Problem 1
For both integrated rate laws, show that (R) decreases as \(t\) increases.
Problem 3
If one obtained data for a second-order reaction, and then made a graph of \(1 /(\mathrm{R})\) versus \(t\), the resulting plot would be a straight line. a) What would be the slope? b) What would be the \(y\) -intercept?
Problem 7
Recall that for a first-order reaction: $$ \ln (\mathrm{R})=\ln (\mathrm{R})_{0}-k t $$ a) When \(t=t_{1 / 2}\), what is the value of \((\mathrm{R})\) in terms of \((\mathrm{R})_{0}\) ? b) Show that \(t_{1 / 2}=\frac{\ln 2}{k}=\frac{0.693}{k}\) for a first-order reaction.
Problem 8
Recall that for a second-order reaction: $$ \frac{1}{(\mathrm{R})}=\frac{1}{(\mathrm{R})_{\mathrm{o}}}+k t $$ a) When \(t=t_{1 / 2}\), what is the value of (R) in terms of \((\mathrm{R})_{0}\) ? b) Show that \(t_{1 / 2}=\frac{1}{k(R)_{0}}\) for a second-order reaction.
