Answer
(a) 1
(b) -3
(c) 1
Work Step by Step
(a) The only gas in this reaction is $CO_2$ in the products, with 1 molecule:
$n_{gas \space products} = 1$
$\Delta n_{gas} = n_{gas \space products} - n_{gas \space reactants}$
$\Delta n_{gas} = 1 - 0 = 1$
(b)There are 2 gases in this reaction, 2 $H_2$ and 1 $O_2$, both in reactants:
$n_{gas \space reactants} = 2+1 =3$
$\Delta n_{gas} = n_{gas \space products} - n_{gas \space reactants}$
$\Delta n_{gas} = 0 -3 = -3$
(c) There are 3 gases in this reaction, 1 $ClF$ in the reactants, 1 $ClONO_2$ and 1 $HF$ in the products:
$n_{gas \space reactants} = 1$
$n_{gas \space products} = 1 + 1 =2$
$\Delta n_{gas} = n_{gas \space products} - n_{gas \space reactants}$
$\Delta n_{gas} = 2 - 1 = 1$
