zumdahl_chemprin_6e_csm_ch15

# zumdahl_chemprin_6e_csm_ch15 - CHAPTER 15 CHEMICAL KINETICS...

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576 CHAPTER 15 CHEMICAL KINETICS Reaction Rates 10. The reaction rate is defined as the change in concentration of a reactant or product per unit time. Consider the general reaction: aA products where rate = dt ] A [ d If we graph [A] vs. t, it would usually look like the solid line in the following plot. An instantaneous rate is the slope of a tangent line to the graph of [A] vs. t. We can determine the instantaneous rate at any time during the reaction. On the plot, tangent lines at t 0 and t = t 1 are drawn. The slope of these tangent lines would be the instantaneous rates at t 0 and t = t 1 . We call the instantaneous rate at t 0 the initial rate. The average rate is measured over a period of time. For example, the slope of the dashed line connecting points a and c is the average rate of the reaction over the entire length of time 0 to t 2 (average rate = Δ [A]/ Δ t). An average rate is determined over some time period, whereas an instantaneous rate is determined at one specific time. The rate that is largest is generally the initial rate. At t 0, the slope of the tangent line is greatest, which means the rate is largest at t 0. The initial rate is used by convention so that the rate of reaction only depends on the forward reaction; at t 0, the reverse reaction is insignificant because no products are present yet. [A] 0 a c b t 1 t 2 time

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CHAPTER 15 CHEMICAL KINETICS 577 11. 0.0120/0.0080 = 1.5; reactant B is used up 1.5 times faster than reactant A. This corres- ponds to a 3 to 2 mole ratio between B and A in the balanced equation. 0.0160/0.0080 = 2; product C is produced twice as fast as reactant A is used up. So the coefficient for C is twice the coefficient for A. A possible balanced equation is 2A + 3B 4C. 12. The coefficients in the balanced reaction relate the rate of disappearance of reactants to the rate of production of products. From the balanced reaction, the rate of production of P 4 will be 1/4 the rate of disappearance of PH 3 , and the rate of production of H 2 will be 6/4 the rate of disappearance of PH 3 . By convention, all rates are given as positive values. Rate s ) L 0 . 2 / mol 0048 . 0 ( t Δ ] PH [ Δ 3 = = = 2.4 × 10 3 mol L 1 s 1 t Δ ] PH [ Δ 4 1 t Δ ] P [ Δ 3 4 = = 2.4 × 10 3 /4 = 6.0 × 10 4 mol L 1 s 1 t Δ ] PH [ Δ 4 6 t Δ ] H [ Δ 3 2 = = 6(2.4 × 10 3 )/4 = 3.6 × 10 3 mol L 1 s 1 13. Using the coefficients in the balanced equation to relate the rates: dt ] N [ d 2 dt ] NH [ d and dt ] N [ d 3 dt ] H [ d 2 3 2 2 = = dt ] H [ d 3 2 dt ] NH [ d or dt ] NH [ d 2 1 dt ] H [ d 3 1 : So 2 3 3 2 = = − Ammonia is produced at a rate equal to 2/3 of the rate of consumption of hydrogen. 14. a. The units for rate are always mol L 1 s 1 . b. Rate = k; k has units of mol L 1 s 1 . c. Rate = k[A], = L mol k s L mol d . R a t e = k [ A ] 2 , 2 L mol k s L mol = k must have units of s -1 . k must have units L mol 1 s 1 .
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zumdahl_chemprin_6e_csm_ch15 - CHAPTER 15 CHEMICAL KINETICS...

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