Atomic Structure and Properties Study Guide Part 4

Chemical Reactions Around 7‒9% of questions on your exam will cover Chemical Reactions. Physical and Chemical Changes Thus far, we have discussed physical changes in chemicals —that is, changes in the state of chemicals or the creation or separation of solutions. Chemical reactions, on the other hand, transform substances into new substances, usually with different chemical compositions. Typical signs that a chemical reaction has occurred include changes like the production of heat, light, or precipitate, or changes in the color of a substance. Net Ionic Equations Chemical reactions are often written as linear equations with reactants on the left, products on the right, and a single or double arrow between, signifying the direction of the reaction. When balancing equations, remember: • • • • • The Law of Conservation of Mass must be followed; thus, the number and types of atoms present in the reactants must also be present in the products. Make sure the number of each element in the products and the reactions are equal. The physical state of molecules in the reaction are denoted by subscripts as gas (g), aqueous (aq), and solid (s). Molecular equations show chemical formulas for reactants and products, but do not take into account ionization in aqueous solutions. Complete ionic equations denote molecules as ions in aqueous solution when appropriate. Net ionic equations remove spectator ions from the equation and only show molecules that participate in the reaction. For example, consider the ionization of calcium chloride salt (CaCl 2 (s)) in water: 2+ 2 CaCl2 (s) + H2 O(aq) → Ca(aq) + 2Cl(aq) + H2 O(aq) In this reaction, CaCl 2 (s) is ionized from solid to individual aqueous ions in water. The reactants consist of 1 part calcium ion, 2 parts chloride ions, and 1 part water. 33 To balance this equation, the reactants also must include these proportions. In this reaction, water participates as a spectator; thus, the net ionic equation would be: 2 CaCl2 (s) → Ca2+ (aq) + 2Cl (aq) Another way to represent reactions is through the particle model. In this model showing propane combustion, each atom in the reaction is represented as a particle. To balance the reaction, make sure that all particles that are present on the reactant side are also present on the product side. Stoichiometry Stoichiometry deals with the quantitative relationship between elements in a reaction. Simply stated, it uses ratios of ions to calculate the amounts of reactants and products in an equation. The factor label-method is often used to convert ratios to molar quantities. This method uses conversion factors to convert one quantity to another quantity. This concept can be used to balance a chemical reaction, determine how many moles are present in a reaction, and even determine conversions for units of measure. For example, we know that 1 foot = 12 inches but we would like to solve how many inches are in 0.6 feet. We can use multiplication and division to solve for this. By remembering that the units must cancel out to give the final unit, inches, we can solve this problem: 12 inches × 0.6 feet = 7.2 inches 1 foot 34 This same concept can be used to for molar conversions. By Avogadro’s number, we know that there are 6.02  1023 atoms in every mole; thus, if we want to identify the number of atoms in 0.4 moles of a substance: 6.02 × 1023 atoms × 0.4 moles = 2.41 × 1023 atoms 1 mole Similarly, we can use this concept to covert moles of substance to mass of substance and vice versa. For example, if we would like to find the mass of 5 moles of potassium, we can turn to the periodic table to find that the atomic weight of potassium is 39.098 g/mol. Thus: 39 .098 grams × 5 moles = 195.49 grams 1 mole This relationship can be used to convert moles to volume. For gasses at STP, one can refer to the standard molar volume of an ideal gas, 22.4 L for every mole. Thus, if we have 15 L of any gas at STP, we can convert to moles of substance: 1 mole × 15 L = 0.67 moles 22.4 L Solutions are often described in terms of molarity (M = moles/liter). Thus, if we would like to find the number of moles in 2.5 L of a 0.5 M solution: 0.5 mole × 2.5 L = 1.25 moles 1L The ratios of molecules in a chemical reaction can be used in a similar way to find the amount of substance involved in a reaction. For these kinds of problems, first make sure the equations are balanced. Then you can treat ratios of molecules in the reaction to relate given information to the substance needed in the answer. Introduction to Titration Titration is a technique used to find the concentration of a solution based on the known concentration of another solution, called the titrant. Titration is based on a chemical reaction between the two solutions that is able to come to completion, which is often marked by a measurable change like the appearance of a color or a precipitate. The point at which the titrant neutralizes the solution is called the equivalence point. Titration curves are used to monitor the progress of the reaction by plotting the titrant added on the x-axis compared to the monitored change, such as change in pH or color. 35 Note that free response questions about titration often appear on the AP exam. Be sure that you are able to estimate the equivalence point and the concentration of the solution based on chemical equations and stoichiometry, as well as features of the titration curve. Types of Chemical Reactions Types of reactions are classified by the processes that produced the reaction. For the purposes of the AP exam, it is useful to be able to identify certain types of chemical reactions. Acid-base reactions involve the transfer of protons between chemicals. Oxidation-reduction reactions involve the movement of electrons between chemicals. Precipitation reactions involve the formation of an insoluble product, called a precipitate. Introduction to Acid-Base Reactions Acids and bases are defined by several theories. Arrhenius theory states that substances that ionize to produce protons (H+) in water are acids and substances that produce hydroxide (OH-) in water are bases. This theory limits acid and base definitions to those that take place in water; thus, the Brônsted-Lowry theory expands on this, stating that substances that donate protons are acids, and those that accept protons are bases. In Brônsted-Lowry equations, the molecule that receives the proton is called a conjugate acid, while the molecule that is left after donating 36 the hydrogen ion is a conjugate base. Acid-base reactions will be covered in more detail in later sections. Oxidation-Reduction (Redox) Reactions Oxidation-reduction (redox) reactions are reactions involving a transfer of electrons between reactants. In redox reactions, there is always an oxidized species, whose electrons are lost, and reduced species, who gain electrons. This can be remembered using the mnemonic < LEO says GER= (Loss of Electron is Oxidation, Gain of Electron is Reduction). Oxidation state or number is the number of electrons that an atom gains, loses, or uses in a reaction and can be a positive or negative integer or 0. An increase in oxidation number reflects oxidation and a decrease reflects reduction. Several rules can be used to assign oxidation numbers: • Free atoms have an oxidation state of 0 • Hydrogen has an oxidation state of +1 (except for hydride) • Oxygen has an oxidation state of -2 (except for peroxide) • In a compound or ion, the oxidation state is equal to the total charge • Fluorine, bromine, and chlorine have an oxidation state of -1, except when bound to a lighter halogen, oxygen, or nitrogen • Group 1 metals are +1, group 2 are +2 Redox reactions occur in various forms: • Combination reactions: A + B → AB • Decomposition reactions: AB → A + B • Replacement reactions: AB + C → A + BC • Combustion with oxygen: Cx Hy + O2 → CO2 + H2 O Redox reactions are balanced using two reactions called half-reactions: oxidation: A → A+ + e2 reduction: B + + e2 → B overall: B+ + A → B + A+ To write net ionic equations for redox reactions, both the number of atoms and the charge are balanced on both sides of the reaction. The method to do this involves sequential steps: 1. Write out the unbalanced equation. 2. Identify and assign oxidation numbers for each atom. 3. Separate out the half reactions, one with the oxidized atoms and one with reduced atoms. Include the number of electrons lost and gained on each side. 37 4. Multiply coefficients so that the gains and losses of electrons are balanced in the half reactions. a. In acidic or aqueous solutions, first balance atoms that are not H or O, then balance charge using H+ and OH-. Then balance oxygen using H2O. 5. Recombine the half reactions. 6. Balance any elements whose oxidation state did not change. 7. Double-check your work by confirming that all elements and charges are balanced. 38 Sample Chemical Reactions Questions What is the final concentration of anions when a solution is made by adding 300.0 mL of 4.0 M MgCl2 to 200.0 mL of 3.0 MNaNO3? A. 0.6 M B. 3.0 M C. 5.0 M D. 6.0 M Explanation: The correct answer is D. Anions are negative ions, and the solutions in the question will contain Cl2 and NO32 ions in solution. Remember that MgCl 2 will produce 2 moles of Cl2 and NaNO3 will produce 1 mole of NO32. Calculate the moles of each anion that will be present in the solution, and divide by the volume of the solution in liters to calculate the molarity. æ 4.0 mol MgCl2 ö (0.3000 L)ç ÷ø (2) = 2.4 mol MgCl2 1L è æ 3.0 mol NaNO3 ö (0.2000 L)ç ÷ø = 0.60 mol NaNO3 1L è 3.0 mol anions = 6.0 M Total Anions 0.500 L When 2.0 g K2CO3(s) was added to a beaker of 75 mL 3 M HNO3(aq), vigorous bubbling occurred. Which statement best explains this phenomenon? A. Water vapor is released. B. The solution was poured too fast. C. K2CO3(s) reacts violently when added to water D. Carbon dioxide is released by the reaction. 39 Explanation: The correct answer is D. This is a gas-evolution reaction. When carbonates and bicarbonates (CO²32 and HCO32) react with acids, the gas product is CO2. The reaction is K2CO3(s) + 2HNO3(aq) → CO2(g) + H2O(l) + 2KNO3(aq). There is not enough energy released to boil the water. What type of reaction best describes this process? Zn0 + Cu2+ → Zn2+ + Cu 0 A. Synthesis reaction B. Decomposition reaction C. Redox reaction D. Neutralization reaction Explanation: The correct answer is C. Redox (or oxidation –reduction) reactions involve the transfer of electrons from one reagent to the other. In this case, Zn 0 transfers two electrons to Cu 2+ to form Zn2+ and Cu0. 40 Kinetics Around 7‒9% of questions on the AP exam will cover Kinetics. Reaction Rate Kinetics is the study of reaction rates, the change in concentration over a given period of time: reaction rate = ∆concentration ∆time Reaction rate can also be expressed in terms of the reaction constituents. Consider the reaction: ý + 2þ → 3ÿ The reaction rate can be expressed as any of the following: reaction rate = 2 ∆[ý] ∆[þ] ∆[ÿ] =2 = ∆�㕡 2∆�㕡 3∆�㕡 Note that as reactants decrease over time, [reactants] will be negative; thus, a negative sign is added to the equation to generate a positive overall reaction rate. To account for differences in molar quantities due to the stoichiometry of the reaction, the coefficients are divided for B and C in this reaction. The rate constant is determined by the Arrhenius equation: ý = ýă 2�㔸�㕎 /�㕅�㕇 ý = an expression of the fraction of molecules reacting at kinetic energy of 0 āþ = activation energy (joules) ā = universal gas constant ă = temperature (Kelvin) As shown by the equation, the rate constant is dependent on the temperature that the reaction takes place, as an increase in temperature increases the kinetic energy of a reaction up to a certain point. An increase in kinetic energy increases the chances of molecules colliding and thus reacting with each other, in turn increasing the reaction rate. This rate follows an exponential scale, meaning an increase in 10 K doubles the reaction rate. 41 Introduction to Rate Law Rate law describes the relationship between reaction rate and the concentrations of reactants. Consider the reaction: ÿý + Āþ → āÿ The rate law is expressed as: reaction rate = ý[ý]Ą [þ]ą Where k is the experimentally determined rate constant for the reaction at a given temperature and s and t are the reaction orders for the A and B, respectively. The reaction order indicates the effect of a reactant on the overall reaction. For instance, if doubling a reactant results in doubling the rate, then the reaction order for that molecule will be 1 ([2] 1 = 2). If doubling a reactant causes a four-fold increase in rate, then the reaction order for that molecule is 2 ([2]2 = 4). The overall reaction order is equal to the sum of the individual reaction orders of reactants: reaction order = s + t In practical terms, these equations mean that the concentration of reactant A decreases by a factor of s and the concentration of reactant B decreases by a factor of t. For example, given the reaction: ý +þ → ÿ reaction rate = ý[ý]1 [þ]1 reaction order = 1 + 1 = 2 In this reaction, both reactants are decreasing by a factor of 1; thus, the reaction order with respect to A = 1 and the reaction order with respect to B = 1. In cases where the reaction rate is not affected by the concentration of reactants, the reaction rate = k and the reaction order is 0. Concentration Changes over Time Using rate equations, one can calculate the reaction order for reactants based on their concentrations in the reaction and the effect on reaction rate, or rate of formation of C. 42 Once the value of the reaction orders is known, the appropriate equations can be used to determine reaction properties at specific times (t) in a reaction: Rate law Integrated rate law Plot to determine k Relationship of k slope of plot Half-life Zero Order First Order slope = 2ý slope = 2ý rate = ý rate = ý[ý] [ý]ą þĀ[ý]ą = 2ý�㕡 + þĀ = 2ý�㕡 + [ý] [A] vs t ln[A] vs t [ý]0 2ý þĀ2 ý Second Order rate = ý[ý]2 1 1 = 2ý�㕡 + [ý]ą [ý]0 1 vs t [ý] slope = ý 1 ý[ý]0 Half-life is the time it takes for half the reactants to convert to products. In radioactive decay, half-life demonstrates first-order kinetics and can range from milliseconds to billions of years. To determine the rate of decay (ü ) given a half-life (�㕡1 ) we use the equation: 2 þĀ2 ü = �㕡1 2 Given the ü and the initial amount of the sample ( �㕁0 ) it is possible to find the amount of a radioactive sample remaining (�㕁ą ) after a given amount of time (t), with the equation: üą ă 2 �㕁ą = �㕁 0 Since half-life is constant for a given isotope, it can be used to estimate the age of an item, as is used in carbon-14 dating using the above equations. Elementary Reactions and Reaction Mechanisms Elementary reactions are the simplest type of reaction, involving only a single step. These are defined by the number of reactants. For example, a unimolecular reaction involves a single reactant. These can include isomerization of a reactant or decomposition reactions, like the decomposition of hydrogen peroxide to water and oxygen: 2H2 O2 → 2H2 O + O2 In bimolecular reactions, two molecules react to form a product. These are the most common types of reactions that you’ll come across. Reactions that involve the collision of three or more 43 molecules at a time are extremely rare; more often, reactions that involve more than two reactants take place in a stepwise fashion and form intermediates between steps that do not show up in the final equation. For example, take the reaction: ý +þ → ÿ+Ā The reaction takes place in two steps that, when added together, result in the overall reaction given above. ý → ÿ +ā ā+þ→Ā In these types of multi-step reactions, the reaction mechanisms are built on several elementary reaction steps; the components include reactants, intermediates, products, and catalysts. The reaction intermediates (E in the equation above) do not show up in the final products. Identifying the reaction intermediates can help you identify the mechanism of the reaction. The slowest step in a multi-step reaction is referred to as the rate-determining (or ratelimiting) step. The rate law for the whole reaction would then be the rate of the rate-determining step. In multi-step reactions where there is no rate limiting step, the rate law is estimated through a steady-state approximation. The assumption for this is that there should be an intermediate that is consumed at the same rate that it is created; thus, its concentration remains constant through the reaction —this is called reaching steady state. Be sure to practice identifying the rate law for steady state reactions as well. Collision Model For reactions to occur, reactant molecules must collide together with enough energy to break chemical bonds and in a proper orientation to form new ones. There are several factors that alter how often these events happen, and thus affect the reaction rate including concentration of reactants, surface area of reactants, the complexity of reactant molecules, temperature, and presence of a catalyst. Reaction Energy Profile Reaction energy diagrams show the relationship between reaction energy ( y-axis) and the phase of the reaction (x-axis). By looking at the diagram for a reaction where A converts to B via a transitional state of C, you should be able to quantify the activation energy (the difference in energy between A and B) as well as the energy change between reactants and products. 44 In multi-step reactions, the energy profile appears with multiple peaks, which correlate to the activation energy for each elementary reaction. 45 Catalysis Activation energy can be modulated by the presence of a catalyst. Catalysts are molecules that lower the activation energy without actually being consumed by a reaction. In biology, catalysts are generally enzymes that put molecules in optimal configurations for reactions to proceed efficiently. When a catalyst is added to a reaction, the reaction rate becomes: 2 �㕎 )/�㕅�㕇 �㔸 ý = ýă 2(�㔸�㕎 Where  āþ is the amount the activation is energy is lowered by the addition of the catalyst. 46 Sample Kinetics Questions Which of the following actions will decrease the rate of the reaction? A. Lowering the temperature B. Increasing the pressure C. Adding a catalyst D. Increasing [N2] (at constant pressure) Explanation: The correct answer is A. Lowering the temperature decreasing the kinetic energy of the gas molecules, meaning fewer have the minimum energy necessary to react. Increasing the pressure will increase the rate at which collisions occur and will accelerate the rate of reaction. Catalysts lower the energy of activation and increase the rate of reaction. Industrially, heterogeneous iron catalysts are used to accelerate this reaction. Finally, increasing the concentration of [N 2] will shift the equilibrium towards the right, but it will not affect the rate of reaction. The reaction of nitrogen dioxide with carbon monoxide to produce nitric oxide and carbon dioxide is a multi-step reaction. Experimental work has determined that the rate law for the equation follows the equation: rate = k[NO2]². Which elementary reaction is most likely the ratedetermining step (RDS)? NO2 + CO → NO + CO2 A. 2NO2 → NO3 + NO B. CONO2 → NO + CO2 C. NO2 + CO → NO + CO2 D. NO2 → NO + O Explanation: The correct answer is A. The overall rate law reflects the rate equation that corresponds to the rate-determining step. Here, since the rate law is second order in [NO2] (rate = k[NO2]²), the RDS must involve 2 molecules of NO2 and no other species. If the half-life of a radioactive element is 6 minutes, which of the following was the initial mass of a sample with 40.0 grams left after 36 minutes? A. 80 grams B. 160 grams C. 2,560 grams D. 5,120 grams Explanation: The correct answer is C. After 36 minutes, six half-life cycles have occurred: Unknown mass × 1 = 40 grams ∴ unknown mass = 2,560 grams 64 48 1 1 ®6® . 64 6