First oder graphs

[Jasmin Argueta 1K]

During lecture Lavelle derived the first order reaction and showed us the graph that correlated. I am a bit confused because the graph for a first order reaction is liner, although he said ln[A] on the y axis is exponential. Why is the graph not exponential if it includes ln?

[Chem_Mod]

So f(x) = ln(x) is itself exponential. However, we make ln[A] the x-axis. Because the x-axis and y-axis are measured with the same units, the graph is linear.

[Andrew Bennecke]

Using the equation ln[A]=-kt+ln[A]o, we see how it has the same format as y=mx + b, the skeleton equation for a linear equation. In this case, y=ln[A], m=-k, x=t, and b=ln[A]o. Therefore, we can graph ln[A] in terms of t, where ln[A]o is the initial concentration of [A] at t=o. ln[A] does not take t as an input, so we don't graph it as a logarithmic function, but as a linear one instead.