subject: Second Order Rate Constant [print this page] Second order rate is obtained from derivatives. The function can be differentiated by two times for finding the second order rate. The constant value of the second order rate of change will be zero. Differentiation of any constant value is always zero. The degree of the second order rate is two. The second order rate of change can be denoted as (d2y / dx^2).
Example Problem for Second Order Rate Constant
Example 1:
Find the second order rate of change of the given function and find the second order rate constant value. Given function
G = 3x^4 + 5x^2 - 8
Solution:
Given function G = 3x^4 + 5x^2 - 8
Differentiate the function with respect to x, we get
dG / dx = 12x^3 + 10x
For finding second order rate of change, once again differentiate the above function
Second order rate of change (d^2G / dx^2) = 36x^2
Here, second order rate constant value is zero
Answer:
Second order rate constant value is zero
Example 2:
Find the second order rate constant of the function x = 4t3 + 2t2 + 3t^4 - 2
Solution:
Given function x = 4t3 + 2t2 + 3t^4 - 2
First order rate of change of the function is given as,
(dx / dt) = 12t2 + 4t + 12t3
Second order rate of change of the function is given as,
(d^2x / dx^2) = 24t + 4 + 36t^2
Here, Constant value is 4
Answer:
The second order rate constant value is 4.
Example 3:
Find the acceleration of the function z = 0.8t^3 - 2t^4 - 0.7t^2
Solution:
Given function is z = 0.8t^3 - 2t^4 - 0.7t^2
Acceleration = d2z/ dt^2
d2z / dt^2 = second order rate change of the function
First order rate of change of the function is given as,
(dz / dt) = 2.4t^2 - 8t^3 - 1.4t
Second order rate of change (d2z / dt^2) = 4.8t - 24t^2 - 1.4
Second order rate constant of the function is - 1.4
Answer:
Acceleration (d2z / dt^2) = 4.8t - 24t^2 - 1.4
Constant value is - 1.4
Practice Problems for Second Order Rate Constant
Example 1:
Find the second order rate constant of the function f(x) = 0.7t^2 + 9.1t^3 - 5t
Answer:
The final answer is 1.4
Example 2:
Find the second order rate constant of the function g(x) = 23t^4 - 64t^3 + 43t^2 - 89t - 7
