Nitrogen monoxide reacts with chlorine according t...

Question

Nitrogen monoxide reacts with chlorine according to the equation:

2NO(g) + Cl2 (g) ⟶ 2NOCl(g)

The following initial rates of reaction have been observed for certain reactant concentrations:

What is the rate equation that describes the rate’s dependence on the concentrations of NO and Cl2? What is the rate constant? What are the orders with respect to each reactant?

Jules Bruno · Accepted Answer

We’re being asked to calculate the rate law and the value of the rate constant (k) based on the reaction and data given.Recall that the rate law only focuses on the reactant concentrations and has a general form of:rate law=kAxByk = rate constantA & B = reactantsx & y = reactant ordersWe’re going to calculate the rate law and the rate constant using the following steps:[readmore]Step 1. Calculate the order of the reaction with respect to NOStep 2. To calculate the order of the reaction with respect to Cl2Step 3. Determine the rate law of the reactionStep 4. Calculate the value of the rate constantStep 5. Determine the rate equation or rate of the reactionStep 1. Calculate the order of the reaction with respect to NO.Look for the data where the concentration of NO changes while the concentration of Cl2 remains the same.Calculate order with respect to NO:rate 2rate 1=NOx at rate 2NOx at rate 1x = order(Larger concentration should be on the numerator)Solve for x:4.561.14=1.00x0.50xsince the numerator and the denominator is raised to the same power, you can simplify the equation to:4.561.14=1.000.50x4=2x2 raised to the 2nd power = 4x = 2 → 2nd order with respect to NOStep 2. To calculate the order of the reaction with respect to Cl2. Look for the experimental data where the concentration of Cl2 changes while the concentration of NO remains the same.Calculate order with respect to Cl2:rate 3rate 2=Cl2y at rate 3Cl2y at rate 2y = order(Larger concentration should be on the numerator)Solve for y:9.124.56=1.00y0.50ysince the numerator and the denominator is raised to the same power, you can simplify the equation to:9.124.56=1.000.50y2=2y2 raised to the power of 1 = 2y = 1 → 1st order with respect to Cl2Step 3. Determine the rate law of the reactionrate law=kAxBySubstitute NO and Cl2 and their orders:rate law = k[NO]2[Cl2]1or simplyrate law = k[NO]2[Cl2]Step 4. Calculate the value of the rate constantGo back to the given data. You can use any experimental data to calculate for k, but let’s use the 1st data for this calculation:[NO] = 0.50 M[Cl2] = 0.100 Mrate = 1.14rate law=kNO2O21.14=k0.5021.001.14=k0.251.001.140.25=k0.250.25k = 4.56To determine the unit of k, we will use the following equation:k=M-n+1·t-1n = overall order of the reactionn = order with respect to NO + order with respect to Cl2 n = 2 + 1n = 3t = hour, hrk=M-3+1·hr-1k = M–2 ∙ hr–1Step 5. Determine the rate equation or rate of the reactionRecall that for a reaction aA → bB, the rate of a reaction is given by:rate = -1a∆[A]∆t =1b∆[B]∆twhere:Δ[A] = change in concentration of reactants or products (in mol/L or M), [A]final – [A]initialΔt = change in time, tfinal – tinitialFor NO2: Since NO2 is a reactant, the rate with respect to NO2 is negative (–) since we’re losing reactants.rate = -12∆[NO]∆tFor Cl2: Since Cl2 is a reactant, the rate with respect to Cl2 is negative (–) since we’re losing reactants.rate = -11∆[Cl2]∆tAnswer: The rate equation that describes the rate’s dependence on the concentrations of NO and Cl2rate = -12∆[NO]∆t = -∆[Cl2]∆tThe rate constant is 4.56. The order of NO is 2nd order and the order of Cl2 is 1st order

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