The data in the table below were obtained for the reaction: a + b → p experiment number [a] (m) [b] (m) initial rate (m/s) 1 0.273 0.763 2.83 2 0.273 1.526 2.83 3 0.819 0.763 25.47 the magnitude of the rate constant is ________.
Accepted Solution
A:
if we tabulate the data given, we obtain the following table; Exp [a](m) [b] (m) Initial rate (m/s) 1 0.273 0.763 2.83 2 0.273 1.526 2.83 3 0.819 0.763 25.47 the rate equation rate = k [a]ˣ[b]ⁿ where k = rate constant x and n are order of reaction with respect to a and b respectively lets take experiment 1 and 2 where [a] is constant so we can find the order of reaction with respect to b
2.83 m/s = k[0.273 m]ˣ[0.763 m]ⁿ ---> 1)
2.83 m/s = k [0.273 m]ˣ[1.526 m]ⁿ ----> 2) 2)/1) 1 = [1.526/0.763]ⁿ 1 = 2ⁿ n = 0 next we have to find out x, we have to take experiment 1 and 3 where [b] remains constant 25.47 m/s =k [0.819]ˣ[0.763]ⁿ --3) 2.83 m/s = k[0.273 m]ˣ[0.763 m]ⁿ ---> 1)
3)/1) 25.47/2.83 = [0.819/0.273 m]ˣ 9 = 3ˣ x = 2 therefore order with respect to a = 2 and order with respect to b = 0 rate = k[a]²[b]⁰ to find k lets substitute 1st experiment values 2.83 m/s = k [0.273 m]² [0.763]⁰ k = 2.83/0.0745 k = 37.98 m⁻¹s⁻¹