Problem 1 . The following is a bunch of chain reactions that depend on chain-branching, where R is a radical, A is a species of interest, and P is a product species. 1. Write down the net production rate of radicals. 2. Using the steady-state assumption for [R], derive the expression of [R]. 3. Derive the expression of the explosion limit of n, which is denoted by nexpl. 4. Derive the expression of nexpl for p0 and p. 5. Analyze the following graph of nexpl vs. p, with respect to the following points, (a) effect of pressure, i.e. why the curve is V-shaped, and (b) effect of temperature