Answer: The mass of oxygen gas required is 36.7 grams.
Explanation:
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex] .....(1)
Given mass of hexane = 10.4 g
Molar mass of hexane = 86.18 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of hexane}=\frac{10.4g}{86.18g/mol}=0.12mol[/tex]
The chemical equation for the combustion of hexane follows:
[tex]2C_6H_{14}+19O_2\rightarrow 12CO_2+14H_2O[/tex]
By stoichiometry of the reaction:
2 moles of hexane reacts with 19 moles of oxygen gas
So, 0.12 moles of hexane will react with = [tex]\frac{19}{2}\times 0.12=1.14mol[/tex] of oxygen gas.
Now, calculating the mass of oxygen gas by using equation 1, we get:
Molar mass of oxygen gas = 32 g/mol
Moles of oxygen gas = 1.14 moles
Putting values in equation 1, we get:
[tex]1.14mol=\frac{\text{Mass of oxygen gas}}{32g/mol}\\\\\text{Mass of oxygen gas}=36.7g[/tex]
Hence, the mass of oxygen gas required is 36.7 grams.
