Question

What is the integrated rate law for a 1st order reaction?

Answer 1

The integrated rate law for a first-order reaction is given by the equation
`[A] = [A]0e^(kt)` shows how the concentration of the reactant decreases exponentially over time, and can also be represented in logarithmic form.

Step-by-step explanation:

The integrated rate law for a first-order reaction relates the concentration of a reactant to the elapsed time of the reaction. This expression can be derived by integrating the first-order differential rate law, which is proportional to the concentration of the reactant (rate = k[A]). The result of this integration is an exponential equation:
`[A] = [A]0e^(kt)` is the concentration of the reactant at time t, [A]0 is the initial concentration, k is the rate constant, and t is the time elapsed. For analysis and plotting purposes, this equation can also be represented in logarithmic form as ln([A]) = ln([A]0) - kt. When ln([A]) is plotted against time, the result is a straight line for a first-order reaction, with the slope being -k.

Answer 2

Answer: In[A]_t = kt + In[A]_0

Expiation: the half-life of a first-order reaction is independent of concentration, and this equation has the form y=mx + b so a plot of the natural log of [A] as a function of time yields a straight line

Source: khanacadamey.org

Hope this helps!