Answer : The correct option is, (D) 115 grams
Explanation :
Mass of [tex]CO_2[/tex] = 346 g
Molar mass of [tex]C_3H_8[/tex] = 44 g/mole
Molar mass of [tex]CO_2[/tex] = 44 g/mole
First we have to calculate the moles of [tex]CO_2[/tex].
[tex]\text{Moles of }CO_2=\frac{\text{Mass of }CO_2}{\text{Molar mass of }CO_2}=\frac{346g}{44g/mole}=7.86moles[/tex]
Now we have to calculate the moles of [tex]C_3H_8[/tex].
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, 3 mole of [tex]CO_2[/tex] obtained from 1 mole of [tex]C_3H_8[/tex]
So, 7.86 moles of [tex]CO_2[/tex] react to give [tex]\frac{1}{3}\times 7.86=2.62[/tex] moles of [tex]C_3H_8[/tex]
Now we have to calculate the mass of [tex]C_3H_8[/tex].
[tex]\text{Mass of }C_3H_8=\text{Moles of }C_3H_8\times \text{Molar mass of }C_3H_8[/tex]
[tex]\text{Mass of }C_3H_8=(2.62mole)\times (44g/mole)=115.28g=115g[/tex]
Therefore, the mass of propane needed are, 115 grams
