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Assuming the volume of a container at equilibrium is 2 L, what is the new equilibrium concentration of NOCl if the volume is changed to 1 L, given that the initial concentration of NOCl is 0.10 M and the equilibrium constant (Kc) is 0.054?

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To solve this problem, we need to use the reaction for the dissociation of NOCl and the equilibrium constant expression. The reaction is:2 NOCl g   2 NO g  + Cl2 g Let's denote the initial concentration of NOCl as [NOCl] = 0.10 M, and the initial concentrations of NO and Cl2 as [NO] = [Cl2] = 0 M. When the volume is changed to 1 L, the initial concentration of NOCl will change. Let's denote the new initial concentration as [NOCl'].Since the number of moles of NOCl remains constant, we can use the formula:n = C  VWhere n is the number of moles, C is the concentration, and V is the volume. For the initial state:n = [NOCl]  V = 0.10 M  2 L = 0.20 molesFor the new state:n' = [NOCl']  V' = [NOCl']  1 LSince the number of moles remains constant:n = n'0.20 moles = [NOCl']  1 L[NOCl'] = 0.20 MNow, let's denote the change in concentration at equilibrium as x. The equilibrium concentrations will be:[NOCl] = 0.20 M - 2x[NO] = 0 M + 2x[Cl2] = 0 M + xThe equilibrium constant expression is:Kc =  [NO]^2  [Cl2]  /  [NOCl]^2 Substitute the equilibrium concentrations and the given Kc value:0.054 =   2x ^2  x  /   0.20 - 2x ^2 Now we need to solve this equation for x. It's a cubic equation, and solving it, we get:x  0.0367Now we can find the new equilibrium concentration of NOCl:[NOCl] = 0.20 M - 2x  0.20 M - 2 0.0367   0.1266 MSo the new equilibrium concentration of NOCl is approximately 0.1266 M.

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