Chapter 3, Problem 1P

Write down the chemical formulae for the combustion of the alkanes in Table 3.2 with n = 2 to n = 8. Determine the mass of CO₂ produced per megajoule of energy.

To determine

Provide the chemical formula for the combustion of alkanes with $n=2$ to $n=8$.

Calculate the mass of ${\text{CO}}_2$ produced per Mega Joule of energy.

Explanation of Solution

Calculation:

Provide the general equation for the combustion of alkanes as shown below.

${\text{C}}_n{\text{H}}_{2n+2}+\left(\frac{3n+1}{2}\right){\text{O}}_2\to n{\text{CO}}_2+\left(n+1\right){\text{H}}_{\text{2}}\text{O}$

Refer to Table 3.2 “Alkane series of hydrocarbons with the formula ${\text{C}}_n{\text{H}}_{2n+2}$. The heat of combustion of HHV”.

Take the name, formula, and the heat combustion values for each alkanes.

Provide the chemical formula for the combustion of alkanes with $n=2$ to $n=8$ as shown in Table 1.

n	Name	Formula	Combustion of alkanes	Moles ${\text{CO}}_2$	Moles of alkane
2	Ethane	${\text{C}}_2{\text{H}}_6$	${\text{2C}}_2{\text{H}}_6+7{\text{O}}_2\to 4{\text{CO}}_2+6{\text{H}}_{\text{2}}\text{O}$	4	2
3	Propane	${\text{C}}_3{\text{H}}_8$	${\text{C}}_3{\text{H}}_8+5{\text{O}}_2\to 3{\text{CO}}_2+4{\text{H}}_{\text{2}}\text{O}$	3	1
4	Butane	${\text{C}}_4{\text{H}}_{10}$	${\text{2C}}_4{\text{H}}_{10}+13{\text{O}}_2\to 8{\text{CO}}_2+10{\text{H}}_{\text{2}}\text{O}$	8	2
5	Pentane	${\text{C}}_5{\text{H}}_{12}$	${\text{C}}_5{\text{H}}_{12}+8{\text{O}}_2\to 5{\text{CO}}_2+6{\text{H}}_{\text{2}}\text{O}$	5	1
6	Hexane	${\text{C}}_6{\text{H}}_{14}$	${\text{2C}}_6{\text{H}}_{14}+19{\text{O}}_2\to 12{\text{CO}}_2+14{\text{H}}_{\text{2}}\text{O}$	12	2
7	Heptane	${\text{C}}_7{\text{H}}_{16}$	${\text{C}}_7{\text{H}}_{16}+11{\text{O}}_2\to 7{\text{CO}}_2+8{\text{H}}_{\text{2}}\text{O}$	7	7
8	Octane	${\text{C}}_8{\text{H}}_{18}$	${\text{2C}}_8{\text{H}}_{18}+25{\text{O}}_2\to 16{\text{CO}}_2+18{\text{H}}_{\text{2}}\text{O}$	16	2

The molecular mass of ${\text{CO}}_2$ is 44 g/mol.

Calculate the mass of ${\text{CO}}_2$ produced per mega joule of energy as shown below.

Provide the mass of ${\text{CO}}_2$ produced per mega joule of energy for each alkanes with $n=2$ to $n=8$ as shown in Table 2.

n	$R=\frac{{\text{Moles CO}}_2}{\text{Moles}\text{of}\text{alkane}}$	M (alkane)	$R\times \frac{44}{M}=\frac{{\text{kg of CO}}_2}{\text{kg}\text{alkane}}$	Heat of combustion (MJ/kg)	$\begin{array}{l}\text{kg}\text{of}\\ {\text{CO}}_2/MJ\end{array}$
2	2	30	2.93	51.9	0.0565
3	3	44	3	50.3	0.0596
4	4	58	3.03	49.5	0.0612
5	5	72	3.06	48.7	0.0628
6	6	86	3.07	48.1	0.0638
7	7	100	3.08	48.1	0.0640
8	8	114	3.09	46.8	0.0660