## General Chemistry: Principles and Modern Applications (10th Edition)

1. Count the atoms in the initial mixture: 4 $SO_2$ 2 $Cl_2$ 12 $SO_2Cl_2$ 2. Now, assume these are the concentrations in the complete mixture, and find the equilibrium amounts. 3. Draw the ICE table for this equilibrium: $$\begin{vmatrix} Compound& [ SO_2 ]& [ Cl_2 ]& [ SO_2Cl_2 ]\\ Initial& 4 & 2 & 12 \\ Change& -x& -x& +x\\ Equilibrium& 4 -x& 2 -x& 12 +x\\ \end{vmatrix}$$ - The exponent of each concentration is equal to its balance coefficient. $$K_C = \frac{[Products]}{[Reactants]} = \frac{[ SO_2Cl_2 ]}{[ SO_2 ][ Cl_2 ]}$$ 4. At equilibrium, these are the concentrations of each compound: $[ SO_2 ] = 4 - x$ $[ Cl_2 ] = 2 - x$ $[ SO_2Cl_2 ] = 12 + x$ $$4.0 = \frac{(12 + x)}{(4 - x)(2 - x)}$$ 5. Solve for x: $x \approx 1$ or $x \approx 5$ But x cannot be greater than 2, because that would result in a negative Cl2 concentration: x = 1 So: $[ SO_2 ] = 4 - 1= 3$ $[ Cl_2 ] = 2 - 1= 1$ $[ SO_2Cl_2 ] = 12 + 1 = 13$ Find the diagram that represents this. (b)