Answer : The mass of Butane needed is 29.946 g.
Solution : Given,
Molar mass of butane = 58.12 g/mole
Molar mass of carbon dioxide = 44.01 g/mole
Mass of carbon dioxide = 90.9 g
The Given net balanced chemical reaction is,
[tex]2C_4H_{10}(g)+13O_2(g)\rightarrow 10H_2O(g)+8CO_2(g)[/tex]
First we have to calculate the moles of carbon dioxide.
[tex]\text{ Moles of }CO_2=\frac{\text{ Given mass of }CO_2}{\text{ Molar mass of }CO_2 }[/tex]
[tex]\text{ Moles of }CO_2=\frac{90.9g}{44.01g/mole}=2.061moles[/tex]
From the given chemical reaction, we conclude that
8 moles of [tex]CO_2[/tex] produced from 2 moles [tex]C_4H_{10}[/tex]
2.061 moles of [tex]CO_2[/tex] produced from [tex]\frac{2moles}{8moles}\times 2.061moles=0.51525moles[/tex] of [tex]C_4H_{10}[/tex]
The moles of [tex]C_4H_{10}[/tex] = 0.51525 moles
Now we have to calculate the mass of [tex]C_4H_{10}[/tex] needed.
Mass of Butane = Moles of Butane × Molar mass of Butane
Mass of Butane = 0.51525 moles × 58.12 g/mole = 29.946 g
Therefore, the mass of Butane needed is 29.946 g.
