PassGAMSAT Science EClass 3 1

PassGAMSAT Science eClass 3

Physical Chemistry Chemistry is the branch of science that deals with the composition, structure and properties of substances and how they change on interacting with other substances and the environment. Physical chemistry explores how substances interact at the atomic level. Learning Objectives On completion of this eclass, students should be able to define thermochemistry and enthalpy, compare exothermic and endothermic reactions, understand the basics of calorimetry and nuclear chemistry and calculate the rate of a chemical reaction as well as pH values. 1. Thermochemistry exothermic and endothermic reactions calorimetry 2. Reaction rates and equilibrium 3. Acids and Bases 4. Nuclear Chemistry radioactivity, isotopes, decay effects and practical uses of radioactivity :nuclear medicine, nuclear power, radiocarbon dating

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THERMOCHEMISTRY Many chemical reactions generate energy in the form of heat. The energy generated in biochemical redox reactions in living systems is stored chemically and released via phophoryl transfers from ATP. The energy is used to power living cells and biological processes, or to generate electricity for batteries or power grids. The heat and energy transformations that occur with chemical reactions are studied under thermochemistry. The total energy content of a system is called enthalpy. It is a function of its internal energy as well as pressure and volume. So, H=U+PV where H, U, P and V denote the enthalpy, internal energy, pressure and volume respectively. The SI unit for measurement of enthalpy is the Joule. In a chemical reaction, the energy transferred to the environment is the change in enthalpy of the system and can be calculated as: ΔH = Σ ΔHf products - Σ ΔHf reactants, when one mole of compound is formed at 25°C and 1 atm from elements in their stable form. Heats of formation for ions and many compounds can be looked up in tables found in many standard textbooks or online. Values used in this lesson are from the Helmenstine references cited below. The heat of formation for an element in its most stable form is defined as zero. As an example, we can calculate the change in enthalpy for the following reaction: 8 Al(s) + 3 Fe3O4(s) --> 4 Al2O3(s) + 9 Fe(s). We know that the heats of formation of the Al and the Fe are zero, so we can eliminate them from the equation. From a table (Helmenstine 2) we find that the heat of formation of Fe 3O4 is -1120.9 kJ and that of Al2O3 is -1669.8 kJ. So our equation becomes ΔH = 4(-1669.8 kJ) - 3(-1120.9 kJ). Solving the equation yields the result ΔH = -6679.2 - (-3362.7) = -3316.5kJ.

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Exothermic vs. Endothermic A reaction that produces heat is called exothermic, and its ∆H value is defined as negative. A reaction that absorbs or uses heat is called endothermic, and its ∆H value is defined as positive. A spontaneous reaction is one that tends to occur without any outside stimulus. The ∆H value is an indicator of the likelihood that a reaction will occur spontaneously. Generally reactions with negative ∆H values (exothermic) reactions are spontaneous. Endothermic reactions (positive ∆H values) are not usually spontaneous, but require the addition of energy or a catalyst. Calorimetry Calorimetry is the process used to directly measure the amount of energy given off by the combustion of any substance. The substance to be measured is placed in a "bomb" that is then sealed and filled with pure O2. The bomb is placed into a well-insulated container and immersed in a measured quantity of water. A temperature sensor is placed in the water and the container is sealed. A spark is sent into the bomb to begin the combustion, and the temperature change of the water is measured. That temperature change, along with the known specific heat and quantity of water, can be used to calculate the amount of heat generated by the combustion of the sample substance. The device used is called a bomb calorimeter.

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REACTION RATES AND EQUILIBRIUM If thermochemistry determines the likelihood of a reaction occurring spontaneously and measures how much heat energy it uses or generates, chemical kinetics determines how fast the reaction will be by tracking what that energy does. In any reaction, the reactants start with a given amount of energy (their heat of formation). They are at point A on the above energy diagram. If there is enough energy present to begin a spontaneous reaction, the reactants proceed to point B, a transition state; this is the point of highest energy. The amount of energy required to get from point A to point B is called Ea, energy of activation. Once the transition state is reached, the reaction proceeds smoothly to the end products, point C. This will be a lower energy level than point B. It may or may not be lower than point A. The difference in energy level between point A and point C is ∆H, the change in enthalpy. So, our hypothetical reaction diagrammed above has a negative ∆H and is exothermic. In general, the higher the energy of activation, the slower the reaction will be. A reaction with a very low Ea, is easily reversible, and at completion there are constant amounts of both reactants and products. This state is called equilibrium. Many things can influence the rate of the reaction. They include temperature, concentration of the reactants, surface area or physical form of the reactants, and the presence of a catalyst. Reactions proceed faster at higher temperatures, with greater concentrations of reactants, and if solid reactants are crushed or dissolved. A catalyst is a substance that is added to a reaction, which increases the reaction rate without itself being consumed. They create an easier path for the reaction, sort of like a snowplow clearing highways so cars can travel more quickly and easily. A 10-degree Celsius increase of temperature increases the reaction rate by approximately a factor of two.

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The rate of the reaction is expressed as M/s, the number of moles of reactant that are converted to product per second. This can be determined experimentally by simply timing how long a reaction takes and then doing a few calculations based on the known starting quantities and concentrations of the reactants. The behavior of the reaction is described in a rate law. There are two types of rate laws: differential and integrated. A differential rate law describes how the concentration of the reactants affects the rate. For a hypothetical reaction A + B → C, the rate law is rate = k[A]x[B]y. k is the rate constant, which is different for every reaction. x and y are the "orders" of the reactants: the change in rate compared to change in concentration. To derive the rate law for a reaction we need to run and time the reaction several times with different concentrations of the reactants. So, for example, the first run would be with both A and B at a concentration of 0.1M, the second with A at 0.2M and B at 0.1M, and the third with A at 0.1M and B at 0.2M. If the experimentally determined rate is 3.0 x 10-5M/s for the first run and 6.0 x 10-5M/s for the second and third, we see that the rate doubles when the concentration of either reactant is doubled. The change in rate is the same as the change in concentration, so x and y in the rate law are both 1. Now we can solve the equation to find k, the rate constant, using the time and concentrations from the first run of the reaction: 3.0 x 10-5 = k[0.1M][0.1m]. For this reaction the rate constant k is 0.3M/s. Now that we know the rate constant, we can predict the rate of reaction with any concentration of the reactants. So if we want to know how fast the reaction would be if A were 0.05M and B were 0.04M we can solve the equation again: rate = [0.3M/s][0.05M][0.04M] = 6.0 x 10 -4M/s.

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An integrated rate law describes how the concentrations of the reactants change as the reaction progresses over time. The mathematical calculations involve integral calculus, but the basic form of the rate law for reaction A → B is rate = k[A]. To relate concentration to time, the rate law becomes (after complex calculus) ln[A] = -kt + ln[Ao]. k is the rate constant, t is time, [Ao] is the initial concentration of A, [A] is the concentration of A after t seconds, and ln is the natural logarithm. This equation allows determination of the half-life of the reaction--the time it takes for the concentration of A to decrease by half. The half-life can be graphed as follows:

1.0

0.75

Concentration (M) 0.5

0.25

10 20 30 40 50 60 70 80 Time (minutes) Half-life of a reaction Swedish chemist Svante Arrhenius developed a method to calculate the activation energy of a reaction in 1889. After performing a reaction at two different temperatures and finding the rate constant k for each, an equation can be used to find Ea: ln(k2/k1) = (Ea/R)(1/T1 - 1/T2). R is the ideal gas constant 8.31J/Kmol; k2 &k1 are the rate constants for each reaction, and T1& T2 are the temperatures (in Kelvins--ᵒC + 273) for each reaction. If we find, for example, the reaction A + B → C has a rate constant of 1.20 mol/s at a temperature of 140ᵒ C and a constant of 2.50 mol/s at 340ᵒ C, we have the information we need to find its activation energy. ln(2.50 mol/s e 1.20 mol/s) = (Eae 8.31J/Kmol)(1/413K - 1/613K) ln(2.08 x 105)

= (Eae 8.31J/Kmol)0.000790K-1 Ea = 1.29 x 105 J/mol

As noted above, reactions with low Ea are easily reversible and 6|Page ©PassGAMSAT

reach a state of equilibrium. Equilibrium doesn't mean that no reaction is occurring. We have seen that as the concentrations of reactants increase, so does the rate of the reaction. In the case of a reversible reaction, where the products react to re-form the original reactants, as the "forward" reaction progresses and concentrations of the products increase, the "backward" reaction starts and increases its rate. Thus, both the "forward" and "backward" reactions are occurring simultaneously, keeping the reactants and products in relatively constant proportions.

Reaction system at equilibrium The ratios of products to reactants will be different for each reaction. If the forward reaction is fast and the backward one is slow, the equilibrium is said to favor the products. In the opposite situation with a slow forward reaction and a fast backward one, the equilibrium favors the reactants. The ratio can be calculated, and the result is an equilibrium constant; the larger the constant, the more the equilibrium favors the products. The equilibrium constant is only "constant" at the same temperature. If the reaction is carried out at a different temperature, Keq will be different. For the reaction aA + bB ↔ cC + dD, the equilibrium constant Keq can be found by solving this equation: Keq = [C]c[D]d/[A]a[B]b. The bracketed letters represent the concentration (in molarity) of each reactant and product. The superscript letters are any quantity coefficients. For example, using the reaction C2H3O2H ↔ H+ + C2H3O2-, the equation would be Keq = [C2H3O2-][H+]/[C2H3O2H]. If the concentrations at equilibrium are 0.68M for C2H3O2H and 3.5 x 10-3M for C2H3O2- and H+, the equation becomes Keq = [3.5 x 10-3]2/0.68 = 0.00352 /0.68 = 0.00001225/0.68 = 1.80 x 10-5.

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ACIDS AND BASES Acids and bases are chemical substances which show specific reactions. Acids react with certain metals to produce hydrogen gas. They usually cause a stinging sensation on the skin, and edible acids taste sour. Some common examples of acids are: vinegar, orange or lemon juice, aspirin, and carbonated water. Bases feel slippery on the skin, react with oils and greases, and edible bases taste bitter. Some common examples of bases are: ammonia, lye (drain cleaner), chlorine bleach, and baking soda. Soluble bases are called alkalis. When acids and bases react with each other they produce water and a type of salt; this is a neutralization reaction. The strength of an acid or base is any solution is measured on the pH scale. The pH scale runs from 0 to 14. Pure water has a pH of 7; it is neutral, neither acidic nor basic. Numbers from 0 to 6 on the pH scale indicate acid; the lower the number, the stronger the acid. Numbers from 8 to 14 on the pH scale indicate base; the higher the number, the stronger the base. pH actually refers to the hydrogen ion concentration in solution. You could use the mnemonic ‘percent hydronium’ as a memory aid. Acids cause litmus paper to turn red, and bases cause litmus paper to turn blue; an easy way to remember that is that the words acid and red both contain the letter D, and the words base and blue both contain the letter B.

NEUTRAL ACID

0

1

2

3

4

5

BASE

6

7

8

9

10

11

12

13

14

Svante Arrhenius was one of the first chemists to define the differences between acids and bases, in the late 1800s. He defined an acid as a compound which dissociated in water and released protons (H+ ion) in solution. A base was defined as a compound which produced hydroxide ions (OH-) when present in solution. In the early 1900s, Johannes Bronsted and Thomas Lowry noticed that hydrochloric acid (HCl) was neutralized by ammonia even in the absence of water. They proposed a different definition of acids and bases. By the Bronsted-Lowry definition, an acid is a compound that can donate a hydronium ion to another compound it reacts with, and a base is a compound that can accept a hydronium ion during a reaction. In the Bronsted-Lowry theory, every acid has a conjugate base. 8|Page ©PassGAMSAT

The conjugate base is the negative ion formed when the acid dissociates. In 1923, G.N. Lewis proposed yet another definition for acids and bases, from his work on covalent bonding. A Lewis acid is a compound which can accept an electron pair in a reaction; it has an unoccupied orbital with two spaces in its outer shell. A Lewis base is a compound which donates an electron pair in a reaction; its outer shell has only two electrons. So, the three definitions of acids and bases are similar, but there are significant differences. They are summarized below.

definition

acid

base

Arrhenius

gives off H+ ion in water

gives off OH- ion in water

Bronsted-Lowry

donates H+ ion in reaction

accepts H+ ion in reaction

Lewis

accepts electron pair in reaction

donates electron pair in reaction

The pH of a compound can be calculated if the concentration of the solution is known. For a strong acid (one which almost completely dissociates in water) the equation is pH = -log[H+]. For hydrochloric acid at a 0.00500M concentration, pH = -log(0.00500M) = 2.30. For a weak acid such as acetic acid, which does not completely dissociate in water, we first need to know the aciddissociation constant Ka in order to find the concentration of H+ at equilibrium. The equation for finding the equilibrium constant is used to find the concentration. For example, acetic acid dissociates in water according to the equation: CH3COOH→CH3COO-- + H+. If we start with a 0.5M solution of acetic acid (C2H3O2H) and the information that its Ka is 1.75 x 10-5, we can set up the equation Ka = [C2H3O2-][H+]/[C2H3O2H] and solve it to find [H+], which we will represent as y. 1.75 x 10-5 = [C2H3O2-][H+]/[0.5] .0000175 x .5 = [C2H3O2-][H+] 0.00000875 = y2 .00296 = y = [H+]

We can now use the pH equation pH = -log[H+] to find a pH of 2.53. To find the pH of a base solution, which doesn't produce hydronium ions, we need to know that

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water dissociates to form a small quantity of H +. We can use its dissociation constant of K w = 1014

and the equation Kw = [OH-][H+], using the known molarity of the base solution for [OH-]. So,

for a 0.5M solution of NaOH we get 10-14 =0.5[H+]. Solving the equation tells us that [H+] = 2.0 x 10-14. Now we can use the pH equation to find that the pH is 13.699. It is possible to determine the unknown concentration of an acid or base using a process called titration. Place a measured quantity of the unknown solution in a beaker, and then add acid or base (whichever is needed to neutralize the unknown) of known molarity in small measured amounts. When the titrated solution reaches the neutral pH of 7.0, the amount of known solution needed to achieve it allows us to calculate the concentration of the unknown. Perhaps the bottle from which we pour the unknown tells us that it is NaOH, but doesn't give the molarity. So pour 150 ml of the NaOH into a beaker along with an indicator such as phenolphthalein. Since NaOH is a base, we will use 1M hydrochloric acid (HCl) to titrate it. Perhaps it takes 250 ml of the HCl to reach a neutral pH. We can use the equation MacidVacid = MbaseVbase. M is molarity and V is volume. In this case Mbase is unknown, but the other quantities are known. So, plugging in the known values we get 1.0M(250ml) = Mbase(150ml). Solving the equation tells us that the concentration of the NaOH solution is 1.66M. In the human body, pH is an important consideration in our physiology. Our blood is slightly basic. It also contains a buffer of a weak acid and its conjugate base to keep the pH stable when we eat or drink acidic foods or beverages. A buffer prevents drastic pH changes when a strong acid or base is added.

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NUCLEAR CHEMISTRY Isotopes Nuclear chemistry studies the spontaneous decomposition of unstable nuclei of atoms, giving out radiations in the process. As we know, each element has a characteristic atomic number which tells us the number of protons in its nucleus. Usually there is the same number of neutrons, but not always. Atoms of an element which have different numbers of neutrons are called isotopes. Collectively the protons and neutrons are referred to as nucleons, and different isotopes of an element are called nuclides. A radioisotope is one whose nucleus gives off various subatomic particles. Isotopes of an element are written with the atomic mass as a superscript before the symbol, or with the symbol followed by a dash and the mass. So uranium could be written as either U or U-238. Nuclear chemistry and nuclear physics are very closely related and have considerable

238

overlap.

Radiation refers to waves of energy passing through a medium. Light, heat and sound are types of radiations but what we are most concerned about is radiation from radioactive materials. Therefore, radiation often has the scary connotation of nuclear accidents such as Chernobyl. Radioactivity Radioactivity was discovered by accident in the early 1890s. Wilhelm Röntgen discovered Xradiation and its ability to penetrate various substances including human body tissue. He and many other researchers including Henri Becquerel began searching for the source of this radiation. Meanwhile medical doctors immediately began to make practical use of X-rays for diagnostic purposes even as chemists and physicists were still trying to understand how they worked. Becquerel was the first to discover natural radioactivity, from a compound of uranium. Others such as Marie and Pierre Curie began discovering other radioactive elements. The Curies along with

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Becquerel won the 1903 Nobel Prize for Physics for their work on radioactivity, a word which was coined by the Curies. Radioactive Decay The cause of radioactive decay is not known. However, many observations have been made since the Curies and Becquerel began to study the phenomenon. All elements with an atomic number higher than 83 are radioactive. The ratio of the number of neutrons to the number of protons is a determining factor; most nuclei with a ratio of between 1.0 and 1.55 are stable. All nuclei with ratios outside that range are unstable, therefore radioactive. There are several different types of radioactive decay, depending on what type(s) of particles are emitted. Alpha radiation occurs among nuclides with very high mass. An alpha particle is the nucleus of a helium atom comprising two protons and two neutrons. Alpha decay causes the atomic number of the atom to decrease by two and it mass to decrease by four.

Alpha decay of Uranium to Thorium

Beta radiation converts a neutron to a proton by emitting an electron. The atomic number increases by one and the mass is unchanged. Nuclides with very high neutron-to-proton ratios are most likely to undergo beta decay.

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beta decay of Iodine-131 to Xenon Gamma rays are electrically neutral high-energy light particles that are emitted during other forms of radioactive decay. Positron emission is the opposite of beta radiation. A positron is the antiparticle of an electron. When it is emitted from the nucleus a proton becomes a neutron. The atomic number decreases by one and the mass is unchanged. This usually happens in nuclides whose neutron-to-proton ratio is less than 1.0.

decay of Nitrogen-12 to Carbon

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In electron capture, an electron from an inner orbital is pulled into the nucleus. As in positron emission, a proton becomes a neutron, and the effect and occurrence are the same.

Half-Life The half-life of a radionuclide is the length of time required for half of the atoms in a sample to undergo radioactive decay. The same laws used to determine the rate of a first-order chemical processes also apply to half-lives. The half-life is determined by the following equation: t1/2 = 0.693/k, where t1/2 is the half-life and k is the rate constant. If we know the half-life, we can find the rate constant by algebraically manipulating the equation to k = 0.693/t 1/2 . We can also then calculate how much of an element will be present after any number of years.

For example, the half-life of

236

Pu is 87.74 years. We can find the rate constant by dividing 0.693

by 87.84; thus, k = 7.90 x 10-3/yr. If we have 175 grams of

Pu and want to know how much

236

we would have left after 225 years, we can use the equation we used earlier to relate reactant

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conentrations with time: ln[A]t = -kt + ln[Ao]. [Ao] is the initial quantity of the isotope, [A]t is the quantity of isotope after time t1/2, k is the rate constant, and t1/2 is the half-life. When we plug our known values into the equation, we get ln[A]t = -( 7.90 x 10-3/yr)(225 yr) + ln[175 g]. Solving the equation gives us the result ln[A]t = -1.78 e 5.16, then [A]t = 29.4 grams. Effects & Practical Uses--Nuclear Medicine, Nuclear Power, Radiocarbon Dating Immediately after the discovery of X-rays, doctors saw their practical application and medical benefit. But in the century or so since its discovery nuclear medicine has become far more than simple pictures of broken bones. Modern diagnostic imaging techniques allow doctors to see soft tissues and even some physiological processes in action. Targeted beams of radiation can selectively destroy cancer cells that are "painted" with radioisotopes, while sparing most of the surrounding healthy cells. Iodine-131, iridium-182, strontium-89 and samarium-153 are the isotopes used in radiation therapy for treatment of cancer. So, radiation is being usefully harnessed for both diagnostics and treatment in medicine. Radioisotopes are routinely used in biological studies as well. Phosphorus-32 which has a half life of 14.2 days is commonly used for labeling nucleic acids. Cysteine, one of the sulphur-containing amino acids can be labeled with the isotope sulphur-35, leading to radioactive uptake by the protein molecules. Tritium (H3) may be used to label proteins and nucleic acids. However since exposure to radioactivity may cause diseases, the experiments in the laboratory are performed in a fume-hood behind a protective shield. Nuclear power can be a controversial subject, mostly due to fears and concerns sparked by famous incidents such as the Chernobyl disaster in 1986. Whether or not one favors the use of nuclear power, it's still a good idea to have at least a basic understanding of how it works; 16% of the world's electricity is generated from nuclear power. Essentially, fissionable radioactive material (usually purified uranium or plutonium) is placed in the reactor core, which is surrounded by a steel pressure vessel. Control rods made of neutron-absorbing material can be inserted or removed to varying degrees to manage the rate of the reaction. Heat generated by fission is transferred to water that circulates through the pressure vessel and into a steam generator. The steam is then piped to a turbine which generates electricity. The turbines used in nuclear power plants are the same as the ones used in fossil-fuel power plants, which also are turned by steam. The main difference is the source of the heat which creates the steam. The entire core, pressure vessel, and steam generator are surrounded by a thick concrete containment structure. A condenser pipes water through and around the turbine housing to dissipate excess heat. Most nuclear power accidents have been the result of human error or 15 | P a g e ©PassGAMSAT

neglect of safety protocols.

Schematic of a common nuclear reactor design Another use of nuclear chemistry is in the fields of archaeology and paleontology--radiocarbon dating. The isotope C-14 is used. All living and formerly living things contain a known amount of carbon, and a known percentage of that carbon is the C-14 isotope. By measuring the amount of C-14 in an archaeological specimen, the age of the specimen can be calculated using the known half-life of the isotope and the known quantity of it that was present when the specimen was alive. There are down-sides to nuclear chemistry. As noted above, carelessness has caused accidents. Rogue states and terrorist organizations can use radioactive waste to make "dirty bombs." Extreme radiation exposure can cause serious illness, even death. Lesser exposure over time can lead to certain cancers. Marie Curie died of aplastic anemia, a cancer almost certainly linked to her years of exposure to radioactive substances. Of course, early researchers did not know the risks they faced, or how to mitigate them. Even if they had known that, however, it's possible that their thirst for knowledge would have driven them to take the risks anyway.

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Exercises 1. Calculate ΔH for the following reaction, with the heats of formation given: C2H4(g) + 3 O2(g) ↔ 2 CO2(g) + 2 H2O(l) ΔHf for C2H4 = +52.3 kJ/mol ΔHf for CO2 = -393.5 kJ/mol ΔHf for H2O = -285.8 kJ/mol

2. Determine whether these reactions are exothermic or endothermic. A. 2Na + 2H2O →2NaOH + H2 B.

C + O2→CO2

C.

Mg(s) + 2HCl(aq) → H2(g) + MgCl2(aq)

3. Draw an energy diagram for an endothermic reaction.

4. Calculate the rate constant k for the reaction A + B → C when it is performed under the following conditions: experiment #

concentration of A [M]

concentration of B [M]

initial rate [M/s}

1

0.3M

0.3M

2.00 x 10-5

2

0.6M

0.3M

4.00 x 10-5

3

0.3M

0.15M

1.00 x 10-5

5. What would be the rate of that reaction if the concentration of A was 1.0M and B was 0.5M?

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6. If the reaction D + E → F has a rate constant of 2.50 mol/s at 800 ᵒC and 1.22 mol/s at 850 ᵒC, what is its activation energy?

7. What is the pH of a solution with a volume of 475 ml which contains 1.20 g of HCl?

8. What is the pH of a 0.75M solution of formic acid (HCO2H) if Ka =1.77 x 104?

9. What is the pH of a 0.00340M solution of LiOH?

10. 200 ml of a solution of HCl of unknown concentration is titrated to neutral by 400ml of 1.0M NaOH. What is the concentration of the HCl?

11. What is the rate constant for alpha decay of

12. If you start with 200 grams of

148

148

Gd, which has a half-life of 75 years?

Gd, how much would be left after 200 years?

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Questions to Think About 1. Think of examples of exothermic and endothermic reactions.

2. How is the half-life of a chemical reaction similar to that of a radioactive element?

3. Think of everyday examples of acids and bases.

4. What other practical applications can you think of for nuclear chemistry?

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