Reaction Rate Law Study Notes

Reaction Rate Law

Rate Law Definition

• The rate law for a certain reaction is expressed as:
  • $rate = k [N₂] [O₃]$
  • Here, (k) is the rate constant, ([N₂]) is the concentration of nitrogen dioxide, and ([O₃]) is the concentration of ozone.

Reaction Orders

• To find the reaction order for each reactant and the overall reaction order, we analyze the rate law:

Reaction Order in N₂

• The reaction order with respect to (N₂) is 1, indicated by the first power of ([N₂]) in the rate law.

Reaction Order in O₃

• The reaction order with respect to (O₃) is also 1, indicated by the first power of ([O₃]) in the rate law.

Overall Reaction Order

• The overall reaction order is calculated by summing the orders of each reactant:
  • Overall order = Order in (N₂) + Order in (O₃)
  • Overall order = 1 + 1 = 2.

Initial Reaction Rate Calculation

• Given that the initial rate of reaction is 0.680 M/s under specific concentrations of (N₂) and (O₃), we analyze the effect of doubling the concentration of (N₂):
  • Original concentrations:
  • ([N₂] = x)
  • ([O₃] = y)
  • When ([N₂]) is doubled, it becomes ([N₂] = 2x).
• To find the new rate, we apply the rate law:
  • New rate = (k [2x][y] = 2k[x][y] = 2 \times rate) (since rate = k[x][y]).
  • Thus, the new initial rate would be:
  • New rate = 2 (\times 0.680) M/s = 1.36 M/s (noting significant digits).

Rate Constant Calculation

• A second part provides specific concentrations and a measured rate to calculate the rate constant (k):
  • Given:
  • Rate = 2.0 x 10³ M/s
  • ([N₂] = 1.2 M)
  • ([O₃] = 1.1 M)
  • Using the rate law:
  • Rate = (k [1.2][1.1])
  • Thus, $k = \frac{Rate}{[N₂][O₃]} = \frac{2.0 \times 10^{3} \text{ M/s}}{(1.2 \text{ M})(1.1 \text{ M})}$
  • Calculate (k):
  • $k = \frac{2.0 \times 10^{3}}{1.32} \approx 1.5151515 \text{ M}^{-1}\text{s}^{-1}$
  • Rounding to the correct number of significant digits (2 sig figs): (k \approx 1.5 \text{ M}^{-1}\text{s}^{-1}$$.