![DETERMINING THE RATE EXPONENT HANDOUT - Example 1 Order for [A]: Order for [B]: Order of overall rxn: k = 1 2 3 2.00 x 10 2 L 2 mol -2 s -1 r=k[A][B] 2 Initial Concentration (mol / L) Initial Rate of Formation of Products (mol/L•s) [A] [B] 0.10 0.10 0.20 0.20 0.10 0.40 0.30 0.10 0.60 0.30 0.20 2.40 0.30 0.30 5.40](https://image.slidesharecdn.com/tang02-determiningtherateexponent-110926165728-phpapp02/85/Tang-02-determining-the-rate-exponent-6-320.jpg)
![DETERMINING THE RATE EXPONENT HANDOUT - Example 2 1 1 2.2 x 10 -5 s -1 Order for [SO 2 Cl 2 ]: Order of overall rxn: k = r=k[SO 2 Cl 2 ] Initial Concentration (mol/L) Initial Rate of Formation of Products (mol/L•s) [SO 2 Cl 2 ] 0.100 2.2 x 10 -6 0.200 4.4 x 10 -6 0.300 6.6 x 10 -6](https://image.slidesharecdn.com/tang02-determiningtherateexponent-110926165728-phpapp02/85/Tang-02-determining-the-rate-exponent-7-320.jpg)
![DETERMINING THE RATE EXPONENT Ex. 2 The decomposition of N 2 O 5 is: 2 N 2 O 5 4 NO 2 + O 2 This is a first order rxn with respect to N 2 O 5 . Given initial rate of 2.1 x 10 -4 mol/L•s and initial [N 2 O 5 ] = 0.40 mol / L, predict the rate when [N 2 O 5 ] = 0.80 M. 2.1 x 10 -4 mol L -1 s -1 = k [0.40mol/L] 2.1 x 10 -4 mol L -1 s -1 = k 0.40mol/L 0.000525 s -1 = k r = k [N 2 O 5 ]](https://image.slidesharecdn.com/tang02-determiningtherateexponent-110926165728-phpapp02/85/Tang-02-determining-the-rate-exponent-9-320.jpg)
![DETERMINING THE RATE EXPONENT Ex. 2 The decomposition of N 2 O 5 is: 2 N 2 O 5 4 NO 2 + O 2 This is a first order rxn with respect to N 2 O 5 . Given initial rate of 2.1 x 10 -4 mol/L•s and initial [N 2 O 5 ] = 0.40 mol / L, predict the rate when [N 2 O 5 ] = 0.80 M. r = k [N 2 O 5 ] = 0.000525 s -1 [0.80mol/L] = 4.2x10 -4 mol L -1 s -1 Notice how this is a first order reaction, so doubling the concentration DOUBLES the rate of reaction Therefore the rate is 4.2x10-4 mol L -1 s -1](https://image.slidesharecdn.com/tang02-determiningtherateexponent-110926165728-phpapp02/85/Tang-02-determining-the-rate-exponent-10-320.jpg)
![DETERMINING THE RATE EXPONENT Since this is a second order reaction, doubling the concentration quadruples the rate. 2 x [ ] = r x 4 Therefore the rate of reaction is 128 mmol/L•min Ex. 3 Given 2C 4 H 6 C 8 H 12 where r = k[C 4 H 6 ] 2 . If the initial rate was 32 mmol C 4 H 6 /L•min at a certain [C 4 H 6 ], what would be the initial rate if the concentration were doubled?](https://image.slidesharecdn.com/tang02-determiningtherateexponent-110926165728-phpapp02/85/Tang-02-determining-the-rate-exponent-11-320.jpg)
Tang 02 determining the rate exponent
- 1. DETERMINING THE RATE EXPONENT
- 2. DETERMINING THE RATE EXPONENT How would you set up an experiment to determine the rate exponent for the following reaction? C 6 H 12 O 6(s) + H 2 SO 4(aq)
- 3. DETERMINING THE RATE EXPONENT Exponents for a rate law expression must be determined experimentally ( empirically ). Concentrations of each reactant must be changed one at a time to see how much the overall reaction rate does or doesn’t change. Related to how the reaction takes place at the atomic level, which we cannot see.
- 4. DETERMINING THE RATE EXPONENT HANDOUT - Table 1 Concentration Factor Change Reaction Rate Factor Change Rate Law Exponent on the Concentration 2x no change 0 3x no change 0 4x no change 0 2x 2 1 = 2 1 3x 3 1 = 3 1 4x 4 1 = 4 1
- 5. DETERMINING THE RATE EXPONENT HANDOUT - Table 1 Concentration Factor Change Reaction Rate Factor Change Rate Law Exponent on the Concentration 2x 2 2 = 4 2 3x 3 2 = 9 2 4x 4 2 = 16 2 2x 2 3 = 8 3 3x 3 3 = 27 3 4x 4 3 = 64 3
- 6. DETERMINING THE RATE EXPONENT HANDOUT - Example 1 Order for [A]: Order for [B]: Order of overall rxn: k = 1 2 3 2.00 x 10 2 L 2 mol -2 s -1 r=k[A][B] 2 Initial Concentration (mol / L) Initial Rate of Formation of Products (mol/L•s) [A] [B] 0.10 0.10 0.20 0.20 0.10 0.40 0.30 0.10 0.60 0.30 0.20 2.40 0.30 0.30 5.40
- 7. DETERMINING THE RATE EXPONENT HANDOUT - Example 2 1 1 2.2 x 10 -5 s -1 Order for [SO 2 Cl 2 ]: Order of overall rxn: k = r=k[SO 2 Cl 2 ] Initial Concentration (mol/L) Initial Rate of Formation of Products (mol/L•s) [SO 2 Cl 2 ] 0.100 2.2 x 10 -6 0.200 4.4 x 10 -6 0.300 6.6 x 10 -6
- 8. DETERMINING THE RATE EXPONENT half-life - the time required for half the concentration of a reactant to be used up in a rxn Ex. 1 If the mass of an antibiotic is 2.464 g, what mass will remain after 6.0 h, if the half-life is 2.0 h, and no more antibiotic is added. m final = m initial (0.5) n n=# of half lives m final = 2.464g (0.5) 6.0/2.0 = 2.464g (0.5) 3 = 0.308g = 0.31g Therefore 0.31g of antibiotic remains
- 9. DETERMINING THE RATE EXPONENT Ex. 2 The decomposition of N 2 O 5 is: 2 N 2 O 5 4 NO 2 + O 2 This is a first order rxn with respect to N 2 O 5 . Given initial rate of 2.1 x 10 -4 mol/L•s and initial [N 2 O 5 ] = 0.40 mol / L, predict the rate when [N 2 O 5 ] = 0.80 M. 2.1 x 10 -4 mol L -1 s -1 = k [0.40mol/L] 2.1 x 10 -4 mol L -1 s -1 = k 0.40mol/L 0.000525 s -1 = k r = k [N 2 O 5 ]
- 10. DETERMINING THE RATE EXPONENT Ex. 2 The decomposition of N 2 O 5 is: 2 N 2 O 5 4 NO 2 + O 2 This is a first order rxn with respect to N 2 O 5 . Given initial rate of 2.1 x 10 -4 mol/L•s and initial [N 2 O 5 ] = 0.40 mol / L, predict the rate when [N 2 O 5 ] = 0.80 M. r = k [N 2 O 5 ] = 0.000525 s -1 [0.80mol/L] = 4.2x10 -4 mol L -1 s -1 Notice how this is a first order reaction, so doubling the concentration DOUBLES the rate of reaction Therefore the rate is 4.2x10-4 mol L -1 s -1
- 11. DETERMINING THE RATE EXPONENT Since this is a second order reaction, doubling the concentration quadruples the rate. 2 x [ ] = r x 4 Therefore the rate of reaction is 128 mmol/L•min Ex. 3 Given 2C 4 H 6 C 8 H 12 where r = k[C 4 H 6 ] 2 . If the initial rate was 32 mmol C 4 H 6 /L•min at a certain [C 4 H 6 ], what would be the initial rate if the concentration were doubled?