Q.i. For the reaction, $\mathrm{N_2(g) + 3\ H_2(g) \longrightarrow 2\ NH_3(g)}$, what is the relationship among $\dfrac{\mathrm{d[N_2]}}{\mathrm{d}t}$, $\dfrac{\mathrm{d[H_2]}}{\mathrm{d}t}$ and $\dfrac{\mathrm{d[NH_3]}}{\mathrm{d}t}$ ?

The rate of a reaction is how rapidly its reactants are consumed or its products appear. It is expressed as either an AVERAGE rate over a finite time interval, $\text{rate}=\Delta c/\Delta t$, or the true INSTANTANEOUS rate at one exact moment, $\text{rate}=dc/dt$, found as the slope of a tangent drawn to a concentration-versus-time curve. For a simple 1:1 reaction $A\rightarrow B$, the rate of consumption of A equals the rate of formation of B: $\text{rate}=-d[A]/dt=+d[B]/dt$. When stoichiometric coefficients differ, as in $aA+bB\rightarrow cC+dD$, each species' own rate of change must first be divided by its own coefficient before the results agree: $\text{rate}=-\dfrac{1}{a}\dfrac{d[A]}{dt}=-\dfrac{1}{b}\dfrac{d[B]}{dt}=\dfrac{1}{c}\dfrac{d[C]}{dt}=\dfrac{1}{d}\dfrac{d[D]}{dt}$. Its units are always concentration/time, e.g. mol dm$^{-3}$ s$^{-1}$.