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Chemistry Exam 1 Study Guide

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by: Alyssa Anderson

Chemistry Exam 1 Study Guide CHEM 1030

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This is the updated version of the study guide for the first chemistry test. These notes cover everything we have discussed in class that pertains to this exam. A detailed periodic table and diagra...
Fundamentals Chemistry I
Dr. Streit
Study Guide
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Cara Benak

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This 19 page Study Guide was uploaded by Alyssa Anderson on Thursday February 4, 2016. The Study Guide belongs to CHEM 1030 at a university taught by Dr. Streit in Spring 2016. Since its upload, it has received 160 views.

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Date Created: 02/04/16
1 Chemistry Exam 1 Study Guide Chemistry- the study of matter and changes that matter undergoes Matter- anything that has mass and occupies space Scientific Method- a procedure/set of guidelines to organize and publish efficiently 1. Gather data through observations and experiments 2. Identify patterns and trends in collected data and note any initial thoughts 3. Summarize findings with a law- a concise statement that makes a relation between phenomena 4. Formulate a hypothesis by observing the cause and effect relationship 5. With time, the hypothesis may evolve into a theory which can predict future occurrences Classification of Matter 1. Solid- particles are held close together in an ordered position and DO NOT conform to the container it is placed in 2. Liquid- particles are held relatively close together but do not have an organized pattern and DO conform to the the container it is placed in 3. Gas- particles are far apart and have no set pattern but DO conform to the container it is placed in 4. In principle, all substances can exist in the solid, liquid, or gaseous stage 5. We can convert a substance by changing its identity 6. Mixtures can be separated by physical means into its component without changing the identities of the components - example: magnet to separate sand and iron (iron is magnetic) - example: boil water to separate salt and water (water has a much lower boiling point) - example: boil water to separate water and alcohol (different boiling points) 2 Chemists classify matter as either a substance or a mixture of substances 1. Substance- a form of matter that has a definite composition and distinct properties - example: salt (NaCl), iron, water (H20), mercury, carbon dioxide (CO2) - substances differ from each other in composition and may be identified by appearance, taste, smell, etc. 2. Mixture- physical combination of 2 or more substances a. homogenous- uniform throughout solution - example: seawater, apple juice, cake b. heterogenous- not uniform throughout solution - example: trail mix, chicken noodle soup, shells in sand Properties of Matter 1. Quantitative- properties measured/expressed with a number/unit (QUANTITY) 2. Qualitative- properties measured without measurements but rather are based on observations using the senses (taste, color, smell, etc.) (QUALITY) 3. Physical Property- one that can be observed or measured without changing the identity of the substance - example: color, melting point, boiling point 4. Chemical Property- one that a substance exhibits as it interact with another substance - example: flammability, corrosiveness, rust 5. Physical Change- change where the state of matter changes but the identity of the matter does not change - example: changes of state (melting, boiling, freezing, condensing) 6. Chemical Change- change in the composition so that the original composition no longer exists - example: digestion, combustion, oxidation 7. Extensive Property- depends on the amount of matter present - example: mass, volume, aka additive properties 8. Intensive Property- does NOT depend on the amount present - example: temperature, density 9. Physical Process- mixtures are separated but the identities do not change 10. Chemical Process- a process of changing mixtures/chemicals 3 Scientific Measurement 1. Properties that can be measured are called quantitative 2. A measured quantity must always include a unit 3. Systems A. English- foot, gallon, pound, Fahrenheit B. Metric- meter, liter, kilogram C. International System of Units (SI units)- universally used by scientists 1. Meter 2. Kilogram 3. Kelvin 4. Second 5. Ampere 6. Mole 7. Candela 4. Mass (g or kg or amu) A. a CONSTANT measure of amount of matter in an object/sample B. Gravity varies from location to location constant so weight = mass x gravity C. the mass of an atom is 1 amu= 1.6605378 x 10^-24 g 5. Temperature (Celsius or Kelvin or Fahrenheit) A. Celcius- for water, freezing point is O*C, boiling point 100*C B. Kelvin (*SI UNIT*)- “absolute” scale because 0 K is the absolute lowest C. K = *C + 273.15 OR C* = K - 273.15 D. Fahrenheit- for water, freezing point is 32*F and boiling point is 212*F E. *F = (9/5)(*C) + 32*F OR *C = (5/9)(*F - 32) 6. Volume (meter^3 or Liter) A. V = (length)^3 B. 1 dm^3 = 1 L C. 1 cm^3 = 1 mL 4 7. Density (kg/m^3) A. d = mass/volume so d = mass/length^3 B. solid = g/cm^3 C. liquid = g/mL D. gas = g/L E. example: if d1>d2 then m1<m2 OR v1>v2 Uncertainty in Measurements 1. Exact Numbers- defined values or counted numbers A. example: 1 kg = 1000 g B. example: 1 dozen = 12 items C example: 28 students in a class 2. Inexact Numbers- measured by anything but counting such as length, volume, mass A. It must be reported to indicate uncertainty by using significant digits B. The last digit reported is called the uncertain digit C. example: if we have an item against a ruler and we think it’s about 2.5 inches long, we know it’s for sure 2 inches but not sure about the .5, so we put 2.5 +/- 0.1 inch, and with a more accurate ruler we could put 2.45 inches +/- 0.01 inch D. Guidelines of Significant Figures 1. Any nonzero numbers ARE significant 2. Zeros between nonzero numbers ARE significant 3. Zeros to the LEFT of the first nonzero digit are NOT significant 4. Zeros to the RIGHT of the nonzero digits in decimals ARE significant 5. Zeros to the RIGHT of the last nonzero digit in a number without a decimal MAY OR MAY NOT be significant - example: 100 could have 1 2 or 3 significant figures 5 Calculations with Measured Numbers 1. Addition/Subtraction- line up the decimals and take the answer with the smaller amount of digits (rounding may be necessary) 2. Multiplication/Division- preform the action then take the fewer amount of digits from the original numbers given (rounding may be necessary) 3. NOTE: Be sure not to include exact numbers, such as the counted number - example: when finding the mass of each of 2 pennies, knowing together they equal 15 grams, 2 is not included in the measurement of significant figures. Therefor, since together they had 15 grams and that is 2 significant figures, your answer will have 2 significant figures 4. Rounding A. Leave rounding for the LAST step. DO NOT ROUND AFTER EACH STEP B. If the last digit is greater than 5, round UP (ex: 318.175 = 318.18) C. If the last digit is less than 5, round DOWN (ex: 318.174 = 318.17) 5. NOTE: Be aware of powers of 10. Make sure that you are calculating variables with the same power, then proceed 6. NOTE: Significant figures matter even when scientific notation changes 7. NOTE: Be sure to calculate the correct mass or volume before proceeding to find density or weight 8. Accuracy- how close the measurement is to the TRUE value 9. Precision- how close a series of measurements are to one another Using Units and Solving Problems 1. Conversion Factor- fraction in which same quantity is expressed one way in the numerator and another in the denominator - example: 1 inch = 2.54 cm aka 1 in/2.54 cm OR 2.54 cm/1 inch 2. Dimensional Analysis- use of conversion factors in problem solving A. Also known as the factor-label method B. example: convert 12 inches to meters (NOTE: only use significant figures of the thing you are converting (so 2 s.f. because 12 inches has 2 s.f.); 12 inches x 2.54 cm/1 inch x 1m/100 cm = 0.3042 = 30.30 m) 6 The Development of the Atom 1. An atom is the smallest quantity of matter that still retains the properties of matter 2. An element is a substance that cannot be broken down into two or more similar substances by any means (such as gold, oxygen, helium) 3. Atoms can also be divided smaller and smaller and eventually only a single atom remains. Dividing it further would make pieces that are no longer atoms. 4. Dalton- said atoms (of which matter consists of) are tiny, invisible particles. 5. Once a single atom has been obtained, dividing it smaller produces subatomic particles. 6. The nature, number, and arrangements of subatomic particles determine the properties of atoms 7. NOTE: LIKE charges repel each other, OPPOSITE charges attract 8. JJ Thompson (1856-1940)- noted easy were repelled by a plate with a negative charge and attracted to a plate bearing a positive charge. He concluded the rays were negatively charged. His contributions include: A. Proposed rays were actually a stream of negatively charged particles B. Negatively charged particles equaled electrons C. By varying the electric field and measuring the degree of deflection of cathode rays, Thompson determined the charge-mass ratio 9. R.A. Milikan (1868-1953)- determined the charge on an electron by examining the motion of tiny oil drops, which was found to be -1.6022 x 10^-19 C 10. The mass of an electron equals the charge divided by the charge multiplied by the mass which means (-1.6022 x 10^-19)/(-1.76 x 10^8 C x grams) which means it equals 9.10 x 10^-28 grams 11.Wilhelm Rotgen (1845-1923)- discovered x-rays which are not deflected by magnetic or electric fields so that they could not consist of charged particles 12. Antoine Becquerel (1852-1908)- discovered radioactivity 13. Alpha rays- consist of positively charged particles called alpha particles (α) 14. Beta rays- electrons that are deflected and made of beta particles (β) 7 15. Ernest Rutherford- used α particles to prove the structure of atoms A. The majority of particles penetrated the gold undeflected B. Sometimes, a gold particle would be deflected at a large angle or even backwards C. Through this, Rutherford concluded the nuclear model which states a positively charged center is concentrated in the middle of a cell at the nucleus and that the nucleus accounts for most of the cell’s mass and is extremely dense at the core within the atom 16. BE SURE TO LOOK AT TABLE 2.1/2.2 IN THE BOOK 17. All atoms can be identified by the number of protons/neutrons they have Characteristics of the Atom 1. Atomic Number- number of protons in the nucleus A. Since atoms must stay neutral, the number of protons equals electrons B. Protons determine the identity of the element 2. Mass Number- number of protons added to neutrons 3. Isotopes- Most atoms have at least two, which mean they have the same amount of protons and electrons, but different number of neutrons, which effects the mass. They usually exhibit the same chemical properties, such as some have the same type of compound with similar reactivities. On occasion, an isotope will be radioactive. 4. Nuclear Stability- can be related to density (note: the total volume is hardly accounted for by the nucleus but the mass is mainly the nucleus alone) A. The higher the density, the stronger the forces are in the atom. B. Stability = Coulomb repulsion - short range attraction C. example: the atomic number of Uranium equals 92 but has 143 neutrons D. Heavy atoms need much more neutrons to remain stable E. The principle factor for nuclear stability is proton to neutron ratio (n/p) F. There are more stable nuclei with 2, 8, 20, 50, 82, or 126 protons and neutrons G. There are more stable nuclei with even numbers H. All elements with atomic numbers greater than 83 are radioactive 6. Atomic Mass- mass of atom in amu (1 amu = half the mass of a carbon-12 atom) 7. Average atomic mass- on the periodic table, it represents the average mass of the naturally occurring mixture of isotopes 8 Elements of the Atom . 1 Protons- positively charged, in the nucleus 2. Neutrons- no charge, in nucleus, slightly larger than protons 3. Electrons- negatively charged particles that orbit around a nucleus The Periodic Table 1. A chart in which elements having chemical and physical properties are grouped together, separated by periods and groups. 2. Numbered by increasing atomic number (protons and electrons) because it regulates all properties of that element (fingerprint of element) 3. There are two important numbers- the average atomic mass and the atomic number 4. Periods- horizontal rows, in order of increasing atomic number A. Metals- good conductors of heat and electricity B. Nonmetals- poor conductors of heat and electricity C. Metalloids- intermediate properties 5. Groups- vertical columns A. Alkali Metals (1A)- Li, Na, K, Rb, Cs, Fr B. Alkaline Earth Metals (2A)- Be, Mg, Ca, Sr, Ba, Ra C. Chalcogens (6A)- O, S, Se, Te, Po D. Halogens (7A)- F, Cl, Br, I, At E. Noble Gases (8A)- He, Ne, Ar, Kr, Xe, Rn F.Transition Metals (1B and 3B-8B) Mole- the amount of a substance that contains as many elementary entities as there are atoms in exactly 12 grams of carbon-12 1. Experimentally determined number- Avagandro’s Number (N ) A 2. NAaka 1 mole = 6.0221415 x 10^23 (usually simplified to 6.022 x 10^23) 3. example: The human body has a total of 30 moles of calcium. Determine the number of atoms of calcium and the number of moles of Calcium in a sample containing 1.00 x 10^26 Ca atoms. work: (30 moles Ca) x (6.022 x10^23/ 1 mole Ca) = 1.807 x 10^25 atoms of Ca 9 Molar Mass- mass in grams of 1 mol of substance 1. By definition, the mass of one mole of carbon-12 is exactly 12 grams 2. The mass of 1 carbon-12 atom equals exactly 12 amu 3. The mass of an atom equals the mass of the mole (just in different units) 4. example: determine the number of moles of carbon in 25 grams of carbon work: (25 grams of C) x (1 mole of C/ 12.01 grams of C) = 2.082 moles of C (10.50 grams He) x (1 mole He/ 4.003 grams C) = 2.633 mol He 5. example: determine the number of moles of He in 10.50 grams of helium work: (0.515 g C) x (1 mol C/ 12.01 g C) x (6.022 x 10^23/ 1 mole C) = 2.58 x 10^22 C atoms Unit of Energy 1. Measured by the Joule (J) 2. Created by English physicist James Joule 3. The amount of energy possessed by a 2 kg mass moving at speed of 1 m/s 4. E K 1/2 x m x u^2 = 1/2 x 2 kg x (1 m/s)^2 = 1 kg x m^2/s^2 5. Joules can also be denied as the amount of energy exerted when a force of 1 Newton is applied over 1 meter. 1 J = 1 N x m The nature of light- visible light is only a small component of the continuum of radiant energy known as the electromagnetic spectrum Properties of waves (all forms of electromagnetic radiation travel in waves) 1. Waves are characterized by wavelength (λ) which is the distance between identical points on successive waves (inversely related to v) 2. frequency (v, nu) is the number of waves that pass through a particular point in 1 second 3. NOTE: short wavelength = high frequency; long wavelength = low frequency 4. Amplitude is the vertical distance of the middle of the wave 5. The speed of light (c) through a vacuum is constant. c = 2.99792458 x 10^8 m/s 6. The speed of light, frequency, and wavelength are all related by the equation c = λ x v (λ is expressed in meters, and v is expressed in s^-1) 10 Quantum Theory 1. Atoms and photons at the microscopic level do not measure equally to the microscopic level 2. The laws for macroscopic are not applicable to the microscopic level 3. All energy is transferred through the measure of waves (E = h x v) 4. E = h x v means energy is calculated by multiplying Planks Constant (6.63 x 10^-34 J x s) by the frequency The Schrodinger Equation 1. Erwin Schrodinger realized the wave and particle characteristics were different in electrons 2. Particle behavior is determined by mass (m) while wave behavior is determined by the wave function (Ψ) in the equation H (m) x Ψ = E x Ψ 3. Quantum Mechanics- defines the region where the electron is most likely to be at a given time 4. The probability of finding an electron in a certain area of space is proportional to Ψ^2 and is called electron density 5. Energy states and wave functions are characterized by a set of quantum numbers 6. Quantum numbers and wave functions describe atomic orbitals Atomic Orbitals 1. All s orbitals are spherical in shape but alter in size ( 1s < 2s < 3s) 2. All p orbitals are dumbbell shaped and have 3 orientations 3. D orbitals vary and have 5 orientations 5. F orbitals vary and have 7 orientations 6. Energy of orbitals- in a hydrogen atom, depends only on n SUMMARY 1. Principle (n)- SIZE 2. Angular (l )- SLOPE/SHAPE 3. Magnetic (ml )- ORIENTATION 11 Quantum Numbers 1. They are required to describe the distribution of electron density in an atom 2. In order to describe an atomic orbital, you must know the three quantum numbers 3. Principal Quantum Number (n) A. Designates SIZE of the orbital B. The larger the value of n the larger the orbitals C. The allowed values of n are integral numbers (1, 2, 3, etc.) D. The collection of orbitals with the sam value of n are frequently called shells 4. Angular Momentum Quantum Numbers (l ) A. Describes the SHAPE of the orbital B. Values of l are integers that depend on the value of n C. Allowed values of l range from 0 to n-1 D. The collection is called a subshell 5. Magnetic Quantum Number (ml ) A. Determines the ORIENTATION of orbitals in space B. Values of ml are integers that depend on the value of l C. - l , 0, + l 6. Quantum Numbers designate shells, subshells, and orbitals- REFER TO TABLE 3.2 Speed (ms) 1. It is not derived by the equation 2. Found through experiments that included a beam of atoms that were split by a magnetic field 3. It was concluded that electrons behave like tiny magnets 4. Specifies the electrons spin 5. ms = +/- 1/2 Example: 2p^2 1. n = 2 2. l = p = 1 3. m l = +1, 0, -1 4. ms = +1/2, -1/2 12 Aufbau Principle 1. States that electrons are added to the lowest energy orbitals first before moving to higher energy orbitals 2. Example: Li has 3 electrons so its configuration is 1s^2 / 2s^1 3. Example: Be has 4 electrons so its configuration is 1s^2 / 2s^2 4. Example: B has 5 electrons so its configuration is 1s^2 / 2s^2 / 2p^1 5. Example: C has 6 electrons so its configuration is 1s^2 / 2s^2 / 2p^2 6. Example: F has 9 electrons so its configuration is 1s^2 / 2s^2 / 2p^5 7. NOTE: 2p orbitals are degenerate Pauli Exclusion Principle 1. No two electrons in an atom can have the same four quantum numbers 2. The principle number, angular momentum number, magnetic number, and speed cannot ALL be the same 3. Only 2 electrons can occupy an atomic orbital Hund’s Rule 1. The most stable arrangement of electrons is the one in which the number of electrons with the same spin is maximized 2. In other words, put 1 electron in each box before pairing NOTE: All the chemical and physical properties of matter are given by how the electrons are arranged in each orbital. Paramagnetism is when there are one or more unpaired electrons in an atom (such as the case of O and F). Diamagnetism is when all the electrons in an atom are paired, such as Neon. 13 Electron Configuration 1. Describes where the electrons are distributed in the various atomic orbitals 2. In the ground state of hydrogen, the electron is found in the 1s orbital (1s^1 means the principal number n = 1 and the angular momentum is s = 0). If hydrogens electrons were found in a higher energy we would say the atom is in an excited state (2s^1) 3. In multi-electron atoms, the orientations of the orbitals are SPLIT (i.e. goes from 3s to 3p then from 4s to 3d) Rules of Electron Configuration 1. Electrons will reside in the available orbitals of the lowest possible energy 2. Each orbital can accommodate a maximum of two electrons 3. Electrons will not pair in degenerate orbitals if an empty orbital is available 4. Orbitals will fill in the order indicated in the figure to the right. Worked example 3.10 Problem: What’s the electron configuration and orbital diagram of Ca (Z= 20)? Solution: 1s^2 / 2s^2 / 2p^6 / 3s^2 / 3p^6 / 4s^2 Noble Gas Core 1. The electron configurations of all elements except H and He can be represented by using a noble gas core 2. K (Z =19) has the configuration 1s^2 / 2s^2 / 2p^6 / 3s^2 / 3p^6 / 4s^1 but since argon (Ar) is 1s^2 / 2s^2 / 2p^6 / 3s^2 / 3p^6 you can adjust and only write [Ar] 4s^1 14 Electron Configuration and the Periodic Table 1. Valence electrons are the outer electron involved in chemical reactions and can be identified by the period number 2. 4f = the lanthanide (rare earth) series 3. 5f = the actinide series 4. Notable exceptions to electron filling in the transition metals: A. Chromium (Z = 24) is [Ar] s3^1 / 3d^5 B. Copper (z = 29) is [Ar] 4s^1 / 3d^10 C. The reason for these anomalies is the slightly greater stability of d subshells that are either half filled (d^5) or completely filled (d^10) Discoveries in the Periodic Table A. In 1864 John Newlands noted that when the elements were arranged in order of atomic number, every eighth element had similar properties. They could be grouped according to their properties and he called it the law of octaves. B. In 1869 Dmitri Mendeleev and Lothar Meyer independently proposed they idea of periodicity. 1. Mendeleev grouped the 66 known elements according to their properties and atomic mass 2. Mendeleev predicted properties for elements not yet discovered such as gallium (Ga) 3. However, Mendeleev could not explain inconsistencies such as argon coming before potassium in the periodic table despite having a higher atomic mass 4. In 1913 Henry Mosley discovered the correlation between the number of protons (atomic number) and frequency of x-rays generated. 5. By ordering the periodic table by atomic number instead of atomic mass, scientist were able to make sense of discrepancies. 6. Entries today include atomic number and symbol and are arranged according to electron configuration 15 Effective nuclear charge (Z subscript eff) is the actual magnitude of positive charge that is ”experienced” by an electron in the atom 1. In a multi electron atom, electrons are simultaneously attracted to the nucleus and repelled by one another (positive nucleus and negative electrons) 2. This results in shielding, where an electron is partially shielded from the positive charge of the nucleus by the other electrons 3. Although all electrons shield one another to some extent, the most effective are the core electrons 4. In general, the effective nuclear charge is given by Z , which is the number of protons in the nucleus 5. σ is the shielding constant Effective nuclear charge 16 Atomic radius is the distance between the nucleus of an atom and its valence shell 1. Atomic radius in metals aka metallic radius is half the distance between the nucleus of two adjacent identical metal atoms 2. Atomic radius in nonmetals aka covalent radius is half the stance between adjacent identical nuclei connected by a chemical bond 3. When we add another layer (shell) of electrons, we increase the radius. Therefore, the radius increases going down the periodic table. 4. When we go across a period, we are not changing the principal quantum number (n) but we are adding an angular number (l ). When l increases, the attraction between the effective nuclear charge and the charge on the valence shell becomes stronger so the electrons are pulled closer in (radius decreases). . 5 The atomic radius decreases left to right across a period due to the increased electrostatic attraction between the effective nuclear charge and the charge on the valence shell. 6. NOTE: The stronger the charge = the higher the attraction = the smaller the radius Worked example: Problem: referring only to a periodic table arrange the elements P, S, O in order of increasing atomic radius. Answer: P, S, O Exceptions to the Rule: 17 Chromium: Z = 24 —> [Ar] 4s^1 / 3d^5 Copper: Z = 29 —> [Ar] 4s^1/ 3d^10 Niobium: Z = 41 —>[Kr]4d^4 / 5s^1 Molybdenum: Z = 42 —> [Kr] 4d^5 / 5s^1   Ruthenium: Z = 44 —> [Kr] 4d^7 / 5s^1   Rhodium:  Z = 45 —> [Kr] 4d^8/ 5s^1   Palladium: Z = 46 —> [Kr] 4d^10   Silver: Z = 47 —> [Kr] 5s^1 / 4d^10 Lanthanum: Z = 57 —> [Xe] 6s^2 / 5d1 Actinium: Z = 89 —> [Rn] 7s^2 / 6d^1 Cerium: Z = 58 —> [Xe] 6s^2 / 4f^1 / 5d^1 Thorium: Z = 90 —> [Rn] 7s^2 / 6d^2 Gadolinium: Z = 64 —> [Xe] 6s^2 / 4f^7 / 5d^1 Protactium: Z = 91 —> [Rn] 7s^2 / 5f^2 / 6d^1 Platinum: Z = 78 —> [Xe] 6s^1 / 4f^14 / 5d^9 Uranium: Z = 92 —> [Rn] 7s^2 / 5f^3 / 6d^1 Gold: Z = 79 —> [Xe] 6s^1 / 4f^14 / 5d^10 Neptunium: Z = 93 —> [Rn] 7s^2 / 5f^4 / 6d^1   Curium: Z = 96 —> [Rn] 7s^2 / 5f^7 / 6d^1   Lawrencium: Z = 103 —> [Rn] 7s^2 / 5f^14 / 7p1 18 For more help on the periodic table check out! 19 Resources sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiC0- n04N7KAhULbD4KHYJqC8QQjB0IBg& %2Flesson%2Fground-state-electron-configuration-definition-example- quiz.html&psig=AFQjCNF8UKlnbc139XTFXnGPJGogs6GOtw&ust=1454697555658620 Electronic_Structure_of_Atoms_and_Molecules/Electronic_Configurations sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiI_Obpquv KAhXG5CYKHeKpCxoQjB0IBg& %2Fchapter8%3FshowComments %3D1&psig=AFQjCNErW6GOTWqQdv5K4k8roUwGoJpp-w&ust=1455129736348704 sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwic2rC1rOvK AhUBTSYKHWOMC5kQjB0IBg& %2Ftutorials%2Fcrystalmaker%2Fatomic-radii %2Findex.html&psig=AFQjCNE5aPJWhRQ- vJJhJn6hqwuamkTdyA&ust=1455130149785880


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