Reaction rate graphs

[victorias]

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I am trying to practice more with graphs since that is my weakness.

So for the reaction rate versus time graph (below).
I know that Rate = -[Substrate]/time
[substrate] = rate x time
Is it correct to say that the area under the graph below is the [substrate]?

If the [substrate] is in excess, meaning that we have a huge abundance of the reactant or that we keep on replenishing it, would the graph just me a straight horizontal line?

 

[aldol16]

Integrating that graph will give you how much substrate is consumed over the time interval you integrate.

If the substrate is in excess, you would not be able to measure a change in substrate concentration over time so if you were trying to do that, then the plot would be a horizontal line. However, in that case, you would simply set up the rate experiment so that you're measuring d[P]/dt.

 

[NextStepTutor_2]

I am trying to practice more with graphs since that is my weakness.

So for the reaction rate versus time graph (below).
I know that Rate = -[Substrate]/time
[substrate] = rate x time
Is it correct to say that the area under the graph below is the [substrate]?

If the [substrate] is in excess, meaning that we have a huge abundance of the reactant or that we keep on replenishing it, would the graph just me a straight horizontal line?

View attachment 200290

Hi @victorias Great question!

While the MCAT will not expect you to integrate or do calculus on test day, you WILL need to interpret graphs. Anytime you have an x-y plot, you can reason the slope as change in y/change in x, and then better understand what mathematical relationship they may be showing. In this case, your graph shows reaction velocity and time, not [product] or [substrate]. Your understanding is right, the velocity should be the rate of change of the reaction we can observe over time. In some cases we can measure velocity as change in [reactant] or even change in [product]. In cases of excess [reactant] (aka substrate) this effectively means mathematically, the concentration is said to be constant throughout. This means we can not do any traditional observations and the plot would be flat vs time if we measured velocity using simple change in [reactant]. However, in that case, as aldol pointed out, we can simply measure the rate of formation of the product, and obtain the same information.

hope this helps, good luck!

 

[aldol16]

In this case, your graph shows reaction velocity and time, not [product] or [substrate].

rate = -d/dt = d[P]/dt. Separate variables and integrate. While the MCAT will not expect you to integrate functions, you should at least know what the area under the rate vs. time graph means - that it will give you the change in substrate concentration over the time interval you integrate. This concept is functionally similar to the idea that the integral of a pressure-volume plot gives you work - a concept you should definitely know for the MCAT.

 

[victorias]

Does the slope of this plot mean anything?

 

[aldol16]

Does the slope of this plot mean anything?

Change in rate over change in time. Does that look like anything else to you? Think back to classical mechanics and complete the analogy since biologists like calling this the "velocity" of a reaction anyway. What's even better for the analogy is that you drew it as v vs. t in your graph so the slope would be dv/dt.

 

[NextStepTutor_2]

Does the slope of this plot mean anything?

Sure does, what is dv/dt? acceleration. What does "acceleration" mean in this case? It's a bit wordy for a post but HERE is a great break down of the various plot types (including pics) one can use to discuss the complex and not so complex measurements of reaction rates using enzymes!

hope this helps, good luck!