Consider the reaction of ammonium ions (NH^+_4) and nitrite ions(NO^-_2) shown i

Question

Consider the reaction of ammonium ions (NH^+_4) and nitrite ions(NO^-_2) shown in Equation 19. NH^+_4(aq) + NO^-_2(aq) rightarrow N_2(g) + 2 H_2O(l) Solutions containing NH^+_4 and NO^-_2? were mixed in various quantities and the following rate data at a constant temperature were obtained: Use the method of initial rates to find the order of the reaction with respect to NH^+_4 Use the method of initial rates to find the order of the reaction with respect to NO^-_2. Calculate the rate constant, k, for the reaction of NH^+_4 and NO^-_2. Write the rate equation for the reaction of NH^+_4 and NO^-_2.

Explanation / Answer

Write the rate law in a general form:

Rate r = k[NH4+]x[NO2-]y

a. Compare the rates from determination 2 and 3

      r2/r3 = (0.150 M/0.300 M )x

      6.08x10-7/ 1.22x10-6 = (1/2)x

        1 / 2 = (1/2)x     x = 1 , first order

b. Compare the rates from determination 1 and 2

      r1/r1 = (7.5x10-3 M/15x10-3 M )y

      3.04x10-7/ 6.08x10-7 = (1/2)y

        1 / 2 = (1/2)y     y= 1 , first order

c. k = rate / ([NH4+][NO2-] )

      Use data from one line of the table, e.g., line 1

        k = 3.04x10-7 M/s/(0.150 M x 7.5x10-3 M) = 2.7x10-4 M-1.s-1

           

d.   r = -d[NH4+]/dt = - d[NO2-]/dt = k[NH4+][NO2-]

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