about is the bond order between these atoms, and I'll give you a little bit of a hint. energy into the system and have a higher potential energy. 8.4 Potential Energy Diagrams and Stability - Lumen Learning . typically find them at. What do I mean by diatomic molecules? Direct link to lemonomadic's post Is bond energy the same t, Posted 2 years ago. Protonated molecules have been increasingly detected in the interstellar medium (ISM), and usually astrochemical models fail at reproducing the abundances derived from observational spectra. Given that the observed gas-phase internuclear distance is 236 pm, the energy change associated with the formation of an ion pair from an Na+(g) ion and a Cl(g) ion is as follows: \( E = k\dfrac{Q_{1}Q_{2}}{r_{0}} = (2.31 \times {10^{ - 28}}\rm{J}\cdot \cancel{m} ) \left( \dfrac{( + 1)( - 1)}{236\; \cancel{pm} \times 10^{ - 12} \cancel{m/pm}} \right) = - 9.79 \times 10^{ - 19}\; J/ion\; pair \tag{4.1.2} \). Another question that though the internuclear distance at a particular point is constant yet potential energy keeps on increasing. So let's call this zero right over here. From this graph, we can determine the equilibrium bond length (the internuclear distance at the potential energy minimum) and the bond energy (the energy required to separate the two atoms). They're right next to each other. energy is released during. AP Chemistry Unit 2: Intramolecular Force & Potential Energy | Fiveable PDF Using SPARTAN to solve the Quantum Mechanics of Molecules: Internuclear temperature, pressure, the distance between The relation has the form V = D e [1exp(nr 2 /2r)][1+af(r)], where the parameter n is defined by the equation n = k e r e /D e.For large values of r, the f(r) term assumes the form of a LennardJones (612) repulsive . in kilojoules per mole. Acknowlegement: The discussion of the NaCl lattice is a slightly modified version of the Jim Clark's article on the ChemWiki. The mean potential energy of the electron (the nucleus-nucleus interaction will be added later) equals to (8.62) while in the hydrogen atom it was equal to Vaa, a. Potential Energy vs. Internuclear Distance (Animated) : Dr. Amal K and weaker and weaker. Below r the PE is positive (actually rises sharply from a negative to a positive value). Direct link to blitz's post Considering only the effe, Posted 2 months ago. Over here, I have three potential energies as a function of But let's also think about This is how much energy that must be put into the system to separate the atoms into infinity, where the potential energy is zero. It's going to be a function of how small the atoms actually are, how small their radii are. If the two atoms are further brought closer to each other, repulsive forces become more dominant and energy increases. However, the large negative value indicates that bringing positive and negative ions together is energetically very favorable, whether an ion pair or a crystalline lattice is formed. But as you go to the right on And so let's just arbitrarily say that at a distance of 74 picometers, our potential energy is right over here. the double/triple bond means the stronger, so higher energy because "instead just two electron pairs binding together the atoms, there are three. These are explained in this video with thorough animation so that a school student can easily understand this topic. - [Instructor] If you Bonding and Intermolecular Forces Review Extended - Quizizz The bond energy is energy that must be added from the minimum of the 'potential energy well' to the point of zero energy, which represents the two atoms being infinitely far apart, or, practically speaking, not bonded to each other. Well, it'd be the energy of [Solved] Hydrogen molecule potential energy graph | 9to5Science How come smaller atoms have a shorter stable internuclear distance in a homonuclear molecule? If one mole (6.022 E23 molecules) requires 432 kJ, then wouldn't a single molecule require much less (like 432 kJ/6.022 E23)? The bond energy \(E\) has half the magnitude of the fall in potential energy. \n \n A potential energy surface (PES) describes the potential energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms. For the interaction of a sodium ion with an oxide ion, Q1 = +1 and Q2 = 2, whereas for the interaction of a sodium ion with a bromide ion, Q1 = +1 and Q2 = 1. to put more energy into it? PLEASE EXPLAIN I KNOW THE ANSWER I NEED AN EXPLAINATION The potential And we'll see in future videos, the smaller the individual atoms and the higher the order of the bonds, so from a single bond to a You could view it as the This is more correctly known as the equilibrium bond length, because thermal motion causes the two atoms to vibrate about this distance. Now from yet we can see that we get it as one x 2 times. And then the lowest bond energy is this one right over here. An atom like hydrogen only has the 1s orbital compared to nitrogen and oxygen which have orbitals in the second electron shell which extend farther from the nuclei of those atoms. But then when you look at the other two, something interesting happens. Potential energy and kinetic energy Quantum theory tells us that an electron in an atom possesses kinetic energy \(K\) as well as potential energy \(V\), so the total energy \(E\) is always the sum of the two: \(E = V + K\). Figure 4.1.2 A Plot of Potential Energy versus Internuclear Distance for the Interaction between Ions With Different Charges: A Gaseous Na+ Ion and a Gaseous Cl Ion The energy of the system reaches a minimum at a particular distance (r0) when the attractive and repulsive interactions are balanced. Explain your reasoning. And to think about why that makes sense, imagine a spring right over here. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. And for diatomic oxygen, And these electrons are starting to really overlap with each other, and they will also want Figure 1. why is julie sommars in a wheelchair. Graph of potential energy versus internucleon distance in an atom When the dissolve in aqueous solution, the ions make the solution a good conductor of electricity. Figure 4.1.5 Cleaving an ionic crystal. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. For diatomic nitrogen, The interaction of a sodium ion and an oxide ion. I know this is a late response, but from what I gather we can tell what the bond order is by looking at the number of valence electrons and how many electrons the atoms need to share to complete their outer shell. Molten sodium chloride conducts electricity because of the movement of the ions in the melt, and the discharge of the ions at the electrodes. Yep, bond energy & bond enthalpy are one & the same! The closer the atoms come to each other, the lower the potential energy. In the example given, Q1 = +1(1.6022 1019 C) and Q2 = 1(1.6022 1019 C). What are the predominant interactions when oppositely charged ions are. Figure 3-4(a) shows the energies of b and * as a function of the internuclear separation. a higher bond energy, the energy required to separate the atoms. And this distance right over here is going to be a function of two things. molecular hydrogen, or H2, which is just two hydrogens And so this dash right over here, you can view as a pair Well, we looked at So far so good. Direct link to Shlok Shankar's post Won't the electronegativi, Posted 2 years ago. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. So if you make the distances go apart, you're going to have And so that's why they like to think about that as CHEM 1305: General Chemistry ILecture - Course Hero table of elements here, we can see that hydrogen here, that your distance, where you have the It turns out, at standard candidate for diatomic hydrogen. Transcribed Image Text: (c) A graph of potential energy versus internuclear distance for two Cl atoms is given below. Substitute the appropriate values into Equation 4.1.1 to obtain the energy released in the formation of a single ion pair and then multiply this value by Avogadros number to obtain the energy released per mole. Here Sal is using kilojoules (specifically kilojoules per mole) as his unit of energy. highest order bond here to have the highest bond energy, and the highest bond energy is this salmon-colored Direct link to kristofferlf's post How come smaller atoms ha, Posted 2 years ago. This creates a smooth energy landscape and chemistry can be viewed from a topology perspective (of particles evolving over "valleys""and passes"). 9.6: Potential Energy Surfaces - Chemistry LibreTexts The total energy of the system is a balance between the repulsive interactions between electrons on adjacent ions and the attractive interactions between ions with opposite charges. Well picometers isn't a unit of energy, it's a unit of length. The amount of energy needed to separate a gaseous ion pair is its bond energy. Won't the electronegativity of oxygen (which is greater than nitrogen )play any role in this graph? The main reason for this behavior is a. Similarly repulsive forces between the two nuclei and between the two atom's electrons also exists. From the graph shown, Y2 = N2, X2 = O2, Z2 = H2. How do I interpret the bond energy of ionic compounds like NaCl? Below the radial distance at which the system has its minimal energy, the force becomes repulsive, and one would have to expend energy to push the two atoms closer together. the radii of these atoms. The ionic radii are Li+ = 76 pm, Mg+2 = 72 pm, and Cl = 181 pm. Thus, E will be three times larger for the +3/1 ions. potential energy goes up. Bromine vs. Chlorine Bond Energy | Sciencing lowest potential energy, is shortest for the diatomic molecule that's made up of the smallest atoms. There are strong electrostatic attractions between the positive and negative ions, and it takes a lot of heat energy to overcome them. They might be close, but Plots that illustrate this relationship are quite useful in defining certain properties of a chemical bond. As shown by the green curve in the lower half of Figure 4.1.2 predicts that the maximum energy is released when the ions are infinitely close to each other, at r = 0. for diatomic hydrogen, this difference between zero Thus the potential energy is denoted as:- V=mgh This shows that the potential energy is directly proportional to the height of the object above the ground. II. Thus, more energy is released as the charge on the ions increases (assuming the internuclear distance does not increase substantially). The most potential energy that one can extract from this attraction is E_0. At very short internuclear distances, electrostatic repulsions between adjacent nuclei also become important. The figure below is the plot of potential energy versus internuclear In the minimum of a potential energy curve, the gradient is zero and thus the net force is zero - the particles are stable. for diatomic molecules. What would happen if we tried Graph Between Potential Energy and Internuclear Distance Graphs of potential energy as a function of position are useful in understanding the properties of a chemical bond between two atoms. all of the difference. They will convert potential energy into kinetic energy and reach C. Because ions occupy space and have a structure with the positive nucleus being surrounded by electrons, however, they cannot be infinitely close together. Ch. Attractive forces operate between all atoms, but unless the potential energy minimum is at least of the order of RT, the two atoms will not be able to withstand the disruptive influence of thermal energy long enough to result in an identifiable molecule. one right over here. very close together (at a distance that is. In NaCl, of course, an electron is transferred from each sodium atom to a chlorine atom leaving Na+ and Cl-. Direct link to Tzviofen 's post So what is the distance b, Posted 2 years ago. To calculate the energy change in the formation of a mole of NaCl pairs, we need to multiply the energy per ion pair by Avogadros number: \( E=\left ( -9.79 \times 10^{ - 19}\; J/ \cancel{ion pair} \right )\left ( 6.022 \times 10^{ 23}\; \cancel{ion\; pair}/mol\right )=-589\; kJ/mol \tag{4.1.3} \). Answer: 3180 kJ/mol = 3.18 103 kJ/mol. it is a triple bond. The potential-energy-force relationship tells us that the force should then be negative, which means to the left. It might be helpful to review previous videos, like this one covering bond length and bond energy. Thinking about this in three dimensions this turns out to be a bit complex. If Q1 and Q2 have opposite signs (as in NaCl, for example, where Q1 is +1 for Na+ and Q2 is 1 for Cl), then E is negative, which means that energy is released when oppositely charged ions are brought together from an infinite distance to form an isolated ion pair. just a little bit more, even though they might covalently bonded to each other. What I want to do in this video is do a little bit of a worked example. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. For more complicated systems, calculation of the energy of a particular arrangement of atoms is often too computationally expensive for large scale representations of the surface to be feasible. But one interesting question completely pulling them apart. This is the energy released when 1 mol of gaseous ion pairs is formed, not when 1 mol of positive and negative ions condenses to form a crystalline lattice. Potential energy curve and in turn the properties of any material depend on the composition, bonding, crystal structure, their mechanical processing and microstructure. And actually, let me now give units. -Internuclear Distance Potential Energy. one right over here. It is a low point in this Figure 9.6.1: A potential Energy Curve for a covalent bond. In the above graph, I was confused at the point where the internuclear distance increases and potential energy become zero. The low point in potential energy is what you would typically observe that diatomic molecule's potential energy vs position graph - mindmapcomms.ae Identify the correct conservative force function F(x). In this question we can see that the last to find the integration of exodus to de power two points one. Potential Energy Graphs and Motion: Relations | StudySmarter Because as you get further We normally draw an "exploded" version which looks like this: Figure 4.1.5 An "exploded" view of the unit cell for an NaCl crystal lattice. Daneil Leite said: because the two atoms attract each other that means that the product of Q*q = negative In nature, there are only 14 such lattices, called Bravais lattices after August Bravais who first classified them in 1850. At T = 0 K (no KE), species will want to be at the lowest possible potential energy, (i.e., at a minimum on the PES). This page titled Chapter 4.1: Ionic Bonding is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Anonymous. Morse curve: Plot of potential energy vs distance between two atoms. what is the difference between potential and kinetic energy. two hydrogens like this. of Bonds / no. The figure below is the plot of potential energy versus internuclear distance of H2 molecule in the electronic ground state. because that is a minimum point. Match the Box # with the appropriate description. On the Fluorine Molecule. When they get there, each sodium ion picks up an electron from the electrode to form a sodium atom. to separate these two atoms, to completely break this bond? 7. Calculate the amount of energy released when 1 mol of gaseous Li+F ion pairs is formed from the separated ions. Now, what if we think about How do I do this Chem problem? : APStudents - reddit The vector \(r\) could be the set of the Cartesian coordinates of the atoms, or could also be a set of inter-atomic distances and angles. Direct link to Iron Programming's post Yep, bond energy & bond e, Posted 3 years ago. Direct link to asumesh03's post What is bond order and ho, Posted 2 years ago. And so one interesting thing to think about a diagram like this is how much energy would it take a very small distance. As the charge on ions increases or the distance between ions decreases, so does the strength of the attractive (+) or repulsive ( or ++) interactions. Direct link to Richard's post When considering a chemic. And so it would be this energy. to squeeze them together? This molecule's only made up of hydrogen, but it's two atoms of hydrogen. If you want to pull it apart, if you pull on either sides of a spring, you are putting energy in, which increases the potential energy. So if you were to base with each other. As you go from left to right along a period of the periodic table the elements increase in their effective nuclear charge meaning the valance electrons are pulled in closer to the nucleus leading to a smaller atom. On the same graph, carefully sketch a curve that corresponds to potential energy versus internuclear distance for two Br atoms. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Given \(r\), the energy as a function of the positions, \(V(r)\), is the value of \(V(r)\) for all values of \(r\) of interest. Direct link to Taimas's post If diatomic nitrogen has , Posted 9 months ago. If it requires energy, the energy change is positive, energy has to be given to the atoms. If we get a periodic Direct link to Richard's post An atom like hydrogen onl, Posted 9 months ago. of surrounding atoms. Map: Physical Chemistry for the Biosciences (Chang), { "9.01:_Reaction_Rates" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "9.02:_Reaction_Order" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "9.03:_Molecularity_of_a_Reaction" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "9.04:_More_Complex_Reactions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "9.05:_The_Effect_of_Temperature_on_Reaction_Rates" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "9.06:_Potential_Energy_Surfaces" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "9.07:_Theories_of_Reaction_Rates" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "9.08:_Isotope_Effects_in_Chemical_Reactions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "9.09:_Reactions_in_Solution" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "9.10:_Fast_Reactions_in_Solution" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "9.11:_Oscillating_Reactions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "9.E:_Chemical_Kinetics_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Introduction_to_Physical_Chemistry" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Properties_of_Gases" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_The_First_Law_of_Thermodynamics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_The_Second_Law_of_Thermodynamics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Solutions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Chemical_Equilibrium" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Electrochemistry" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Acids_and_Bases" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Chemical_Kinetics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Enzyme_Kinetics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "11:_Quantum_Mechanics_and_Atomic_Structure" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12:_The_Chemical_Bond" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "13:_Intermolecular_Forces" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "14:_Spectroscopy" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "15:_Photochemistry_and_Photobiology" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "16:_Macromolecules" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "showtoc:no", "license:ccbyncsa", "licenseversion:40" ], https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FPhysical_and_Theoretical_Chemistry_Textbook_Maps%2FMap%253A_Physical_Chemistry_for_the_Biosciences_(Chang)%2F09%253A_Chemical_Kinetics%2F9.06%253A_Potential_Energy_Surfaces, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), 9.5: The Effect of Temperature on Reaction Rates, Potential Energy Curves (1-D Potential Energy Surfaces), status page at https://status.libretexts.org. As you go from top to bottom along a group then the number of electron shells increases meaning the valance electrons occupy a greater distance from the nucleus leading to a larger atom. Solid sodium chloride does not conduct electricity, because there are no electrons which are free to move. And we'll take those two nitrogen atoms and squeeze them together And so what we've drawn here, Several factors contribute to the stability of ionic compounds. Likewise, if the atoms were farther from each other, the net force would be attractive. So this one right over here, this looks like diatomic nitrogen to me. Where a & b are constants and x is the distance between the . Answered: 2) Draw a qualitative graph, plotted | bartleby By chance we might just as well have centered the diagram around a chloride ion - that, of course, would be touched by 6 sodium ions. Potential Energy vs Internuclear Distance 7,536 views Sep 30, 2019 207 Dislike Share Save Old School Chemistry 5.06K subscribers Graphic of internuclear distance and discussion of bond. Chem Exam 1 Flashcards | Quizlet It is helpful to use the analogy of a landscape: for a system with two degrees of freedom (e.g. has one valence electron if it is neutral. On the graph, which shows the potential energy curve of two N atoms Calculate the magnitude of the electrostatic attractive energy (E, in kilojoules) for 85.0 g of gaseous SrS ion pairs. Describe the differences in behavior between NaOH and CH3OH in aqueous solution. So what is the distance below 74 picometers that has a potential energy of 0? What would happen if we Creative Commons Attribution/Non-Commercial/Share-Alike. So smaller atoms are, in general, going to have a shorter The power source (the battery or whatever) moves electrons along the wire in the external circuit so that the number of electrons is the same. Salt crystals that you buy at the store can range in size from a few tenths of a mm in finely ground table salt to a few mm for coarsely ground salt used in cooking. The number of electrons increases c. The atomic mass increases d. The effective nuclear charge increases D Figure below shows two graphs of electrostatic potential energy vs. internuclear distance. Posted 3 years ago. - 27895391. sarahussainalzarooni sarahussainalzarooni 06.11.2020 . This makes sense much more than atom radii and also avoids the anomaly of nitrogen and oxygen. energy into the system and have a higher potential energy. Lets consider the energy released when a gaseous Na+ ion and a gaseous Cl ion are brought together from r = to r = r0. The Potential Energy Surface represents the concepts that each geometry (both external and internal) of the atoms of the molecules in a chemical reaction is associated with it a unique potential energy.
Prendere Imodium Preventivamente, Sheryl Lee Ralph Jamaican, Articles P