First order reaction

I am little bit confuse about relating the half life time period of a first order reaction something like

$$\ce{2A -> B + C}$$

Here the rate of reaction will be half of the rate at which $$\ce{A}$$ is used up.

$$\text{Rate of reaction} = k[\ce{A}]$$

$$\text{Rate of disapperance of}~\ce{A} = 2k[\ce{A}]$$

Integrating it half life will be $$\displaystyle\frac{\ln 2}{2k}$$. Am I wrong somewhere?

• It is absolutely correct. – Harsh Wasnik May 12 at 18:06
• Is there something else you are confused about? Your math may be correct, but you seem to be implying that there is a problem with your answer. – Michael Lautman May 14 at 20:27
• Am I being obtuse here but $\ce{A+A\to \cdots}$ is a second order reaction, not a first order one which would be $\ce{A\to\cdots}$. You can also calculate the half life of a second order reaction. – porphyrin May 16 at 18:33