Answer
a. There are necessary 1.25 moles of C to react with 0.500 mole of $SO_2$.
b. The reaction of 1.2 moles of C produces 0.96 mole of $CO$
c. It is necessary to have 1.0 mole of $SO_2$ to produce 0.50 mole of $CS_2$
d. The reaction of 2.5 moles of C produces 0.50 mole of $CS_2$
Work Step by Step
a. Find the conversion factors, and calculate the amount of $ C $ moles
$ SO_2 $ and $ C $:
$$ \frac{ 2 \space moles \space SO_2 }{ 5 \space moles \space C } \space and \space \frac{ 5 \space moles \space C }{ 2 \space moles \space SO_2 }$$
$$ 0.500 \space mole \space SO_2 \times \frac{ 5 \space moles \ C }{ 2 \space moles \space SO_2 } = 1.25 \space moles \space C $$
b. Find the conversion factors, and calculate the amount of $ CO $ moles
$ C $ and $ CO $: $$ \frac{ 5 \space moles \space C }{ 4 \space moles \space CO } \space and \space \frac{ 4 \space moles \space CO }{ 5 \space moles \space C }$$
$$ 1.2 \space moles \space C \times \frac{ 4 \space moles \ CO }{ 5 \space moles \space C } = 0.96 \space mole \space CO $$
c. Find the conversion factors, and calculate the amount of $ SO_2 $ moles
$ CS_2 $ and $ SO_2 $: $$ \frac{ 1 \space mole \space CS_2 }{ 2 \space moles \space SO_2 } \space and \space \frac{ 2 \space moles \space SO_2 }{ 1 \space mole \space CS_2 }$$
$$ 0.50 \space mole \space CS_2 \times \frac{ 2 \space moles \ SO_2 }{ 1 \space mole \space CS_2 } = 1.0 \space mole \space SO_2 $$
d. Find the conversion factors, and calculate the amount of $ CS_2 $ moles
$ C $ and $ CS_2 $: $$ \frac{ 5 \space moles \space C }{ 1 \space mole \space CS_2 } \space and \space \frac{ 1 \space mole \space CS_2 }{ 5 \space moles \space C }$$
$$ 2.5 \space moles \space C \times \frac{ 1 \space mole \ CS_2 }{ 5 \space moles \space C } = 0.50 \space mole \space CS_2 $$
