About this video
This lesson derives the integrated rate law for a second-order reaction. Starting from a rate law that depends on the square of the concentration of A, it separates variables, integrates from time zero to t, and rearranges to get 1/[A] = kt + 1/[A]0. A plot of 1/[A] against time is therefore a straight line whose slope is the rate constant k.
You'll be able to
- write the differential rate equation for a second-order reaction in terms of [A]
- separate variables and integrate to derive the integrated rate law
- use a straight-line plot of 1/[A] versus time to find the rate constant
Key words
- Second-order reaction
- A reaction whose rate depends on the concentration of a reactant raised to the second power.
- Rate constant (k)
- The proportionality constant in the rate law, which is the slope of the 1/[A] versus t plot for second order.
- Integrated rate law
- An equation that gives the concentration of a reactant as a function of time, obtained by integrating the rate law.
- Separation of variables
- A method for solving a differential equation by moving all terms in one variable to one side and the other variable to the other.
- Instantaneous rate
- The rate at a specific moment, written as the derivative of concentration with respect to time.
Transcript
- [Voiceover] Diabetes mellitus is a group of disorders that's caused by improper function of the hormone insulin, which is secreted by the pancreas. Now, this results in disregulation of blood glucose levels in the body, specifically resulting in hyperglycemia or high blood sugar, which is the hallmark of diabetes.
Now, since diabetes is a group of disorders, this implies that there are multiple different conditions that can lead to diabetes mellitus, which is true. So let's break down diabetes into three major types. Type I, Type II, and a third category which we'll just label as miscellaneous.
Now, before we dive into these three types of diabetes, let's briefly review how the hormone insulin works. In response to increase in blood glucose levels, the pancreas produces and secretes a hormone known as insulin into the bloodstream. And this insulin acts on cells throughout the body to remove the glucose from the bloodstream by either taking it up to use it for energy or to store it in the form of glycogen.
And as a result, the blood glucose levels decrease. And these decreased blood glucose levels then serve as a feedback mechanism to inhibit the pancreas from secreting more insulin. So you can see that there are two major steps in this insulin pathway. First, insulin must be secreted by the pancreas in response to this increasing blood glucose level.
And second, the cells throughout the body must respond to the insulin in order to carry out its metabolic functions in order to lower the glucose levels. Now, this mechanism can be thought of as similar to that of a thermostat in an air conditioning within a home.
When the temperature goes up, this is sensed by the thermostat, which then sends an electrical signal to turn on the air conditioner, which will then decrease the temperature. And as the temperature goes down, this will inhibit the thermostat from continuously keeping the air conditioner on.
And this mechanism here is gonna become very important in just a minute as we differentiate the different types of diabetes mellitus. So let's go through each of these types individually. Type I diabetes presents mostly during childhood. And it's caused by a genetic predisposition plus some sort of environmental trigger.
Exactly what this is isn't quite known. But the combination of these two results in an auto-immune disorder in which the immune system attacks the beta cells of the pancreas to prevent them from producing insulin. On the other hand, Type II diabetes typically, although not always, presents during adulthood.
And it's even more strongly associated with a genetic predisposition. But in Type II diabetes, instead of this unknown trigger, the genetic predisposition is accompanied with other predisposing conditions, such as obesity or hypertension. And this combination of factors results in an inability of these cells throughout the body to respond to insulin.
Then although Type I and Type II diabetes are the most common causes of diabetes mellitus, there are a couple other important causes of the disease. And these include diabetes caused by medications, known as drug-induced diabetes. And drug-induced diabetes most commonly occurs with a group of medications that are known as glucocorticoids, which are steroid medications most frequently prescribed to decrease inflammation throughout the body, such as with conditions like chronic asthma or Crohn's disease.
And the other miscellaneous cause of diabetes mellitus that's really important to mention is the diabetes that's associated with pregnancy, known as gestational diabetes. Now, let's tie this all together to receive a better understanding of how these different types of diabetes affect this underlying insulin pathway and result in diabetes mellitus.
In Type I diabetes, this auto-immune attack on the beta cells of the pancreas prevent the production and secretion of insulin into the blood. Thus, Type I diabetes inhibits this first step in the insulin pathway. And since it decreases the production of insulin, it's referred to as an insulin deficiency.
However, in Type II diabetes as well as drug-induced and gestational diabetes, the pancreas continues to secrete insulin. However, it's the cells throughout the body that are unable to adequately respond to it. So in a sense, these mechanisms inhibit the second step in the insulin pathway.
And this is known as insulin resistance, which can be thought of as a relative insulin deficiency. So going back to this thermostat analogy, if either the thermostat or the air conditioner is broken, the system as a whole doesn't work. The temperature inside the house is gonna continue to rise.
Similarly, in diabetes mellitus, it doesn't matter whether the underlying mechanism affects this first step, such as with Type I diabetes, or the second step as with Type II diabetes, drug-induced diabetes, and gestational diabetes. Regardless, there's gonna be either an insulin deficiency or a relative insulin deficiency.
So this pathway will not work. And the body won't be able to decrease glucose levels. This results in an increase level of glucose, which is known as hyperglycemia, which as I mentioned at the beginning, is the hallmark finding in diabetes mellitus.
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