The following results were obtained during study of the reaction 2 NO ( g )+ Cl ₂( ~g ) 2 NOCl ( g ) . Determine the value of [ X ] in mol / L array |c|c|c|c| Experiment & [NO] mol/L & [ Cl ₂ ] mol/L & Initial rate of formation. [NOCl] mol/L/min I & 0.2 & 0.2 & 6.0 10⁻³ II & 0.2 & 0.4 & 2.4 10⁻² III & 0.4 & 0.2 & 1.2 10⁻² IV & X & 0.6 & 1.35 10⁻¹ array

Step-by-step solution

The rate law for the reaction 2 NO (g) + Cl ₂(g) 2 NOCl (g) is given by r = k[ NO ]^a[ Cl ₂]^b . From experiment I and II, keeping [ NO ] constant at 0.2 mol/L : 2.4 10⁻² 6.0 10⁻³ = ( 0.4 0.2 )^b 4 = 2^b b = 2 . From experiment I and III, keeping [ Cl ₂] constant at 0.2 mol/L : 1.2 10⁻² 6.0 10⁻³ = ( 0.4 0.2 )^a 2 = 2^a a = 1 . The rate law is r = k[ NO ][ Cl ₂]^2 . Using experiment I to find k : 6.0 10⁻³ = k(0.2)(0.2)^2 = k(0.2)(0.04) = k(0.008) . k = 6.0 10⁻³ 8.0 10⁻³ = 0.75 L ^2 mol ⁻² min ⁻¹ . For experiment IV: