question_answer 1)

Bromine monochloride \[\left( BrCl \right)\]decomposes into bromine and chlorine and reaches the equilibrium: \[2BrCl(g)\rightleftharpoons B{{r}_{2}}(g)+C{{l}_{2}}(g)\] The value of\[{{K}_{c}}\] is 32 at 500 K. If initially pure \[BrCl\] is present at a concentration of\[3.3\times {{10}^{-3}}mol{{L}^{-1}}\], what is its molar concentration in the mixture at equilibrium?

Answer:

The given reaction is: \[\underset{\begin{smallmatrix} t=0 \\ At\,equilibrium \end{smallmatrix}}{\overset{{}}{\mathop{{}}}}\,\underset{\underset{0.0033-2x}{\mathop{0.0033}}\,}{\mathop{2BrCl(g)}}\,\rightleftharpoons \underset{\begin{smallmatrix} 0 \\ x \end{smallmatrix}}{\mathop{B{{r}_{2}}(g)}}\,+\underset{\begin{smallmatrix} 0 \\ x \end{smallmatrix}}{\mathop{C{{l}_{2}}(g)}}\,\] \[{{K}_{c}}=\frac{[B{{r}_{2}}][C{{l}_{2}}]}{{{[BrCl]}^{2}}}\] \[32=\frac{{{x}^{2}}}{{{(0.0033-2x)}^{2}}}\] \[5.656=\frac{x}{0.0033-2x}\] \[x=1.5\times {{10}^{-3}}\] \[[BrCl]=0.0033-2x\] \[=0.0033-2\times 1.5\times {{10}^{-3}}=3\times {{10}^{-4}}M\]