Answer : The limiting reactant is [tex]O_2[/tex]
Explanation : Given,
Mass of [tex]C_3H_8[/tex] = 30.0 g
Mass of [tex]O_2[/tex] = 75.0 g
Molar mass of [tex]C_3H_8[/tex] = 44 g/mole
Molar mass of [tex]O_2[/tex] = 32 g/mole
First we have to calculate the moles of [tex]C_3H_8[/tex] and [tex]O_2[/tex].
[tex]\text{ Moles of }C_3H_8=\frac{\text{ Mass of }C_3H_8}{\text{ Molar mass of }C_3H_8}=\frac{30.0g}{44g/mole}=0.682moles[/tex]
[tex]\text{ Moles of }O_2=\frac{\text{ Mass of }O_2}{\text{ Molar mass of }O_2}=\frac{75.0g}{32g/mole}=2.34moles[/tex]
Now we have to calculate the limiting and excess reagent.
The balanced chemical reaction is,
[tex]C_3H_8+5O_2\rightarrow 3CO_2+4H_2O[/tex]
From the balanced reaction we conclude that
As, 5 mole of [tex]O_2[/tex] react with 1 mole of [tex]C_3H_8[/tex]
So, 2.34 moles of [tex]O_2[/tex] react with [tex]\frac{2.34}{5}\times 1=0.468[/tex] moles of [tex]C_3H_8[/tex]
From this we conclude that, [tex]C_3H_8[/tex] is an excess reagent because the given moles are greater than the required moles and [tex]O_2[/tex] is a limiting reagent and it limits the formation of product.
Therefore, the limiting reactant is [tex]O_2[/tex]