Rate Law and Reaction Orders Study Notes

Rate Law and Reaction Orders

Definition of Rate Law

• The rate of a reaction indicates how quickly reactants are being converted to products. The rate can be expressed mathematically through a rate law.

• The general form of a rate law is: $ext{Rate} = k[A]^m[B]^n$ where:

  • $k$ is the rate constant

  • $[A]$ and $[B]$ are the concentrations of the reactants

  • $m$ and $n$ represent the reaction orders with respect to each reactant.

Given Rate Law

• For a specific reaction, the rate law is given as:
  $ext{Rate} = k[H<em>2][NH</em>3]$

Reaction Order in H₂

• The reaction order for H₂ is determined by the exponent of its concentration in the rate law.

• Conclusion: The reaction order in H₂ is 1 (since it is raised to the first power).

Reaction Order in NH₃

• Similarly, the reaction order for NH₃ is also determined from its exponent in the rate law.

• Conclusion: The reaction order in NH₃ is 1.

Overall Reaction Order

• The overall reaction order is the sum of the individual reaction orders.
  $ext{Overall Reaction Order} = m + n$

• In this case:

  • $m = 1$ (for H₂)

  • $n = 1$ (for NH₃)

• Conclusion: The overall reaction order is 2.

Effect of Concentration Change on Reaction Rate

• The initial rate of the reaction is observed to be 92.0 M/s at a specific concentration of H₂ and NH₃.

• If the concentration of H₂ is halved, the new concentration of H₂ would be $rac{1}{2}[H_2]$.

• Given the rate law, the new rate can be computed as follows: ext{New Rate} = kigg[ rac{1}{2}[H2]igg][NH3]

  • This indicates that the reaction will decrease in rate because of the halving of the concentration of H₂.

• The relationship is proportional to the concentration, thus: $ext{New Rate} = rac{1}{2} imes 92.0 ext{ M/s} = 46.0 ext{ M/s}$

  • Conclusion: The initial rate of the reaction when the concentration of H₂ is halved is 46.0 M/s. Ensure to report this value with the correct number of significant digits.

Calculation of Rate Constant (k)

• When the concentrations of H₂ and NH₃ are given as 1.1 M and 1.8 M respectively, and the measured rate is 2.0 x 10⁵ M/s, the rate constant can be calculated using the rate law:
  $2.0 imes 10^5 = k[1.1][1.8]$

• Rearranging for k gives: $k = rac{2.0 imes 10^5}{1.1 imes 1.8}$

  • Calculating this gives:
    $k = rac{2.0 imes 10^5}{1.98} \ k <br>ightarrow 1.01 imes 10^5$

• However, following through correctly and ensuring significant digits,

• Conclusion: The value of the rate constant $k$ is 9.1 × 10³ M².s⁻¹.