7.22. Bromine monochloride (BrCl) decomposes into bromine and chlorine and reaches the equilibrium:
2BrCl (g) ​⇌ Br₂ (g) + Cl₂ (g)
The value of Kc is 32 at 500 K. If initially pure B_rCl is present at a concentration of 3.3 x10^-3mol L^-1, what is its molar concentration in the mixture at equilibrium?        

<p>&nbsp;Let x moles of&nbsp;BrCl&nbsp;decompose in order to attain the equilibrium. The initial molar concentration and the molar concentration at equilibrium point of different species may be represented as follows:<br>2BrCl₂?(g) ?→?Ar_2?(g)+Cl₂?(g)</p><p>3.3×10⁻³m&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0</p><p>3.3×10⁻³−2αα?&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; α</p><p>&nbsp;</p><p>∴&nbsp;Kc?= (α×α)? /(3.3×10−3−2α)²</p><p>⇒&nbsp;α² / (3.3×10−3−2α)²?=32</p><p>⇒&nbsp;α / (3.3×10−3−2α)^2?=4</p><p>⇒&nbsp;α=18.67×10−3−8 α</p><p>⇒&nbsp;(1+ 8 α =18.67×10⁻³</p><p>⇒&nbsp;α= 1.5162×10⁻³</p><p>∴&nbsp;Molar concentration of&nbsp;BrCl&nbsp;at equation&nbsp;</p><p>[BrCl] =3.3×10⁻³−2α</p><p>=3.3×10⁻³−2×1.562×10⁻³</p><p>=0.267×10⁻³M</p>

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