## Exponential Curve

$\frac{d[R]}{dt}=-k[R]; \ln [R]=-kt + \ln [R]_{0}; t_{\frac{1}{2}}=\frac{0.693}{k}$

Chase Yonamine 1J
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### Exponential Curve

Why does a plot of [Reactants] vs time for a 1st order reaction give an exponential curve?

Posts: 35
Joined: Fri Sep 28, 2018 12:19 am

### Re: Exponential Curve

The integrated rate law can be expressed in exponential form as [A]=[A].e−kt
First order reactions show an exponential decay of reactants as a function of time. Because natural log (ln) was introduced into the integration, we had to use "e" to make calculations easier. In doing that, the right side of the equation became an exponential function of the form y = a(1 - r)^x.

jonathanjchang2E
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### Re: Exponential Curve

The plot is an exponential curve because as the reaction progresses, there are fewer and fewer reactants and the reaction rate decreases. The reaction rate decreases because there are fewer successful collisions between the reactants to form products since there are fewer reactants as time goes on.

Clarissa Cabil 1I
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### Re: Exponential Curve

JadeSebti1L wrote:The integrated rate law can be expressed in exponential form as [A]=[A].e−kt
First order reactions show an exponential decay of reactants as a function of time. Because natural log (ln) was introduced into the integration, we had to use "e" to make calculations easier. In doing that, the right side of the equation became an exponential function of the form y = a(1 - r)^x.

Just to clarify, is the exponential form k[A] = k[A]0e-kt just another version of the integrated rate law of a first order reaction? Can someone explain the distinction between the two and describe when we should use either form?

SydBenedict2H
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### Re: Exponential Curve

I thought on Monday he said first order rate laws would always have a linear slope? -k?

Ian Marquez 2K
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### Re: Exponential Curve

This exponential curve is modeled as a linear function because of the ln[A] on the left side of the equation. If you were to solve this equation for just [A], you would see that the function would be a decreasing exponential curve. Since the left is not solving for [A] and is in terms of ln[A], this plot is shown through linear regression.

Raj_Bains_2C
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### Re: Exponential Curve

This is because the reactant concentration decreases exponentially in a first order reaction.