d) 2Al(s) + Fe2O3(s)  2Fe(l) + Al2O3(s)

Oxidation
2Al(s)  2Al+ + 2e-
Reduction
Fe23+ + 3e-  2Fe(l)

Oxidation numbers for chlorine
HCl = -1
MnO2(s)= +4
KMnO4(s)= +7

Oxidation numbers for manganese
Mn(s)= ?
MnCl2(s)= +7
Mn2+(aq)= ?
MnO4- =?

And then SO4 is so confusing...
H2SO4 =?
PbSO4 = ?

d) 2Al(s) + Fe2O3(s) „³ 2Fe(l) + Al2O3(s)

Oxidation
2Al(s) „³ 2Al+ + 2e-
Reduction
Fe23+ + 3e- „³ 2Fe(l)


2Al(s) + Fe2O3 ==> 2Fe(l) + Al2O3
did you mean Fe(l) or Fe(s). It doesn't matter for the purpose of balancing Or for oxidation state. This is the "thermite" reaction, in which Fe gets so hot it melts, so you may have intended liquid.
Al ==>Al^+3 + 3e
Fe^+3 + 3e ==> Fe

Oxidation numbers for manganese
Mn(s)= ? All elements in the free state (uncombined with something) = 0
MnCl2(s)= +7 Cl is -1 so Mn must be +2 in order for MnCl2 to be zero
Mn2+(aq)= ? The oxidation state of elements in the ion form is the charge on the ion. Here Mn is +2
MnO4- =? Oxygen is -2 each for a total of -8, so Mn must be +7 in order to leave a -1 charge on the ion.

And then SO4 is so confusing...
H2SO4 =? H is +1 each for total of +2. O is -2 each for a total of -8. Therefore, S must be +6 to make H2SO4 zero.
PbSO4 = ? Pb is +2, S is +6, O is -2, for the same reasons in H2SO4.
S is one of those elements with multiple oxidation states. +2 in SO, zero in S(s), -2 in H2S, +4 in SO2 and SO3^-2, and +6 in SO3 and SO4^-2.

To determine the oxidation numbers for various elements in a compound, follow these guidelines:

1. The sum of the oxidation numbers in a neutral compound is always zero.
2. The sum of the oxidation numbers in a polyatomic ion is equal to the charge of the ion.

Oxidation numbers for manganese:
a. Mn(s) (elemental manganese) = 0. This is because the oxidation number of any element in its elemental form is always 0.
b. MnCl2(s) (manganese dichloride) = +2. Since the overall compound is electrically neutral and there are two chloride ions (-1 each) in the formula, the oxidation number of manganese must be +2 to balance the charges.
c. Mn2+(aq) (manganese(II) ion) = +2. The charge of the ion is given in the formula.
d. MnO4- (permanganate ion) = +7. The sum of the oxidation numbers in the permanganate ion is equal to its charge. Since the overall charge of the ion is -1, the oxidation number of manganese must be +7 to balance the charges.

Oxidation numbers for sulfur (S):
a. H2SO4 (sulfuric acid) = +6. The oxidation number of hydrogen is +1, so (2 x 1) = +2. The oxidation number of oxygen is usually -2, so (4 x -2) = -8. Therefore, the oxidation number of sulfur must be +6 to balance the charges. Additionally, the overall charge of sulfuric acid is neutral.
b. PbSO4 (lead(II) sulfate) = +6. The oxidation number of lead is +2. The oxidation number of oxygen is -2, so (4 x -2) = -8. Therefore, the oxidation number of sulfur must be +6 to balance the charges.

Note: Always remember that these oxidation numbers are based on the rules and guidelines for assigning them in compounds. They are not absolute values but are determined by following the rules.

To determine the oxidation number of an element in a compound, you need to follow some general rules:

1. The oxidation number of an element in its elemental state is always 0. For example, Mn(s) would have an oxidation number of 0.

2. The oxidation number of a monatomic ion is equal to its charge. For example, Mn2+ would have an oxidation number of +2.

3. The sum of the oxidation numbers in a neutral compound is always zero.

4. In compounds, certain elements have fixed oxidation numbers. For example, in HCl, hydrogen (H) always has an oxidation number of +1, and chlorine (Cl) always has an oxidation number of -1.

Now let's determine the oxidation numbers for the given compounds:

1. HCl:
Since hydrogen (H) always has an oxidation number of +1 and the overall compound is neutral, the oxidation number of chlorine (Cl) must be -1.

2. MnO2:
The total oxidation number of a compound is equal to the overall charge, which is 0 in this case. The oxidation number of oxygen (O) is usually -2, so we can set up an equation to solve for the unknown oxidation number of manganese (Mn):
(+4) + 2(-2) = 0
Solving this equation gives the oxidation number of Mn as +4.

3. KMnO4:
Similar to MnO2, we can set up an equation to solve for the unknown oxidation number of manganese (Mn):
(+1) + Mn + 4(-2) = 0
Solving this equation gives the oxidation number of Mn as +7.

Moving onto sulfur (S):

1. H2SO4:
The total oxidation number of the compound is equal to 0. Hydrogen (H) always has an oxidation number of +1, and oxygen (O) always has an oxidation number of -2. We can set up an equation to solve for the unknown oxidation number of sulfur (S):
2(+1) + S + 4(-2) = 0
Solving this equation gives the oxidation number of S as +6.

2. PbSO4:
Similar to H2SO4, we can set up an equation to solve for the unknown oxidation number of sulfur (S):
Pb + S + 4(-2) = 0
Solving this equation gives the oxidation number of S as +6. The oxidation number of lead (Pb) can be calculated by subtracting the sum of the oxidation numbers of the other atoms from the total charge, which in this case is 0:
+2 + 6 + 4(-2) = 0
Solving this equation gives the oxidation number of Pb as +2.