CHEM 3310

What is physical chemistry? Application of the principles and methods of physics and math to chemistry to study how and why chemical reactions occur. Chemical Kinetics (rates and factors that affect the rate of chemical processes) (4-5 weeks) Chemical Thermodynamics (as applied to the study of energy transfers in chemical processes) (8-9 weeks) CHEM 3310 2 2

Rates Chemical Reactions Reaction Rates Concentration Measurements Chemical Kinetics Rates Chemical Reactions Reaction Rates Concentration Measurements Graphing Rate-Law reaction order zeroth-order first-order second-order Initial rates Reversible reactions Reaction mechanisms Temperature Activation Energy Arrhenius Equation Elementary Reactions Catalysts CHEM 3310 3

Reaction kinetics is the study of the rates of reactions and the factors which affect the rates. CHEM 3310 4

What are kinetic studies good for? CHEM 3310 5

Setting of dental fillings Synthesis of pharmaceutical drugs How to speed up: Paint drying Setting of dental fillings Synthesis of pharmaceutical drugs 4. Breakdown of synthetic plastics and other materials in landfills 5. Industrial manufacture of chemicals 6. Destruction of air pollutants in automobile exhaust CHEM 3310 6

Rate at which materials burn in fire How to slow down: Food decay Rate at which materials burn in fire Rusting of metal objects composed of iron Corrosion Fading of clothes through washing Destruction of the ozone layer CHEM 3310 7

What are factors which influence reaction rates? CHEM 3310 8

Factors which influence reaction rates: 1. Chemical nature of the reactants. - What are the chemical properties of the reactants. Do the reactants have strong bonds or weak bonds? - What about the number of bonds that need to be broken and reformed? CHEM 3310 9

Factors which influence reaction rates: 2. The ability of the reactants to come in contact with each other. - Surface area consideration - The greater the surface area, the greater the ability the reactants can meet, and therefore, the greater the reaction rate. - Phase consideration - Homogeneous reaction or Heterogeneous reaction CHEM 3310 10

Factors which influence reaction rates: 3. The ability of the reactants to come in contact with each other. Aqueous ions > Gases or Liquids > Solids (Fastest) (Slowest) CHEM 3310 11

Factors which influence reaction rates: 4. Concentration of the reactants When the reactant concentration increases, the reaction rate increases. CHEM 3310 12

Factors which influence reaction rates: 5. Temperature When the temperature increases, the reaction rate increases. CHEM 3310 13

Factors which influence reaction rates: 6. Pressure When the gaseous reactant pressure increases, more reactant is compressed into a given volume (i.e. the reactant concentration increases), the reaction rate increases. CHEM 3310 14

Factors which influence reaction rates: 7. Presence of Catalysts Catalyst is a chemical which can be added to a chemical reaction to increase the rate of the reaction. The catalyst is not consumed in the reaction. CHEM 3310 15

How do we measure reaction rates quantitatively? CHEM 3310 16

What would we time? CHEM 3310 17

Possible ways to measure reaction rates: Cu (s) + 4 HNO3 (aq) Cu(NO3)2 (aq) + 2 H2O (l) + 2 NO2 (g) + heat Blue solution Method Observation Calculation of Rate 1. Mass change Mass of copper decreases overtime 2. Temperature change Exothermic reaction - Temperature rises 3. Colour change Measure the intensity of the blue colour using colourimetry CHEM 3310

Possible ways to measure reaction rates: Cu (s) + 4 HNO3 (aq) Cu(NO3)2 (aq) + 2 H2O (l) + 2 NO2 (g) + heat Blue solution Method Observation Calculation of Rate 4. Pressure change - Carry out reaction in a sealed vessel equipped with a pressure gauge 5. Concentration change Reaction will have decreasing [HNO3]. Measure pH increasing over time. CHEM 3310

Unit: To measure the reaction rate is the measure of the change in some properties over time. Unit: = M s-1 NOTE: Read “moles per liter per second” or “molarity per second” The change in the measured property can be related back to the change in concentration. CHEM 3310

Let’s look at Experiment 1 CHEM 3310

What do the coefficients of a balanced chemical reaction tell us? 22

1 C3H8 (g) + 5 O2 (g)  3 CO2 (g) + 4 H2O (g) The coefficients tell the relative rates of the disappearance of reactants and appearance of products. Their rates are linked by the reaction stoichiometry, or by the coefficients in the balanced equation. 1 C3H8 (g) + 5 O2 (g)  3 CO2 (g) + 4 H2O (g) (propane) O2: is consumed 5x faster than propane is consumed. CO2: is formed 3x faster than propane is consumed. H2O: is formed 4x faster than propane is consumed. CHEM 3310

2 C4H10 (g) + 13 O2 (g)  8 CO2 (g) + 10 H2O (g) Experimentally when butane is burned, it decreases at a rate of 0.20 M s-1. 2 C4H10 (g) + 13 O2 (g)  8 CO2 (g) + 10 H2O (g) (butane) What is the rate at which O2 concentration is decreasing? What are the rates at which the product s (CO2 and H2O) concentrations are increasing? Answer CO2 : (0.20 M s-1 • 8/2) = 0.80 M s-1 is the rate that CO2 is produced. H2O : (0.20 M s-1 • 10/2) = 1.0 M s-1 is the rate that H2O is produced. Answer O2 : (0.20 M s-1 • 13/2) = 1.3 M s-1 is the rate that O2 is consumed. CHEM 3310

Experimental Measurement of Reaction Rates Let’s study the decomposition reaction of hydrogen iodide at 508oC. 2 HI (g)  H2 (g) + I2 (g) (purple) We can study any reactant or products since the rate of decrease of HI and the rates of production of H2 and I2 are all related. It’s easiest to monitor I2 because it is the only coloured substance. We can use an instrument to monitor the change in colour intensity of the reaction chamber and relate it back to the concentration of I2. If the concentration of I2 is known, then we can relate it to the concentration of HI. CHEM 3310

Concentration of HI (M) Experimental Measurement of Reaction Rates The decomposition reaction of hydrogen iodide at 508oC. 2 HI (g)  H2 (g) + I2 (g) (purple) Experimental Data: Time (s) Concentration of HI (M) 0. 0.100 50. 0.0716 100. 0.0558 150. 0.0457 200. 0.0387 250. 0.0336 300. 0.0296 350. 0.0265 Easiest way to see the behaviour of the reaction is to plot the data graphically. CHEM 3310

2 HI (g)  H2 (g) + I2 (g) Experimental Measurement of Reaction Rates The decomposition reaction of hydrogen iodide at 508oC. 2 HI (g)  H2 (g) + I2 (g) Concentration of HI Vs. Time From the graph, we observe that reaction rate is not the same throughout the reaction. CHEM 3310

2 HI (g)  H2 (g) + I2 (g) Experimental Measurement of Reaction Rates The decomposition reaction of hydrogen iodide at 508oC. 2 HI (g)  H2 (g) + I2 (g) Concentration of HI vs. Time From the graph, we can calculate the average rate of the reaction. Let’s calculate the average rate of the reaction between t=100 s and t=150 s. CHEM 3310

Concentration of HI (M) Experimental Measurement of Reaction Rates The decomposition reaction of hydrogen iodide at 508oC. 2 HI (g)  H2 (g) + I2 (g) Time (s) Concentration of HI (M) 0. 0.100 50. 0.0716 100. 0.0558 150. 0.0457 200. 0.0387 Concentration of HI Vs. Time The average rate over the time interval from t=100 s to t=150 s. CHEM 3310

A  B For a general reaction where A is the reactant and B is the product. We can express rate as: [A]2 = concentration at t2 [A]1 = concentration at t1 t2 = the end of a given time interval of the reaction t1 = the beginning of that interval. Since [A]2 < [A]1 T, a ‘-’ sign is introduced to express rate as a POSITIVE quantity. The rate of disappearance of A 2. The rate of appearance of B When rates are expressed over a time interval, t, these are AVERAGE rates. CHEM 3310

2 HI (g)  H2 (g) + I2 (g) Experimental Measurement of Reaction Rates The decomposition reaction of hydrogen iodide at 508oC. 2 HI (g)  H2 (g) + I2 (g) Concentration of HI Vs. Time From the graph, we can calculate the instantaneous rate of the reaction. Let’s calculate the instantaneous rates of the reaction at t = 0 s. CHEM 3310

2 HI (g)  H2 (g) + I2 (g) Experimental Measurement of Reaction Rates The decomposition reaction of hydrogen iodide at 508oC. 2 HI (g)  H2 (g) + I2 (g) Concentration of HI Vs. Time At t = 0 s, the rate of decrease in [HI] is 0.00077 M s-1. The rate of decrease of [HI] is faster at the beginning of the reaction. This is the INITIAL rate. CHEM 3310

2 HI (g)  H2 (g) + I2 (g) Experimental Measurement of Reaction Rates The decomposition reaction of hydrogen iodide at 508oC. 2 HI (g)  H2 (g) + I2 (g) Concentration of HI Vs. Time From the graph, we can calculate the instantaneous rate of the reaction. Let’s calculate the instantaneous rates of the reaction at t=100 s and t=150 s. CHEM 3310

Experimental Measurement of Reaction Rates 2 HI (g)  H2 (g) + I2 (g) We can draw a tangent line at any time t and determine the slope of the tangent line. Concentration of HI Vs. Time The rate of decrease in [HI]: at t = 100 s, is 0.00025 M s-1 At t=100 s, Slope = -0.00025 M/s At t=150 s, Slope = -0.00016 M/s at t = 150 s, is 0.00016 M s-1 (100, 0.056) The slope of the tangent line at any chosen time t will give us the instantaneous rate at time t. 0.28 M (150, 0.046) 110 s CHEM 3310

A  B (1:1) For a general reaction Mathematically, the expression of instantaneous rate is CHEM 3310

For a general reaction where the stoichiometric ratio is NOT 1:1, A  2B i.e. The appearance of B is 2x as fast as the disappearance of A. Mathematically, the expression of instantaneous rate is or R1 ≠ R2 2R1 = R2 By convention, we will adopt the practice of dividing each differential rate term by its stoichiometric coefficient in the reaction. CHEM 3310

a A + b B → g G + h H For a general reaction, where A and B are reactants, G and H are products, and a, b, g, and h are stoichiometric coefficients in the balanced chemical equation. Regardless of which species whose concentration is measured, the rate of the reaction can be determined. CHEM 3310

For the hypothetical reaction, A + 2 B  → 3 C CHEM 3310

NOTE: A and B are initially present in stoichiometric For the hypothetical reaction, A and B are reactants, and C is the product. We could monitor the concentration change over time of species A, B, or C. A + 2 B  → 3 C NOTE: A and B are initially present in stoichiometric amounts. Species C Compare the slope for each species at any time t. They are related to their stoichiometric ratios. mb = 2 ma mc = - 3 ma mc = - 1.5 mb Species B Species A CHEM 3310

HI is changing with time Experimental Measurement of Reaction Rates 2 HI (g)  H2 (g) + I2 (g) (0, 0.10) Rt=0=0.00077 M/s Concentration of HI Vs. Time (100, 0.056) Rt=100=0.00025 M/s The graph summarizes how fast the concentration of HI is changing with time (150, 0.046) Rt=150=0.00016 M/s An interesting result is obtained when the instantaneous rate of reaction is calculated at various points along the curve. CHEM 3310

Rate = k [HI]2 2 HI (g)  H2 (g) + I2 (g) Experimental Measurement of Reaction Rates The decomposition reaction of hydrogen iodide at 508oC. 2 HI (g)  H2 (g) + I2 (g)  [HI]2 (0, 0.10) Rt=0=0.00077 Ms-1 Concentration of HI Vs. Time Rate = k [HI]2 where k is the proportionality constant (100, 0.056) Rt=100=0.00025 Ms-1 At t = 0 s, Rate = 0.00077M s-1  (0.10 M)2 At t = 100 s, Rate = 0.00025 M s-1  (0.056 M)2 At t = 150 s, Rate = 0.00016 Ms-1  (0.046 M)2 k = 0.077 M-1 s-1 (150, 0.046) Rt=150=0.00016 Ms-1 k = 0.080 M-1 s-1 kaverage = 0.078 M-1 s-1 Rate = k[HI]2 is an experimentally determined relationship that describes the rate of the decomposition reaction of HI at 508oC. It is called the rate law for the reaction. The proportionality constant, k, is known as the rate constant. k = 0.076 M-1 s-1 CHEM 3310

Summary: 2 HI (g)  H2 (g) + I2 (g) The decomposition reaction of hydrogen iodide at 508oC. 2 HI (g)  H2 (g) + I2 (g) This is a 2nd order reaction!! Every 50 s, we measured the colour intensity of the reaction chamber, related it back to the concentration of I2 , which is then related back to the concentration of HI. 2. We collected data of the reaction for 350 s. 3. We plotted a “Concentration of HI vs. Time” graph for the reaction. 4. We calculated several instantaneous rates of the reaction (i.e. t = 0, 100, 150 s) 5. We found a relationship between the instantaneous rates and [HI] at 508oC to be Rate = k[HI]2 This is the RATE LAW! CHEM 3310

Rate  [X]m [Y]n Reaction Rate Law Reaction rates usually depend on concentrations. The rate law is mathematical equation which relates the reaction rate to the reactant concentrations. For a general reaction, a X + b Y  products where a and b are the coefficients in the balanced chemical equation, X and Y are the reactants. Rate  [X]m [Y]n The rate of a reaction is proportional to the products of the reactants each raised to some power. CHEM 3310

Rate  [X]m [Y]n Rate = k [X]m [Y]n Reaction Rate Law a X + b Y  products A mathematical equation which relates rate to the reactant concentrations. Rate  [X]m [Y]n To remove the proportional symbol, , we introduce a proportionality constant, the rate constant, k. Rate = k [X]m [Y]n k, m, and n are numbers that are determined experimentally!! CHEM 3310

Rate = k [X]m [Y]n Reaction Rate Law a X + b Y  products k, m, and n are numbers that are determined experimentally!! The reaction is determined to be: mth order with respect to X nth order with respect to Y The overall reaction order is m+n. CHEM 3310

Rate = k [X]m [Y]n Reaction Rate Law a X + b Y  products k, m, and n are numbers that are determined experimentally!! k is the rate constant. The bigger the rate constant, k, the faster the reaction. k is temperature dependent. k is reaction dependent. k has units that depend on the order of the reaction. CHEM 3310

Reaction Rate Law 2 N2O5 (g)  4 NO2 (g) + O2 (g) Rate = k [N2O5] Determined experimentally!! This reaction is 1st order with respect to N2O5. The overall reaction order is 1. Units of k CHEM 3310

Reaction Rate Law 2 HI (g)  H2 (g) + I2 (g) Rate = k [HI]2 Determined experimentally!! This reaction is 2nd order with respect to HI. The overall reaction order is 2. Units of k CHEM 3310

2 NO (g) + 2 H2 (g)  N2 (g) + 2 H2O (g) Reaction Rate Law 2 NO (g) + 2 H2 (g)  N2 (g) + 2 H2O (g) Rate = k [NO]2[H2] Determined experimentally!! This reaction is 2nd order with respect to NO, 1st order with respect to H2. The overall reaction order is 3. Units of k CHEM 3310

Overall Reaction Order Reaction Rate Law for a reaction with an overall order of p Rate = k [X]p Unit of concentration is M Unit of Rate is M s-1 Units of k will be M s-1 / Mp = M1-p s-1 Overall Reaction Order Units of k M s-1 1 s-1 2 M-1 s-1 3 M-2 s-1 CHEM 3310

Rate = k [X]m [Y]n Reaction Rate Law a X + b Y  products k, m, and n are numbers that are determined experimentally!! Knowing the rate law allows us to PREDICT the effect on the rate of the reaction when the concentrations are changed. CHEM 3310

Determined experimentally!! Reaction Rate Law a X + b Y  products Rate = k [X] [Y]2 Determined experimentally!! What will happen to the reaction rate when the concentration of Y is tripled? Rate increases 9x [i.e. 32 = 9] CHEM 3310

Determined experimentally!! Reaction Rate Law a X + b Y  products Rate = k [X] [Y]2 Determined experimentally!! What will happen to the reaction rate when the concentration of X is tripled? Rate increases 3x [i.e. 31 = 3] CHEM 3310

Determined experimentally!! Reaction Rate Law a X + b Y  products Rate = k [X] [Y]2 Determined experimentally!! What will happen to the reaction rate when the concentration of X is tripled and the concentration of Y is halved? Rate decreases i.e. CHEM 3310

The Rate Law of a reaction must be determined experimentally!! The Rate Law Versus the Stoichiometry of a Reaction The rate law for a reaction cannot be predicted from the stoichiometry of the reaction; It must be determined experimentally. Sometimes, the rate law is consistent with what we expect from the stoichiometry of the reaction. But not always! 2 N2O5(g)  4 NO2(g) + O2(g) Rate = k[N2O5] 2 HI(g)  H2(g) + I2(g) Rate = k[HI]2 2nd order 1st order The Rate Law of a reaction must be determined experimentally!! CHEM 3310