Rate Eqn. & Order of Rxn C. Y. Yeung (CHW, 2009) p.01

Rate Equation (Rate Law) the mathematical equation relating the rate of rxn to the [reactants]. 3A + 2B  C p.02 Examples: rate  [A] x [B] y order of rxn w.r.t. [A] order of rxn w.r.t. [B]

p.03 rate = rate constant (varies with temp.!!) k[A] x [B] y Therefore, the rate equation shows that:  rate of rxn is affected by [reactants]  rate of rxn is affected by temperature * usually, order of reaction = 0, 1 or 2.

p.04 rate = k [A] m [B] n Example: If [B] and temp. are kept constant, when [A] doubles, rate of reaction increases 4 times. Find the value of m. rate = k’ [A] m  rate 1 = k’ [A] m and rate 2 = k’ (2[A]) m then rate 1 rate 2 = k’ [A] m k’ (2[A]) m =14 = m  m = 2  the rxn is 2 nd order w.r.t. [A].

p.05 If [B] and temp. are kept constant, when [A] doubles, rate of reaction increases 4 times. How to do it? [A][B]Initial rate Expt. 1[A] 01 [B]Rate 1 Expt. 2[A] 02 [B]Rate 2 Expt. 3[A] 03 [B]Rate 3 ….. kept constant t[A] [A] 03 [A] 02 [A] 01 initial rate method Repeat expt. with constant [A] and different [B], find n!

Plot rate vs [A] : p.06 Determination of k, m and n by graphical method rate = k’ [A] m [A][B]Initial rate Expt. 1[A] 1 [B]Rate 1 Expt. 2[A] 2 [B]Rate 2 Expt. 3[A] 3 [B]Rate 3 ….. rate[A] m = 0 m = 1 m = 2 Only m could be found!

p.07 rate = k’ [A] m log (rate) = m log [A] + log k’ log (rate) log [A] y = mx + c m = 0 m = 1 m = 2 log k’ i.e. Both k (=k’/[B]) and m could be found!

p Paper II, Q.2(a)

p Paper II, Q.2(a) : Ans.

p.10 rate = Differential Rate Equation: = k’ [A] m - d[A] dt slope of tangent at a point on the conc. - time graph. (NOT accurate!) = k’ - d[A] dt if m = 0 = k’dt - d[A] = k’ dt - d[A]  = k’t + C - [A] when t = 0, [A] = [A] 0  C = - [A] 0  [A] = - k’t + [A] 0 integrated rate eqn. (zeroth order) No calculation of tangent slope!

p.11  [A] = - k’t + [A] 0 Therefore …. for Zeroth Order Rxn Monitor the variation of conc. along with time by Chemical / Physical Method, Timet1t1 t2t2 t3t3 t4t4 [A][A] 1 [A] 2 [A] 3 [A] 4 [A]t [A] 0 slope = - k’

To conclude …. (1) p.12 Rate Equation shows that the rate of rxn is affected by conc. (order) & temp (k). Find the order of rxn (m, n) by Initial Rate Method (many combinations of [A] & [B]!) Plot log (rate) = m log[A] + log k’, both m, k’ and k could be found.

p.13 Initial Rate Method gives Differential Rate Equation, but m and k may not be accurately found from the initial rates (=slope of tangent). Integrated Rate Equation can give better m and k, as no calculation of tangent is involved. To conclude …. (2)

p.14 To collect data for Integrated Rate Eqn., only one combination of [A] & [B] is needed. Measure [A] at different t. To conclude …. (3) Integrated Rate Eqn. of Zeroth Order: [A] = -k’t + [A] 0

Next …. p.15 Integrated Rate Eqn. of 1 st and 2 nd Order To study whether the decomposition of H 2 O 2 is 1 st order w.r.t. [H 2 O 2 ]. (expt. 8)

Assignment p.16 Pre-lab [due date: 12/2(Thur)] p.47 Q.1-6 [due date: 12/2(Thur)]