Conisder the chemical reaction
`N_(2)(g) + 3H_(2)(g) rarr 2NH_(3)(g)`
The rate of this reaction can be expressed in terms of time derivatives of the concentration of `N_(2)(g), H_(2)(g)`, or `NH_(3)(g)`. Identify the correct relationship among the rate expresisons.

Options

A. `Rate = (d[N_(2)])/(dt) = -(1)/(3) (d[H_(2)])/(dt) = (1)/(2) (d[NH_(3)])/(dt)`
B. `Rate = -(d[N_(2)])/(dt)= -3 (d[H_(2)])/(dt)= 2 (d[NH_(3)])/(dt)`
C. `Rate = (d[N_(2)])/(dt) = (1)/(3) (d[H_(2)])/(dt)= -(1)/(2) (d[NH_(3)])/(dt)`
D. `Rate = -(d[N_(2)])/(dt)= -(d[H_(2)])/(dt) = (d[NH_(3)])/(dt)`

Answer

A

Explanation

The average rate and the instananeous rate are equal for only one instant in any time interval. As the time interval becomes smaller, the average rate becomes a better and better approximation of the instantaneous rate. The average rate will be the ssame as the instantaneous rate when the time interval is zero.
Instanteous rate `=underset(Deltatrarr0)(lim)(-Delta[A])/(Deltat)`
The instantaneous rate is the limit of the average rate as `Deltat` approaches zero. Using the notation of ther calculus, we write the expression for this limit as `-d[A]//dt` . The rate of most chemical reaction depends in some way on the concentration of one or more of the reaction proceeds, their concentrations decrease and the rate of the reaction decreases.
The instantaneous rate changes continuously. At first, the instantaneous rate is higher than the average rate but at the end of the interval, the instantaneous rate is lower than the average rate.