Final answer:
To find the concentration as a function of time, we can use the solution of the differential equation and then graph it. We can also determine the rate of change of concentration with respect to time and analyze the behavior of the concentration graph in relation to the initial conditions. Finally, we can evaluate the significance of the solution in a real-world context.
Step-by-step explanation:
To calculate the concentration function as a function of time, we need to use the solution of the differential equation provided in exercise 37. Then, we can plot the concentration function on a graphing utility. Let's go through the steps:
a) Calculate the concentration function:
Using the given solution of the differential equation, substitute the values of time, rate constant, and initial concentration into the equation to calculate the concentration at any given time.
b) Graph the concentration function:
Using a graphing utility, plot the concentration values as a function of time to visualize the concentration-time relationship.
c) Determine the rate of change of concentration:
Take the derivative of the concentration function with respect to time to find the rate of change of concentration at any given time.
d) Analyze the behavior of the concentration graph:
Observe the graph to understand how the concentration changes over time and compare it to the initial conditions to analyze the initial rate and the instantaneous rate of the reaction.
e) Evaluate the significance in a real-world context:
Consider the reaction being studied and determine the practical implications and applications of the obtained concentration function.