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The following reaction occurs in a rigid, closed container with a moveable piston.

$TiCl_{4(l)}+804.2 kJ \rightleftarrows Ti_{(s)}+2 Cl_{2(g)}$



After equilibrium is established, the piston is pulled out, increasing the volume of the container. Complete the table to indicate how the concentration of each reactant and product changes as the volume increases.



Substance		Concentration increasesConcentration decreasesConcentration does not change

$TiCl _{4(l)}$		◯◯◯

$Ti _{(s)}$		◯◯◯

$Cl _2(g)$		◯◯○

Verified Answer :

  • The concentration of pure solids and liquids (\(TiCl_{4(l)}\) and \(Ti_{(s)}\)) is constant and independent of the container volume.
  • The concentration of the gaseous component \(Cl_{2(g)}\) is governed by the equilibrium constant \(K = [Cl_2]^2\), which is constant at a fixed temperature.
  • Because \(K = [Cl_2]^2\), the equilibrium concentration \([Cl_2] = \sqrt{K}\) must be the same before and after the volume change at the same temperature.
  • Therefore, the concentration of all species does not change at equilibrium.

Explanation

  1. Analysis of Concentrations at Equilibrium

The equilibrium reaction is given by:
\[TiCl_{4(l)} + 804.2 \text{ kJ} \rightleftarrows Ti_{(s)} + 2Cl_{2(g)}\]
We are analyzing the effect of increasing the volume of the container at constant temperature.

  • Liquids and Solids: The concentration of pure condensed phases (like \(TiCl_{4(l)}\) and \(Ti_{(s)}\)) is defined by their density and molar mass. This value is intensive and does not depend on the total volume of the reaction vessel, as long as the substance exists in the container. Therefore, the concentration of \(TiCl_{4(l)}\) and \(Ti_{(s)}\) remains constant.
  • Gases: The gaseous species \(Cl_{2(g)}\) is involved in the equilibrium constant expression. For this specific reaction, the equilibrium constant \(K\) is defined as:

\[K = [Cl_2]^2\]
The equilibrium constant \(K\) is solely a function of temperature. Since the temperature is assumed to be constant throughout the volume expansion process, the equilibrium concentration of \(Cl_{2(g)}\) is determined by \(K\):
\[[Cl_2] = \sqrt{K}\]
When the volume is increased, the system undergoes a temporary perturbation; however, to re-establish the equilibrium state at the same temperature, the concentration of the gaseous product must return to its original value, \(\sqrt{K}\). Thus, at the new equilibrium state, the concentration of \(Cl_{2(g)}\) is the same as it was before the expansion.

  1. Summary Table of Changes

Based on the analysis, the concentration of all three substances remains unchanged at the final equilibrium state compared to the initial state.

| Substance | Concentration increases | Concentration decreases | Concentration does not change |
| :--- | :---: | :---: | :---: |
| \(TiCl_{4(l)}\) | ◯ | ◯ | ⦿ |
| \(Ti_{(s)}\) | ◯ | ◯ | ⦿ |
| \(Cl_{2(g)}\) | ◯ | ◯ | ⦿ |

Examples

Consider a sealed container used in industrial chemical processing where a reaction involving a gas is kept at equilibrium. Understanding that for reactions where the equilibrium constant depends only on gas concentration (like our \(Cl_2\) example), the final concentration of that gas at equilibrium remains fixed regardless of volume changes (as long as temperature is constant) helps engineers predict reaction yields. This knowledge ensures that when adjusting vessel sizes or throughput in industrial synthesis, the concentration levels that drive reaction rates remain predictable.

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