In a chemistry class, a student follows the breakdown of a gas in a closed vessel…

In a chemistry class, a student follows the breakdown of a gas in a closed vessel. The concentration $c$ of the gas, in mol/L, depends on the time $t$ in seconds. A data book says that the breakdown is a second-order reaction: the rate of fall of $c$ is proportional to the square of $c$. The rate constant is $0.40\ \text{L/(mol s)}$, so $\dfrac{dc}{dt} = -0.40\,c^2$. At the start, $t = 0\ \text{s}$, the concentration is $2.0\ \text{mol/L}$. The student wants two values. The first is the concentration after $5\ \text{s}$. The second is the half-life, the time taken for the concentration to fall to half of its starting value. She also asks herself whether the half-life would be the same if the experiment started from a different concentration. Find the two values, and decide whether her guess is right.