Which of the following sets of compounds and ions have linear geometry?

• (A) CH₄, NH₄⁺, BH₄⁻
• (B) CO₃²⁻, NO₄⁻, BF₃
• (C) NO₂⁺, CO₂, N₃⁻
• (D) BeCl₂, BCl₃, CH₄

To determine which set of compounds and ions has a linear geometry, we need to look at the molecular shapes based on VSEPR (Valence Shell Electron Pair Repulsion) theory.

Linear Geometry Overview

Linear geometry occurs when a molecule has two bonding pairs of electrons and no lone pairs, resulting in a bond angle of 180 degrees.

Analysis of Each Option

• Option A: CH₄, NH₄⁺, BH₄⁻ - All these compounds have tetrahedral geometry, not linear.
• Option B: CO₃²⁻, NO₄⁻, BF₃ - CO₃²⁻ has trigonal planar geometry, while NO₄⁻ and BF₃ are also not linear.
• Option C: NO₂⁺, CO₂, N₃⁻ - NO₂⁺ is linear, CO₂ is linear, and N₃⁻ is also linear. This set has linear geometry.
• Option D: BeCl₂, BCl₃, CH₄ - BeCl₂ is linear, but BCl₃ and CH₄ are not.

Conclusion

The correct answer is Option C: NO₂⁺, CO₂, N₃⁻, as all these species exhibit linear geometry.