I'm a mathematician who's currently teaching a course on differential equations. Though I don't know much about chemistry, I like to include examples from chemistry in my course, and I prefer for the details to be accurate. Here is a typical exam problem:
When a container of gaseous nitrogen dioxide is heated above 150°C150 °C, the gas begins to decompose into oxygen and nitric oxide: $$ 2\;\mathrm{NO}_2 \;\longrightarrow\; \mathrm{O}_2 + 2\;\mathrm{NO} $$$$\ce{2NO2 -> O2 + 2NO}$$ The rate of this reaction is determined by the equation $$ \frac{d\,[\mathrm{NO}_2]}{dt} \;=\; -k\,[\mathrm{NO}_2]^2 $$$$\frac{\mathrm d\left[\ce{NO2}\right]}{\mathrm dt} = -k\left[\ce{NO}_2\right]^2$$ where $k$ is a constant.
(a) Find the general solution to the above equation.
(b) A large container holds 50.0 moles of NO2$\ce{NO2}$ at a constant temperature of 600°C600 °C. After one hour, only 34.3 moles remain. How much NO2$\ce{NO2}$ will there be after another hour?
So my questions are:
Is the science in this problem reasonably accurate? Is there anything you would change? (I looked up a suitable value of the rate constant $k$ to make sure that the time in part b was reasonable.)
What are some other examples of reactions that are governed by simple rate laws? Ideally, I'd like to have several examples each of reactions governed by the equations $$ \frac{dy}{dt} = -ky,\qquad \frac{dy}{dt}=-ky^2,\qquad\text{and}\qquad \frac{dy}{dt}=-ky^3. $$$$ \frac{\mathrm dy}{\mathrm dt} = -ky,\qquad \frac{\mathrm dy}{\mathrm dt}=-ky^2,\qquad\text{and}\qquad \frac{\mathrm dy}{\mathrm dt}=-ky^3. $$ (Is $y^3$ really possible? Are non-integer powers of $y$ possible?)
