The increasing order of the strength of hydrogen bond in the following mentioned linkage is :
(P) `"O"-"H---S"`
(Q) `"S"-"H---O"`
(R) `"F"-"H---F"^(-)`
(S) `"F"-"H---O"`

Options

A. P < Q < S < R
B. Q
C. P < Q < R < S
D. Q < P < R < S

Answer

To determine the increasing order of the strength of hydrogen bonds among the given linkages, we need to analyze each bond based on the electronegativity of the atoms involved and the nature of the hydrogen bond itself.

### Step 1: Identify the linkages and their components
The given linkages are:
- (P) `"O"-"H---S"`
- (Q) `"S"-"H---O"`
- (R) `"F"-"H---F"^(-)`
- (S) `"F"-"H---O"`

### Step 2: Analyze the hydrogen bonds
1. **Linkage (P) `"O"-"H---S"`**:
- Here, oxygen (O) is bonded to hydrogen (H), but it is hydrogen bonding with sulfur (S). Sulfur is less electronegative than oxygen, which means the hydrogen bond strength will be weak.

2. **Linkage (Q) `"S"-"H---O"`**:
- In this case, sulfur (S) is bonded to hydrogen (H), and hydrogen is bonding with oxygen (O). Similar to (P), sulfur's lower electronegativity compared to oxygen results in a weak hydrogen bond.

3. **Linkage (R) `"F"-"H---F"^(-)`**:
- Here, fluorine (F) is highly electronegative, and the negative charge on the fluorine increases the strength of the hydrogen bond significantly. This bond will be quite strong due to the high electronegativity of fluorine.

4. **Linkage (S) `"F"-"H---O"`**:
- In this case, hydrogen is bonded to fluorine (F) and is forming a hydrogen bond with oxygen (O). Both fluorine and oxygen are highly electronegative, leading to a strong hydrogen bond.

### Step 3: Compare the strengths of the hydrogen bonds
Based on the analysis:
- The weakest hydrogen bond is in (P) and (Q) due to the presence of sulfur, which is less electronegative.
- The hydrogen bond in (R) is stronger than (P) and (Q) because of the highly electronegative fluorine.
- The hydrogen bond in (S) is stronger than (R) because both F and O are highly electronegative.

### Step 4: Establish the increasing order of strength
Based on the above analysis, the increasing order of the strength of hydrogen bonds is:
1. (P) `"O"-"H---S"` (weakest)
2. (Q) `"S"-"H---O"`
3. (R) `"F"-"H---F"^(-)`
4. (S) `"F"-"H---O"` (strongest)

### Final Answer:
The increasing order of the strength of hydrogen bond in the following mentioned linkage is:
**(P) < (Q) < (R) < (S)**