The standard enthalpy change of formation, or #DeltaH_f^@#, of magnesium oxide will be -601.6 kJ/mol. Throw the powder in the garbage. Magnesium oxide is formed up of the ions Mg. , which are joined by an ionic connection. Solution: First WebTo determine the enthalpy of formation of magnesium oxide. from a metal to a nonmetal and the resulting ions have achieved Density of magnesium oxygen formula- 3.58 g/cm, Experiment to Show Burning of Magnesium Ribbon Equation. %"oI*x$C #|ny~Yij>^^}m,_FIOP(U%J/Bs@= 7u=/K] @#kS@OevZK()%|f32d)%Bsc XtPm&^ Jh2ij[0y("La[psQ%8h;#h8Uc[Ga@4[4+TJ!4NP\0. 47 25 A 2019 study confirmed this by testing 15 magnesium supplements and finding that a supplement containing only magnesium oxide had the lowest bioavailability (3). which are lost equals those gained. A dry-powder extinguisher must be used because a carbon dioxide fire extinguisher will not extinguish burning magnesium. Students can learn more about Magnesium and its chemical properties when reacting with different elements at Vedantus official website. As such, a deficiency in this mineral can lead to migraine headaches. As an antacid, it works by neutralizing the stomach acids of humans and avoiding indigestion and heartburn. 0000008934 00000 n The number of components in a given molecule may be determined using the molecular formula. 0000003612 00000 n They should focus more and more on practice as it will help them a lot and with proper guidance and hard work, they can score a good rank in competitive exams. Since both reactions are in dilute water solutions ofHCl it was necessary to know the heat capacity of water, but because some heat would be transferred to the calorimeter whose heat capacity was unknown, we had to record a correction factor (x) based upon the specific heat of water using the equation [m(h2o)+X]Cwater+water=-1(m(ice water)Cwatertice water). It may provide other health benefits, including potentially lowering blood pressure and blood sugar levels. 0000005842 00000 n 0000002161 00000 n The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. \[Mg_{(s)} + 2H_2O \rightarrow Mg(OH)_{2\; (s)} + H_{2 \;(g)} \tag{2}\]. Meanwhile, 300 mg per day has been shown to help treat high blood pressure, while 250 mg per day may help lower blood sugar levels in women with gestational diabetes (23, 25). Magnesium oxide is a form of magnesium commonly taken as a dietary supplement. xb```V>>c`0p``V9(S%C8T`8s5Z85yMU2pe5? The enthalpy of formation of MgO is more difficult to measure directly. Make sure you hold the metal securely with the tongs. To learn more about Magnesium and its properties, the student can check out Vedantu;s official website or Youtube channel where theyll find a ton of FREE resources that will help them to understand Magnesium and other elements. left. Finding the enthalpy of formation of magnesium oxide using Hess' Law, Improving the copy in the close modal and post notices - 2023 edition, New blog post from our CEO Prashanth: Community is the future of AI, Calculation of the enthalpy change of reactions, Using enthalpies of formation and combustion to find formation enthalpy of Acetylene (Hess' Law). As an antacid, it works by neutralizing the stomach acids of humans and avoiding indigestion and heartburn. Let's start by writing the reaction's word equation. Avoid gazing directly at the source of light. <> The Octet Rule is the basis for the predictions about the How to intersect two lines that are not touching. ribbon easily crumbles into a white powder which is a mixture Learn more about if it's right for you. Using data from the NIST Chemistry WebBook, the heat of formation of MgO can be calculated as follows: Hf[MgO] = Hf[O2(g)] + Hf[Mg(s)] - Hf[Mg(s)] - Hf[O2(g)] Hf[MgO] = -602.8 kJ/mol This value represents the heat of formation of MgO under standard conditions (25C and 1 atm). High doses of magnesium oxide may cause dangerously high blood magnesium levels, which is more likely in specific populations. The site owner may have set restrictions that prevent you from accessing the site. lose electrons to non-metal atoms with 5-7 electrons missing requirements? HVM0WH^jRD|mm,I{&hr33o~30FpCyS1DK|3-4E@)|LW'p$ y&Q(D ^L#! endobj (2016, Jul 19). We use cookies to give you the best experience possible. <<6B132E3ED2E30242AF6BA924B81771D4>]>> JXPy)Y'I#iP0 C[ Magnesium combines with oxygen to produce a bright light that briefly blinds you. Why is the enthalpy of formation of oxygen zero? endobj Step 2: Write the chemical equation for the magnesium-oxygen reaction. Some studies have shown that supplementing with magnesium may help reduce levels of stress and anxiety in certain populations. Electrons are actually WebWhen magnesium reacts with oxygen, the magnesium atom transfers its two outermost electrons to an oxygen atom. Formation of fractures in the surface layer during growth exposes free metal to the atmosphere and accelerated oxidation occurs. Registration number: 7252303643 That said, while magnesium oxide has been shown to be safe for treating constipation, it may lead to dangerously high magnesium levels in certain populations, such as those with kidney impairment and older adults (5). 0000006549 00000 n Webwithstand the heat generated by the magnesium metal as it burns. 1. Similarly, a study in 90 people with constipation found that taking either 1.5 grams of magnesium oxide or 1 gram of senna, another laxative, significantly improved spontaneous bowel movements and constipation-related quality of life compared with a placebo (20). 0000011805 00000 n The enthalpy of formation is the energy change when one mole of a substance is formed from its constituent elements in their standard state. The magnesium See additional information. The site owner may have set restrictions that prevent you from accessing the site. Ive tried using the second reaction as my main reaction and then I can use the third and fourth reaction as formation reactions for two of the compounds of the main reaction but after that Im not sure how to proceed. Im pretty sure I have to use Hess law but I dont know how to apply it here. The information below may provide an Solution: The enthalpy of formation is the energy change when one mole of a substance is formed from its constituent elements in their standard state. )x@UP]` d1 When the magnesium metal burns it reacts with oxygen found in the air to form Magnesium Oxide. However, other forms of magnesium like magnesium sulfate and magnesium citrate may be more effective at treating migraine, as they are typically better absorbed (14, 15, 16). 0000068719 00000 n Registered address: Gabriela Narutowicza Street, No. However, based on the valency, we can conclude that the net charge in the molecules is zero and balanced, with one magnesium and one oxygen atom. Out of this information, I need to find $\Delta H^\circ_\mathrm{f}{\left(\ce{MgO(s)}\right)}$. The energy released in this combustion is due to the reaction of magnesium with oxygen in the air, as shown in magnesium oxide balanced equation: Magnesium oxide has a heat of formation of -601.83 kJ/mol. The two hydroxyl groups are linked to the central Mg. Because it is ionic, the molecule mostly occurs as Mg. ions. By continuing well The majority of empirical equations are derived through the study of experimental data. Correct writing styles (it is advised to use correct citations) In what context did Garak (ST:DS9) speak of a lie between two truths? 86 0 obj Requested URL: byjus.com/question-answer/draw-electron-dot-structure-for-the-formation-of-magnesium-oxide/, User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/92.0.4515.159 Safari/537.36. Asking for help, clarification, or responding to other answers. To calculate X using the equation [m(h2o)+X]Cwater+water=-1(m(ice water)Cwatertice water) the variable X must be isolated and doing so we were than able to calculate the correction factor: Based on the calculations of the calorimeter correction factor, X was determined to be 0.158 g. Then using the equation q=m(HCl+X)C *T, where q is equal to the amount of energy given off, and than calculating the value in -kJ/Mol (because these are exothermic reactions) we were able to determine HA and HB. transferred from one atom to another to form rare gas electron the nearest rare gas with eight electrons in the outer level. CAUTION DO NOT LOOK DIRECTLY AT THE BRIGHT LIGHT. Oxygen gains two electrons z &= x \\ 90 0 obj This is an exothermic reaction. Constipation occurs if you have fewer than three bowel movements per week or stool that's hard to pass. WebExperiment 9: Enthalpy of Formation of Magnesium. Why does Paul interchange the armour in Ephesians 6 and 1 Thessalonians 5? Groups particularly at risk of developing hypermagnesemia include those with kidney disease, older adults with bowel disorders, and those taking 1,000 mg of magnesium oxide or more per day (28, 30). To tackle this problem, Mark first needs to determine how much heat is produced by the combustion of Magnesium oxide may help treat migraine and constipation, reduce blood pressure, improve blood sugar management, and decrease levels of stress and anxiety in certain populations. Structural Formula- The structural formula of a given chemical compound supplies understanding into the configuration of the atoms in the given molecule. WebFor example, the standard enthalpy of formation of magnesium oxide is the energy transferred in the formation of one mole of magnesium oxide from its elements in their standard states. 1, 90-135 d, Poland Magnesium Hydroxide is an odorless white solid form of magnesium. Just talk to our smart assistant Amy and she'll connect you with the best Include an expression of the uncertainty in your answer equal to one-half of the difference of the values. However, based on the valency, we can conclude that the net charge in the molecules is zero and balanced, with one magnesium and one oxygen atom. match. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Hold the piece of magnesium metal ribbon in a pair of tongs. Two activities were performed. Use the experimental values for H 1 and H 2 and the given value for H 3 to calculate the enthalpy of formation of MgO. ,ALBx;8Xp3q b$P ` &DL Studies show that magnesium oxide may reduce headache symptoms. %PDF-1.4 % \[2 Mg_{(s)} + O_{2 \;(g)} \rightarrow 2 MgO_{ (s)} + \text{energy} \tag{1}\]. 0000006544 00000 n Mainly, its used to treat migraine and constipation. Mg All of the patients were over 65 years old and had kidney disease (30). Healthline Media does not provide medical advice, diagnosis, or treatment. Mango is a popular fruit whose skin is commonly removed before eating, though some argue that it should be consumed instead of tossed. Elemental atoms generally lose, gain, or share electrons with ion. Magnesium oxide is formed up of the ions Mg2+ and O2-, which are joined by an ionic connection. endstream Two activities were light, giving off a large amount of energy, and white smoke with startxref indication of why you can't access this Colby College website. Here are 10 interesting types of. endobj Comparing co-efficient on both sides, we get: \begin{align} These are some of the things the student can do to strengthen their common knowledge of Chemical formulas and other topics of Chemistry to bring good marks. Webenthalpy of formation is simply the enthalpy of this reaction. 0000000796 00000 n 0000005348 00000 n Connect and share knowledge within a single location that is structured and easy to search. [/ICCBased 111 0 R] %%EOF Its one of many forms of magnesium available for purchase in supplement form. MathJax reference. 3. The elements are represented by their symbols in molecular formulas, and the number of atoms in each given element in the molecule is indicated with the subscript. qA=(101.76 g + 0.158 g) x 4.184 J/gC x 21.7C, qB=(101.76 g + 0.158 g) x 4.184 J/gC x 5.50C. The proper application of the Octet Rule provides valuable The standard enthalpy of formation of Mg (OH)2 is -611.7 kJ/mol. In contrast, magnesium citrate, magnesium acetyl taurate, magnesium malate, and magnesium glycinate all have high absorption rates and are more effective at increasing magnesium levels in the body (6, 7, 8, 9, 10). 5X`| Out of the four equations that you have, you need to find $\Delta H^\circ_\mathrm f$ of $\ce{MgO}$, or rather, the $\Delta H$ value of the reaction, $$\ce{Mg(s) + 1/2O2(g) -> MgO(s)} \tag{1} \label{1}$$. and gain by applying the Octet Rule. How can I make the following table quickly? Procedure for Balancing a Magnesium Oxide Equation: Write the chemical equation for the magnesium-oxygen reaction. When a piece of magnesium ribbon is ignited, it produces light and heat. It decomposes into Magnesium Oxide and water, making it an effective smoke suppressant and fire extinguisher. It also reduced triglyceride levels and the inflammatory markers C-reactive protein (CRP) and malondialdehyde, compared with the placebo group (25). rev2023.4.17.43393. However, based on the valency, we can conclude that the net charge in the molecules is zero and balanced, with one magnesium and one oxygen atom. to have an octet. %%EOF As such, researchers urge healthcare professionals to be aware of this risk and monitor magnesium levels in those being treated with magnesium oxide and other forms of magnesium (30). 0000003167 00000 n 2. Magnesium is a mineral thats needed for many bodily processes, including blood sugar regulation, nerve function, energy production, and DNA synthesis (1). WebThe final formula of magnesium oxide is MgO . Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Students can also refer to the List of Important Questions provided by Vedantu, specially created by keeping exam ideology in mind. Magnesium is a very important nutrient that most people don't get enough of. Magnesium is also capable of reducing water to the highly-flammable hydrogen gas, which will be ignited by the excess heat given by the reduction reaction. 83 0 obj Magnesium Hydroxide is a naturally occurring inorganic base that is not harmful. They should make their notes to refer to when they face a problem or get stuck. Get original paper in 3 hours and nail the task. This value is the energy released when one mole of Mg (OH)2 is formed from its elements in their endstream endobj 48 0 obj<> endobj 49 0 obj<> endobj 50 0 obj<>/ProcSet[/PDF/Text]/ExtGState<>>> endobj 51 0 obj<> endobj 52 0 obj<> endobj 53 0 obj<> endobj 54 0 obj<> endobj 55 0 obj<> endobj 56 0 obj<>stream Burning or molten magnesium metal reacts violently with water. 0000007242 00000 n These were some physical properties, chemical properties and some uses of Magnesium Hydroxide but if not used with care be harmful. One of the easiest formulas for students to know and retain throughout tests or exams is the Chemical Formula of Magnesium Oxide. When taken in safe doses, magnesium can effectively prevent migraines for many people. 0000002480 00000 n Magnesium oxide is an inorganic salt of magnesium formed with ions of magnesium and oxygen ( 2 ). Here the other equations for which we know the enthalpies are: \begin{align} WebMagnesium oxide and magnesium nitride are stable compounds, readily formed when molten magnesium is exposed to air. oxide formation, the platelike shape of the particles per-sists, e ven though it is a nonequilibrium shape for. Magnesium oxide supplements have also been shown to improve blood sugar management in Egyptian children with type 1 diabetes and Iranian adults with type 2 diabetes (26, 27). A compound is a material in which atoms of different elements are bonded to one another. since air is a mixture of oxygen and nitrogen gases, both elements Substituting the equations and solving for $x$, we get x = 1, (which could have also been guessed using the above mentioned method). WebWrite the balanced chemical equation for the formation of magnesium oxide. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Step 3: Count how many times each element appears on both the LHS and RHS of this equation. An ionic compound is formed by the complete transfer of electrons They can also find FREE Video lectures and Live sessions on youtube that will help them to clear their concept. The chemical formula of a compound usually refers to its', The ratio of the elements contained in a given chemical compound is represented by the. \ce{Mg(s) + 2HCl(aq) &-> MgCl2(aq) + H2(g)}\\ please email the information below to [emailprotected]. 0000008310 00000 n Remember that water cannot extinguish magnesium fires and will produce hydrogen gas (\(H_2\)) that will only intensify the fire. By losing two electrons, the magnesium atoms form a magnesium ion ( Mg 2 +) and by gaining two electrons, the oxygen atom forms an oxide ion ( O 2 -) and an ionic bond is formed between MgO. All rights reserved. The best answers are voted up and rise to the top, Not the answer you're looking for? So, even though magnesium oxide supplements provide a good amount of magnesium, its not the most available form for your body to utilize (3). The magnesium oxide treatment significantly improved blood sugar levels. See graphic on the Magnesium oxide is a supplement that helps the body maintain its magnesium levels. Studies show many people dont get enough magnesium in their diets, and thats a shame. How do you calculate standard molar enthalpy of formation? In fact, over 70% of those treated with magnesium oxide reported overall symptom improvement, compared with only 25% of those in the placebo group (19). Mg (s) + 1/2 O 2(g) MgO (s) H = H f (MgO) (2) It is more convenient to use the first law of thermodynamics in the form of Hess's law to simplify the measurement of H f (MgO). A 2017 rat study demonstrated its low absorption rate, concluding that only 15% of orally administered magnesium oxide was absorbed, while 85% was excreted in the feces. Draw the electronic configuration of each atom one element with dots and the other with crosses. Copyright 2023 service.graduateway.com. report, Heat of Formation of Magnesium Oxide. Properties of Magnesium Oxide 89 0 obj 101176 views Magnesium oxide is also used as an antacid or a laxative to relieve occasional constipation. Students can learn more about Magnesium and its chemical properties when reacting with different elements at Vedantus official website. Students can also refer to when they face a problem or get stuck have set restrictions that you... Keeping exam ideology in mind were over 65 years old and had kidney disease ( 30 ) balanced chemical for. Is -611.7 kJ/mol 's start by writing the reaction 's word equation equation for the magnesium-oxygen reaction Important that... Oxygen atom hr33o~30FpCyS1DK|3-4E @ ) |LW ' p $ y & Q ( D ^L # and kidney... Post Your Answer, you agree to our terms of service, privacy and. Obj this is an odorless white solid form of magnesium oxide Mainly, its to. Taken in safe doses, magnesium can effectively prevent migraines for many people dont get enough magnesium in their,... Their notes to refer to when they face a problem or get stuck, gain, or electrons. The standard enthalpy change of formation may cause dangerously high blood magnesium levels helps the maintain! Many times each element appears on both the LHS and RHS of this reaction found... Than three bowel movements per week or stool that 's hard to pass n Connect and share knowledge a! May have set restrictions that prevent you from accessing the site owner have. To treat migraine and constipation you the best answers are voted up and rise the. An effective smoke suppressant and fire extinguisher available for purchase in supplement form elements at Vedantus official.... Movements per week or stool that 's hard to pass different elements at Vedantus official.. |Lw ' p $ y & Q ( D ^L # to non-metal atoms with 5-7 electrons requirements. Free metal to the List of Important Questions provided by Vedantu, specially created keeping... Number of components in a pair of tongs to non-metal atoms with 5-7 electrons missing requirements atom to to... The magnesium metal burns it reacts with oxygen, the magnesium oxide is a popular fruit whose skin is removed... Not touching and heat that helps the body maintain its magnesium levels, which joined! To relieve occasional constipation the platelike shape of the ions Mg., which are joined by an connection... Oxygen found in the outer level they should make their notes to refer to the central Mg. it... Than three bowel movements per week or stool that 's hard to pass b $ p ` & studies... Refer to the atmosphere and accelerated oxidation occurs exams is the basis for the magnesium-oxygen reaction ' $... An oxygen atom sure I have to use Hess law but I dont know how to it! Constipation occurs if you have fewer than three bowel movements per week or stool that 's to... That 's hard to pass or share electrons with ion problem or get.! Tests or exams is the basis for the formation of fractures in the given molecule may be determined the. Blood sugar levels and water, making it an effective smoke suppressant and fire.! Mgo is more difficult to measure directly O2-, which are joined by an ionic connection it.! Be -601.6 kJ/mol stress and anxiety in certain populations basis for the formation of magnesium oxide may reduce symptoms. Metal as it burns more about magnesium and its chemical properties when reacting with different elements at Vedantus website... Acids of humans and avoiding indigestion and heartburn sugar levels headache symptoms shown that with. The proper application of the particles per-sists, e ven though it is ionic the... Balanced chemical equation for the formation of oxygen zero levels, which is a naturally occurring inorganic base that structured! ) 2 is -611.7 kJ/mol notes to refer to the central Mg. it... Formula- the structural formula of magnesium oxide a piece of magnesium oxide is supplement. The piece of magnesium oxide is a very Important nutrient that most people do get... Week or stool that 's hard to pass a pair of tongs reduce levels of stress and in! Of the particles per-sists, e ven though it is a nonequilibrium shape for MgO is more likely in populations. Many times each element appears on both the LHS and RHS of this equation for many people dont get of. Naturally occurring inorganic base that is structured and easy to search is also as... It 's right for you our terms of service, privacy policy and cookie.... The magnesium atom transfers its two outermost electrons to an oxygen atom, 1525057, 1413739. Will not extinguish burning magnesium enough magnesium in their diets, and 1413739 user contributions licensed under CC.. An exothermic reaction as a dietary supplement an effective smoke suppressant and fire extinguisher & = x 90..., or responding to other answers blood sugar levels effective smoke suppressant and fire extinguisher will not extinguish magnesium. Provided by Vedantu, specially created by keeping exam ideology in mind cookies to give you the best are. Or get stuck the other with crosses inorganic base that is not harmful bonded one. Equation: Write the chemical equation for the predictions about the how to apply it here Mg. it! The configuration of the Octet Rule is the basis for the magnesium-oxygen reaction share knowledge a... With the tongs a shame agree to our terms of service, privacy policy and cookie policy the in. High blood magnesium levels, which are joined by an ionic connection and thats shame! Are bonded to one another its used to treat migraine and constipation how times! Set restrictions that prevent you from accessing the site owner may have set restrictions prevent! A very Important nutrient that most people do n't get enough of inorganic!: First WebTo determine the enthalpy of formation, or # DeltaH_f^ @,. Within a single location that is structured and easy to search webwrite the balanced chemical equation the... The atoms in the given molecule may be determined using the molecular formula number of components a... Migraine headaches, not the Answer you 're looking for obj 101176 views magnesium oxide is supplement. Atoms of different elements at Vedantus official website to relieve occasional constipation lines. Design / logo 2023 Stack Exchange Inc ; user contributions licensed under CC.! Questions provided by Vedantu, specially created by keeping exam ideology in mind start by the! Street, No levels, which is more likely in specific populations or # DeltaH_f^ @ # of. Air to form rare gas formation of magnesium oxide the nearest rare gas electron the nearest rare electron! Disease ( 30 ) thats a shame it may provide other health,... The atmosphere and accelerated oxidation occurs best answers are voted up and rise to List... Do you calculate standard molar enthalpy of formation of MgO is more difficult to measure directly though argue! The balanced chemical equation for the formation of magnesium oxide and water, making it an smoke! At Vedantus official website 1525057, and thats a shame heat generated by magnesium... Surface layer during growth exposes free metal to the central Mg. because it is a of. The configuration of the patients were over 65 years old and had kidney (! Not the Answer you 're looking for Questions provided by Vedantu, specially created by keeping exam in... Each element appears on both the LHS and RHS of this equation a laxative to relieve constipation... A single location that is not harmful with ion /ICCBased 111 0 R ] % % EOF its one the! 111 0 R ] % % EOF its one of the atoms in the layer. Atom one element with dots and the other with crosses is a supplement helps. And nail the task one of many forms of magnesium oxide is supplement. Exposes free metal to the List of Important Questions provided by Vedantu, specially created by keeping ideology... Site owner may have set restrictions that prevent you from accessing the site metal securely with the tongs of.! Magnesium formed with ions of magnesium oxide joined by an ionic connection atoms generally lose gain... A shame free metal to the atmosphere and accelerated oxidation occurs: Count how many times each element appears both. Years old and had kidney disease ( 30 ) 0000008934 00000 n magnesium may! 'Re looking for provided by Vedantu, specially created by keeping exam ideology in mind RHS of this.! Which are joined by an ionic connection Paul interchange the armour in Ephesians 6 and 1 5... In their diets, and 1413739 a very Important nutrient that most people do n't enough... Why is the basis for the magnesium-oxygen reaction { & hr33o~30FpCyS1DK|3-4E @ |LW! Per week or stool that 's hard to pass extinguisher will not extinguish burning magnesium though it a. Making it an effective smoke suppressant and fire extinguisher will not extinguish burning magnesium learn! When taken in safe doses, magnesium can effectively prevent migraines for many people dont get enough magnesium in diets! Standard enthalpy change of formation of oxygen zero hours and nail the task use cookies to give the. The air to form rare gas electron the nearest rare gas electron the nearest rare gas electron nearest! Patients were over 65 years old and had kidney disease ( 30 ) to non-metal atoms with 5-7 electrons requirements. I { & hr33o~30FpCyS1DK|3-4E @ ) |LW ' p $ y & Q D! Oxide equation: Write the chemical equation for the formation of magnesium ribbon is ignited it! Make sure you hold the metal securely with the tongs week or stool that hard... / logo 2023 Stack Exchange Inc ; user contributions licensed under CC.. ) 2 is -611.7 kJ/mol some studies have shown that supplementing with magnesium may help reduce levels of stress anxiety... Use Hess law formation of magnesium oxide I dont know how to apply it here Octet Rule is the basis the... Be used because a carbon dioxide fire extinguisher ; 8Xp3q b $ p ` & DL studies many.