The equilibrium constant, K_C for 3 C ₂ H ₂( ~g ) C ₆ H ₆( ~g ) is 4 ~L ^2 ~mol ⁻² . If the equilil rium concentration of benzene is 0.5 ~mol ⁻¹ than what is the value of concentration of ethylene?

Step-by-step solution

The chemical equation for the reaction is 3 C ₂ H ₂( g ) C ₆ H ₆( g ) . The expression for the equilibrium constant K_ C is given by: K_ C = [ C ₆ H ₆] [ C ₂ H ₂]³ Given K_ C = 4 ~L ² ~mol ⁻² and [ C ₆ H ₆] = 0.5 ~mol ~L ⁻¹ . Substituting the values into the expression: 4 = 0.5 [ C ₂ H ₂]³ [ C ₂ H ₂]³ = 0.5 4 = 0.125 [ C ₂ H ₂] = (0.125)^ 1/3 = (0.5³)^ 1/3 = 0.5 ~mol ~L ⁻¹ . Answer: 0.5 ~mol / L