Question:

Assign oxidation numbers to the underlined elements in each of the following species: 
  1. \(NaH_2\underline PO_4\) 
  2. \(NaH\underline SO_4\) 
  3. \(H_4\underline P_2O_7\) 
  4. \(K_2\underline {Mn}O_4\) 
  5. \(Ca\underline O_2\) 
  6. \(Na\underline BH_4\) 
  7. \(H_2\underline S_2O_7\) 
  8. \(KAl(\underline SO_4)_2.12 H_2O\)

Updated On: Nov 17, 2023
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Solution and Explanation

(a) \(NaH_2\underline PO_4\)
Let the oxidation number of\( P\) be \(x\)
We know that, 
Oxidation number of \(Na\) = \(+1\)
Oxidation number of \(H\) = \(+1\) 
Oxidation number of \(O\) = \(-2\)
\(\Rightarrow \overset{+1}Na\overset{+1}H_2\overset{x}P\overset{-2}O_4\)
Then, we have

\(1(+1) + 2(+1) + 1(x) + 4(-2) = 0\)
\(1 + 2 + x -8 = 0\)
\(x = +5\)
Hence, the oxidation number of \(P\) is \(+5\).


(b) \(NaH\underline SO_4\)
\(\overset{+1}Na\overset{+1}H\overset{x} S\overset{-2}O_4\)
Then, we have
\(1(+1) + 1(+1) + 1(x) + 4(-2) = 0\)
\(\Rightarrow\)\(1 + 1 + x -8 = 0\)
\(\Rightarrow\)\(x = +6\)
Hence, the oxidation number of \(S\) is \(+ 6\).


(c) \(H_4\underline P_2O_7\)
\(\overset{+1} H_4\overset{x} P_2\overset{-2}O_7\)
Then, we have
\(4(+1) + 2(x) + 7(-2) = 0\)
\(\Rightarrow\)\(4 + 2x – 14 = 0\)
\(\Rightarrow\)\(2x = +10\)
\(\Rightarrow\)\(x = +5\)
Hence, the oxidation number of \(P\) is \(+ 5\).


(d) \(K_2\underline {Mn}O_4\)
\(\overset{+1}K_2\overset{x} {Mn}\overset{-2}O_4\)
Then, we have 
\(2(+1) + x + 4(-2) = 0\)
\(\Rightarrow\)\(2 + x – 8 = 0\)
\(\Rightarrow\)\(x = +6\)
Hence, the oxidation number of \(Mn\) is \(+ 6\).


(e) \(Ca\underline O_2\)
\(\overset{+2}Ca\overset{x} O_2\)
Then, we have
\((+2) + 2(x) = 0\)
\(\Rightarrow\) \(2 + 2x = 0\)
\(\Rightarrow\) \(2x = -2\)
\(\Rightarrow\) \(x = -1\)
Hence, the oxidation number of \(O\) is \(- 1\).


(f) \(Na\underline BH_4\)
\(\overset{+1}Na\overset{x} B\overset{-1}H_4\)
Then, we have
\(1(+1) + 1(x) + 4(-1) = 0\)
\(\Rightarrow\) \(1 + x -4 = 0\)
\(\Rightarrow\) \(x = +3\)
Hence, the oxidation number of \(B\) is \(+ 3\).


(g) \(H_2\underline S_2O_7\)
\(\overset{+1}H_2\overset{x} S_2\overset{-2}O_7\)
Then, we have
\(2(+1) + 2(x) + 7(-2) = 0\)
\(\Rightarrow\) \(2 + 2x – 14 = 0\)
\(\Rightarrow\) \(2x = +12\)
\(\Rightarrow\) \(x = +6\)
Hence, the oxidation number of \(S\) is \(+ 6\).


(h) \(KAl(\underline SO_4)_2.12 H_2O\)
\(\overset{+1}K\overset{+3}Al\bigg(\overset{x} S\overset{2-}O_4\bigg)_2.12 \overset{+1}H_2\overset{-2}O\)
Then, we have
\(1(+1) + 1(+3) + 2(x) + 8(-2) + 24(+1) + 12(-2) = 0\)
\(\Rightarrow\) \(1 + 3 + 2x – 16 + 24 – 24 = 0\)
\(\Rightarrow\) \(2x = +12\)
\(\Rightarrow\) \(x = +6\)
Or, 
We can ignore the water molecule as it is a neutral molecule. Then, the sum of the oxidation numbers of all atoms of the water molecule may be taken as zero. 
Therefore, after ignoring the water molecule, we have:
\(1(+1) + 1(+3) + 2(x) + 8(-2) = 0\)
\(1 + 3 + 2x -16 = 0\)
\(2x = 12\)
\(x = +6\)
Hence, the oxidation number of \(S\) is \(+ 6\).

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Concepts Used:

Redox Reactions

Redox Reaction:

Redox reactions are chemical reactions where oxidation and reduction take place simultaneously. In this type of reaction, there is a gain of electrons for one chemical species while the other loses electrons or simply involves transfer of electrons. The species that loses electrons is oxidized while the one that gains electrons is reduced. 

Types of Redox Reactions:

Redox reactions can be differentiated into 4 categories namely combination reactions, decomposition reactions, displacement reactions, and disproportionation reactions. Each is explained separately below:

Combination Reaction:

In this, the molecules combine to form new compounds. For example, when magnesium reacts to nitrogen.

Decomposition Reaction:

Opposite to the combination reaction, here there is a breakdown of compounds to simpler substances. For example, electrolysis of water.

Displacement Reaction:

In this, the more reactive metal will displace the less reactive one in a chemical reaction. The reactivity of an element is represented in a series called the reactivity series (arranged in decreasing order of reactivity) which makes it easier to determine the chemical reaction and its products.

Disproportionation Reaction:

This is a peculiar type of reaction where an element showing a particular oxidation state will be oxidized and reduced simultaneously. Another thing to note is that these reactions will always have an element that can exhibit three oxidation states.