## k in first order reactions

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

Posts: 97
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### k in first order reactions

In section 7B, why are the rate constants for first order reactions positive ? If the plot of the first order reaction has a negative slope then shouldn't k be negative in the solutions?

Ryan Yee 1J
Posts: 101
Joined: Sat Aug 17, 2019 12:16 am

### Re: k in first order reactions

Rate constants are positive, but the slopes are negative because rate measures the disappearance of reactant (which is why k is negative). In a first order reaction, the negative of the slope is equal to k.

Juliana Chopelas 1A
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Joined: Sat Aug 24, 2019 12:16 am

### Re: k in first order reactions

Rate constants are always positive due to the Arrhenius equation but the slope is negative because it shows how the reactants are affected in the first order reaction.

Helen Struble 2F
Posts: 97
Joined: Sat Aug 24, 2019 12:17 am

### Re: k in first order reactions

Rate constants are always positive. In the plot of ln[A] by time, for first order reactions, the slope is equal to -k. So, while the slope is technically negative, the rate constant, as with any rate constant, is positive.