Arrange the following compounds in order of increasing molar conductivity .
`(i) K[Co(NH_(3))_(2)(NO_(2))_(4)]" " (ii) [Cr(NH_(3))_(3)(NO_(2))_(3)]`
`(iii) [Cr(NH_(3))_(5)(NO_(2))]_(3)[Co(NO_(2))_(6)]_(2)" " (iv) [Cr(NH_(3))_(6)]Cl_(3)`

Answer

To arrange the given compounds in order of increasing molar conductivity, we need to analyze how each compound dissociates in solution and count the total number of ions produced. Molar conductivity is directly proportional to the number of ions in solution; more ions result in higher conductivity.

Let's break down each compound step by step:

1. **Compound (i): K[Co(NH₃)₂(NO₂)₄]**
- This compound has one potassium ion (K⁺) outside the coordination sphere and one coordination complex [Co(NH₃)₂(NO₂)₄] which does not dissociate further.
- Total ions produced: 1 (K⁺) + 1 ([Co(NH₃)₂(NO₂)₄]) = **2 ions**.

2. **Compound (ii): [Cr(NH₃)₃(NO₂)₃]**
- This compound is a neutral complex with no counter ions outside the coordination sphere.
- Total ions produced: 1 ([Cr(NH₃)₃(NO₂)₃]) = **1 ion**.

3. **Compound (iii): [Cr(NH₃)₅(NO₂)]₃[Co(NO₂)₆]₂**
- This compound consists of three coordination complexes of [Cr(NH₃)₅(NO₂)] and two coordination complexes of [Co(NO₂)₆].
- The dissociation will yield: 3 ([Cr(NH₃)₅(NO₂)]) + 2 ([Co(NO₂)₆]) = **5 ions**.

4. **Compound (iv): [Cr(NH₃)₆]Cl₃**
- This compound has three chloride ions (Cl⁻) outside the coordination sphere and one coordination complex [Cr(NH₃)₆].
- Total ions produced: 3 (Cl⁻) + 1 ([Cr(NH₃)₆]) = **4 ions**.

Now, we can summarize the total number of ions for each compound:
- (i) K[Co(NH₃)₂(NO₂)₄] → 2 ions
- (ii) [Cr(NH₃)₃(NO₂)₃] → 1 ion
- (iii) [Cr(NH₃)₅(NO₂)]₃[Co(NO₂)₆]₂ → 5 ions
- (iv) [Cr(NH₃)₆]Cl₃ → 4 ions

**Arranging in order of increasing molar conductivity:**
1. (ii) [Cr(NH₃)₃(NO₂)₃] → 1 ion (least conductivity)
2. (i) K[Co(NH₃)₂(NO₂)₄] → 2 ions
3. (iv) [Cr(NH₃)₆]Cl₃ → 4 ions
4. (iii) [Cr(NH₃)₅(NO₂)]₃[Co(NO₂)₆]₂ → 5 ions (highest conductivity)

**Final order:**
(ii) < (i) < (iv) < (iii)

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