Determine the oxidation number of each atom in the following: (a) propene (e) (E)-2-chloro-2-butane (b) 1-butane (f) \(1,1-\) dichloropropane (c) cis-2-butane (g) acetic acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) (d) 1-chloro-2-butane (h) methanethiol, \(\mathrm{CH}_{3} \mathrm{SH}\)

Propene can be represented as \(C_3H_6\), with a double bond between the first two carbon atoms. The structure is as follows: $$ \\mathrm{H}_{2}\\mathrm{C} = \\mathrm{C} - \\mathrm{CH}_3 $$

According to rules 2 and 6, hydrogen has an oxidation state of +1. The carbon atoms in the double bond will have the same oxidation state. To determine this, we will consider rule 1, as the sum of the oxidation states of all atoms in the molecule must be zero. Let x be the oxidation state of the two carbons in the double bond, and y be the oxidation state of the carbon in the methyl group: $$ 2x + y + 6(1) = 0 $$ As the oxidation states of the two carbons in the double bond must be the same, we can write two equations for them: $$ x - 2(1) = 0\\ y - 3(1) = 0 $$ Solving these equations, we get oxidation states x = +2 and y = +3. So, the oxidation state of each carbon in propene is: $$ \\mathrm{C}^{+2} - \\mathrm{C}^{+2} - \\mathrm{C}^{+3} $$ (e) (E)-2-chloro-2-butane

(E)-2-chloro-2-butane has the IUPAC name (E)-1-chloro-2-butene, and the structure can be represented as follows: $$ \\mathrm{Cl} - \\mathrm{CH} = \\mathrm{CH} - \\mathrm{CH}_2 - \\mathrm{CH}_3 $$

For (E)-2-chloro-2-butane, we will apply the previously mentioned rules to find the oxidation state of each element. As before, the carbon atoms in the double bond have the same oxidation state, which we will denote as x. The oxidation state of chlorine is -1. We can set up the following equation considering the sum of all oxidation states in the molecule must be zero: $$ 3x + (-1) + 5(1) = 0 $$ The equation for the oxidation state of each carbon is: $$ x - (1) = 0 $$ Solving these equations, we get the oxidation state of x = +1. So, the oxidation state of each carbon in (E)-2-chloro-2-butane is: $$ \\mathrm{Cl} - \\mathrm{C}^{+1} = \\mathrm{C}^{+1} - \\mathrm{CH}_{2}^{+1} - \\mathrm{CH}_{3}^{+1} $$ For the other compounds, follow the same steps of finding the structure of the molecule and using the rules to assign the oxidation states. This will allow you to determine the oxidation number for each element.