Please if anyone can help me, I was in a class with myMy lecturer when he mentioned that the formula for the rate constant in$k$ for the first order reaction is this
$$k = \frac{2.0303}{t_{1/2}}\,\log\frac{[\ce{A}]_0}{[\ce{A}]_{t_{1/2}} - [\ce{A}]_0},\tag{1}$$
where $t_{1/2}$ is the half-life; $[\ce{A}]_0$ is the initial concentration; $[\ce{A}]_{t_{1/2}}$ is the concentration at half-life.
In which what I know recently is that the rate constant offor the first order reaction is
$$ \begin{align} & & \ln\frac{[\ce{A}]_t}{[\ce{A}]_0} &= -kt \tag{2}\\ &\implies & [\ce{A}]_t &= [\ce{A}]_0\,\mathrm e^{-kt}\tag{3} \end{align} $$
I ask himmy teacher, but he said I should go and do more research on it and I have be on internet for Moro than a hour now, but I couldn't find it please can anyone help me.
