Q.Write the rate expression for:

[!FORMULA] $\mathrm{2\ N_2O(g) \longrightarrow 4\ NO_2(g) + O_2(g)}$

[!NOTE]
The book prints the reactant as 2 N$_2$O(g), which cannot give this product set -- only N$_2$O$_5$ balances (the book's own Problem 6.1 and Section 6.5.6 print the same decomposition correctly as 2 N$_2$O$_5$(g) $\longrightarrow$ 4 NO$_2$(g) + O$_2$(g)). The equation is transcribed as printed; the answer derives the rate expression for the intended N$_2$O$_5$ reaction and says so.

Step 1. As printed, the box's equation reads 2 N$_2$O(g) $\longrightarrow$ 4 NO$_2$(g) + O$_2$(g). N$_2$O cannot give this product set (2 N$_2$O carries 2 O atoms; 4 NO$_2$ + O$_2$ carries 10), so the intended reactant is N$_2$O$_5$ -- the book's own Problem 6.1 and Section 6.5.6 print the same decomposition correctly as 2 N$_2$O$_5$(g) $\longrightarrow$ 4 NO$_2$(g) + O$_2$(g).

Step 2. For a general reaction aA $\longrightarrow$ bB + cC, the rate of reaction divides each species' rate of change by its own stoichiometric coefficient: rate = $-\frac{1}{a}$ d[A]/dt = $+\frac{1}{b}$ d[B]/dt = $+\frac{1}{c}$ d[C]/dt.

Step 3. With a = 2, b = 4, c = 1 for the intended equation: …

General rate expression from stoichiometric coefficients, rate = -(1/a)d[A]/ …

• Forgetting the negative sign for a reactant's rate of disappearance. …