Consider the following ligands `NH_(2)^(-),` acac, `OH^(-)`, Gly, `O_(2)^(-)`, Phen, DMG, `NO_(2)^(-),CO_(3)^(2-),Cl^(-),CH_(3)COO^(-),en,SO_(4)^(2-)`. Then calculate vlaue of "P+Q-R-S" here
P: total number of ligands which act as bridging as well as monodentate only.
Q: Total number of flexidentate ligands.
R: Total number of bidentate ligands only
S: Total number of unsymmetrical bidentate ligands.

Explanation

To solve the question, we need to analyze the ligands provided and categorize them based on their denticity and bridging capabilities. Let's break down the steps to calculate the value of "P + Q - R - S".

### Step 1: Identify Monodentate and Bridging Ligands (P)
Monodentate ligands are those that can donate only one pair of electrons to the metal ion. Bridging ligands can act as both monodentate and bridging ligands.

**Ligands provided:**
- `NH2^-` (Monodentate)
- `acac` (Bidentate)
- `OH^-` (Monodentate)
- `Gly` (Bidentate)
- `O2^-` (Monodentate)
- `Phen` (Bidentate)
- `DMG` (Bidentate)
- `NO2^-` (Monodentate)
- `CO3^(2-)` (Can act as bridging or monodentate)
- `Cl^-` (Monodentate)
- `CH3COO^-` (Monodentate)
- `en` (Bidentate)
- `SO4^(2-)` (Can act as bridging or monodentate)

**Count of Monodentate Ligands:**
- `NH2^-`, `OH^-`, `O2^-`, `NO2^-`, `Cl^-`, `CH3COO^-` = 6 ligands

**Count of Bridging Ligands:**
- `CO3^(2-)`, `SO4^(2-)` can act as bridging ligands.

**Total for P (Bridging and Monodentate):**
- `CO3^(2-)`, `SO4^(2-)` can be included as bridging ligands.
- Total = 6 (monodentate) + 2 (bridging) = 8 ligands.

### Step 2: Identify Flexidentate Ligands (Q)
Flexidentate ligands can change their denticity based on the metal they coordinate with.

**Flexidentate Ligands:**
- `CO3^(2-)`
- `SO4^(2-)`
- `NO2^-` (can act as bidentate or monodentate)

**Count of Flexidentate Ligands:**
- Total = 3 ligands.

### Step 3: Identify Bidentate Ligands (R)
Bidentate ligands can donate two pairs of electrons to the metal ion.

**Bidentate Ligands:**
- `acac`, `Gly`, `Phen`, `DMG`, `en`

**Count of Bidentate Ligands:**
- Total = 5 ligands.

### Step 4: Identify Unsymmetrical Bidentate Ligands (S)
Unsymmetrical bidentate ligands do not have a symmetrical structure.

**Unsymmetrical Bidentate Ligands:**
- `DMG`, `Gly`

**Count of Unsymmetrical Bidentate Ligands:**
- Total = 2 ligands.

### Final Calculation
Now we can calculate the value of "P + Q - R - S":
- P = 8 (Bridging + Monodentate)
- Q = 3 (Flexidentate)
- R = 5 (Bidentate)
- S = 2 (Unsymmetrical Bidentate)

**Calculation:**
\[ P + Q - R - S = 8 + 3 - 5 - 2 \]
\[ = 11 - 7 \]
\[ = 4 \]

### Final Answer
The value of "P + Q - R - S" is **4**.