$\Delta n_{gas} = n_{gas \space products} - n_{gas \space reactants}$
$\Delta n_{gas} = 3 - 0 = 3$
(b)The only gas in this reaction is $O_2$ in the reactants, with 1 single molecule:
$n_{gas \space reactants} = 1$
$\Delta n_{gas} = n_{gas \space products} - n_{gas \space reactants}$
$\Delta n_{gas} = 0 - 1 = -1$
(c) The only gas in this reaction is Xe in the products, with 3 molecules:
$n_{gas \space products} = 3$
$\Delta n_{gas} = n_{gas \space products} - n_{gas \space reactants}$
$\Delta n_{gas} = 3 - 0 = 3$
