Respuesta :
Answer: The volume of carbon dioxide gas is [tex]4.73\times 10^2L[/tex]
Explanation:
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Given mass of hexane = 0.290 kg = 290 g (Conversion factor: 1 kg = 1000 g)
Molar mass of hexane = 86.2 g/mol
Putting values in above equation, we get:
[tex]\text{Moles of hexane}=\frac{290g}{86.2g/mol}=3.36mol[/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 produces 12 moles of carbon dioxide
So, 3.36 moles of hexane will produce = [tex]\frac{12}{2}\times 3.36=20.16mol[/tex] of carbon dioxide
To calculate the volume, we use the equation given by ideal gas equation:
PV=nRT
where,
P = pressure of the gas = 1 atm
V = Volume of carbon dioxide gas = ?
n = number of moles of gas = 20.16 moles
R = Gas constant = [tex]0.0821\text{ L atm }mol^{-1}K^{-1}[/tex]
T = temperature of the gas = [tex]13^oC=[13+273]K=286K[/tex]
Putting values in above equation, we get:
[tex]1atm\times V=20.16mol\times 0.0821\text{ L atm }mol^{-1}K^{-1}\times 286K\\\\V=\frac{20.16\times 0.0821\times 286}{1}=473.4L[/tex]
Hence, the volume of carbon dioxide gas is [tex]4.73\times 10^2L[/tex]
