How to find the initial rate of a rate plot? [closed]








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[![enter image description here](https://i.stack.imgur.com/LM5Vj.jpg)](https://i.stack.imgur.com/LM5Vj.jpg)


In the graph above, how do I find the initial rate of $$\frac{d[A]}{dt}$$


My balanced chemical equation is $$\ce{3A + B -> 2C}\\[1em]$$




To get the most accurate results, simply draw a line from the first two point of the graph and find its slope. This can also be done numerically. Say the first two observations are $[A]\_{t\_0}$ and $[A]\_{t\_1}$ at times $t\_0$ and $t\_1$, respectively:


$$
\left(\dfrac{d[A]}{dt}\right)\_{t\_{0}} \approx \dfrac{[A]\_{t\_1}-[A]\_{t\_0}}{t\_1 - t\_0}
$$


**Note:** we are approximating the *initial* rate at $t\_0$ with the *average* rate between $t\_0$ and $t\_1$. The initial rate will be slightly more negative than the average rate we have calculated.


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