So4 2- lewis structure - The Lewis structure of C2, the chemical formula for diatomic carbon, is written with two Cs connected by two straight lines. Each C also contains one pair of dots, for a total of t...

 
Science. Chemistry. Chemistry questions and answers. lewis structure for SO4 2- ion?. Gordon food near me

For sulfuric acid, computational analysis (with natural bond orbitals) confirms a clear positive charge on sulfur (theoretically +2.45) and a low 3d occupancy. Therefore, the representation with four single bonds is the optimal Lewis structure rather than the one with two double bonds (thus the Lewis model, not the Pauling model). Q. )) View Solution. Click here:point_up_2:to get an answer to your question :writing_hand:according to lewis structure the number of lone pair bond pair of electrons in 5628cf 1.As seen from the above examples, The charge of SO 4 is 2-. In this way, you can easily find the charge of SO4 by looking at what it is bonded to. Method 2: By calculating the formal charge using lewis structure. In order to calculate the formal charge on SO4 (Sulfate ion), you should know the Lewis dot structure of SO4 (Sulfate ion).The Lewis structure of the methane (CH4) molecule is drawn with four single shared covalent bonds between the carbon and hydrogen atoms each. Moreover, as there exist sigma bonds only and one 2s and three 2p orbitals of the carbon produce four new hybrid orbitals, the hybridization of CH4 is sp3. It is interesting to realize that irrespective ...See full list on geometryofmolecules.com Lewis Dot of the Sulfate Ion. SO 42-. Back. 70 More Lewis Dot Structures. S does not follow the octet rule. It will hold more than 8 electrons. Sulfur having valence electrons in …Step 1. To depict the Lewis structure for ₄ ² ⁻ SO ₄ ² ⁻ , we need to determine the total number of valence electrons for sulfur and oxygen ... View the full answer Step 2. Unlock. Answer. Unlock.The first subtitle focuses on explaining the fundamental concepts behind the Lewis structure of the sulfate ion (SO4 2-) in the context of Mathematics education. It aims to provide a clear understanding of how to represent the molecule using Lewis dot diagrams. Lewis structure for SO4 (2+) This was a question on a review sheet for Lewis structures. Now I could draw SOX4X2− S O X 4 X 2 − with no issues, but I can't make …When it comes to decorating your home, lighting is one of the most important elements. A table lamp can be a great way to add a touch of style and personality to any room. At John ...The Lewis Dot Structure for SO 4 2-: The sulfate anion (SO 4 2-) results from the complete ionization of sulfuric acid (H 2 SO 4 ). The representation of the valence electron distribution is properly shown by drawing the Lewis structure.Sulfate is a very weak oxidizing agent. Since sulfur is in its maximum oxidation number in sulfate ion, this ion cannot act as a reducing agent. This page titled Sulfate Ion (SO₄²⁻) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by James P. Birk. Sulfate ion is a very weak base.Long Lewis Ford has been serving the city of Hoover, Alabama for years, providing car shoppers with top-notch vehicles and exceptional customer service. If you’re in the market for...Shopping online can be a great way to save time and money, but it can also be a bit daunting if you’ve never done it before. John Lewis is one of the most popular online retailers ...How to draw the Lewis Structure for SO4 2- (sulfate ion)||Lewis structure of so4 2- negative ion step by stepSulfur is an exception to the octet rule due t...Lewis Structures. A Lewis Structure is a representation of covalent molecules (or polyatomic ions) where all the valence electrons are shown distributed about the bonded atoms as either shared electron pairs (bond pairs) or unshared electron pairs (lone pairs). A shared pair of electrons is represented as a short line (a single bond).Jul 2, 2020 · This chemistry video tutorial explains how to draw the lewis structure of the nitrate ion NO3-.How To Draw Lewis Structures: https://www.youtube.... May 19, 2021 · How to draw the Lewis Structure for SO4 2- (sulfate ion)||Lewis structure of so4 2- negative ion step by stepSulfur is an exception to the octet rule due t... The atoms are placed at a 109.5° angle. In order to understand the structure, students can learn to draw the Lewis structure of sulfate and also know about the formal charges and the total number of valence electrons needed for sulfate. Properties of Sulphate. We will discuss some of the physical and chemical properties of sulphate ions below.What is the Lewis structure of [//substance:SO4^2-//]? Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, …Lewis Structure for SO4 2- (Sulfate Ion) Lewis Structure for SO 42- (Sulfate Ion) We draw Lewis Structures to predict: -the shape of a molecule. -the reactivity of a molecule and …Connect each atom to the central atom with a single bond (one electron pair). Subtract the number of bonding electrons from the total. Distribute the remaining electrons as lone pairs on the terminal atoms (except hydrogen), completing an octet around each atom. Place all remaining electrons on the central atom.Question: 1. For SO42 -, sulfate ion, draw the Lewis structure (by counting valence electrons of each atom), determine the a) electron-domain geometry b) molecular geometry c) hybridization d) 1. For SO 42 -, sulfate ion, draw the Lewis structure (by counting valence electrons of each atom), determine the. d) show the angle between the bonds in ...If you’re in the market for a new table lamp, John Lewis is a brand that you can trust. Known for their high-quality and stylish home furnishings, John Lewis offers a wide selectio...6 Steps to Draw the Lewis Structure of CO3 2-Step #1: Calculate the total number of valence electrons. Here, the given ion is CO3 2- ion. In order to draw the lewis structure of CO3 2- ion, first of all you have to find the total number of valence electrons present in the CO3 2- ion. (Valence electrons are the number of electrons present in the …Draw the best lewis structure for the sulfate ion ( SO4^2-) that has the least possible formal charge. Here’s the best way to solve it. Oct 11, 2023 · The Lewis structure of a sulfate [SO4]2- ion consists of 1 sulfur (S) atom and 4 atoms of oxygen (O). The sulfur atom is present at the center of the Lewis structure while the oxygen atoms occupy terminal positions. There are a total of 4 electron density regions around the central S atom in the Lewis structure of [SO4]2-. Let's do the SO4 2- Lewis structure, for the sulfate ion. On the periodic table: Sulfur, 6 valence electrons; Oxygen also has 6, we have 4 Oxygens, multiply by 4; and these 2 …A step-by-step explanation of how to draw the Sulfate Ion Lewis Dot Structure (SO42- ). We'll also look at the molecular geometry, bond angles, electron geo... Chemistry. Chemistry questions and answers. What is the lewis structure for SO42- and the formal charge?HSO4- same queston?SO3 same question?BrO2- same question?Jan 6, 2021 · Lewis Structure for sulphate includes an expanded octet for the central sulphur atom.0:00 Lewis structure2:10 Shape and angles3:13 Dipoles5:16 Formal charges... Step #1: Calculate the total number of valence electrons. Here, the given molecule is SO (Sulfur monoxide). In order to draw the lewis structure of SO, first of all you have to find the total number of valence electrons present in the SO molecule. (Valence electrons are the number of electrons present in the outermost shell of an atom).Molecules formed from these elements are sometimes called hypervalent molecules. Figure 4.1.4 4.1. 4: shows the Lewis structures for two hypervalent molecules, PCl 5 and SF 6. Figure 4.1.4 4.1. 4: In PCl 5, the central atom phosphorus shares five pairs of electrons. In SF 6, sulfur shares six pairs of electrons.If you’re in the market for a new or used car in Hays, KS, chances are you’ve come across Lewis Ford Toyota. With a reputation for quality vehicles and exceptional customer service...Re: Lewis Structure of SO4^2- and Formal Charge. We are supposed to calculate formal charge when drawing every Lewis structure and try to minimize it as much as possible. I don't think you have to draw multiple resonance structures unless the question specifically asks for them.A: Solution- Lewis structure of SbO4-2 ; Q: Write the Lewis structure for each molecule. SiH4. A: Concept introduction: Lewis structure is used to represents the covalent molecule structure with the…. Q: Write the Lewis structure for each molecule. HCOOH (both O bonded to C) Q: In the hypervalent ion ICl3-, the central iodine atom forms ...Oct 1, 2020 ... Estructuras de Lewis sulfato [SO4]2- y fosfato [PO4]3- | EXPANSIÓN DEL OCTETO. 8.4K views · 3 years ago ...more ...Dec 1, 2011 · Lewis structures SO4^2- and PO4^3-. Postby Chem_Mod » Thu Dec 01, 2011 11:31 pm. I was wondering why the compound SO4^2- has three Lewis structures whereas PO4^3- has only two. In the book, one of the structures for SO4^2- has 12 electrons attached to the central S-atom. For the Lewis structures for PO4^3-, the most that the P-atom holds is ... Science. Chemistry. Chemistry questions and answers. lewis structure for SO4 2- ion?A) Draw the Lewis dot structure for SO4-2 ion. B) What is the formal charge on each atom? C) What is the overall formal charge on each Oxygen atom? A) Draw a single bond, a double bond and a triple bond between two carbon atoms. B) What is the hybridization of each carbon atom? C) How does the bond length of each bond compare to the others? PH3 e. SO4 2-. Draw the Lewis structure (dot diagram) for each of the following molecules and predict the electron pair geometry and the molecular shape. a. BF3 b. CCl4 c. NO3¯ d. PH3 e. SO4 2-. Here’s the best way to solve it.The Lewis structure for sulfate is dependent on the formal charge of sulfur. Sulfates molecular formula is SO42-. Two double bonds and two single bonds are used to link oxygen to the sulfur atom.What is usually the first step when drawing a Lewis dot structure? Q. Draw the Lewis structure for CO2− 3. Q. Draw the Lewis dot structure of SN F 3 , consistent with V SEP R . Q. Draw the Lewis dot structure of the following. CO2− 3, HClO4, HN O3. Q. Draw lewis structures for the following molecules HCOOH.CO2− 2.Sulfate is a very weak oxidizing agent. Since sulfur is in its maximum oxidation number in sulfate ion, this ion cannot act as a reducing agent. This page titled Sulfate Ion (SO₄²⁻) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by James P. Birk. Sulfate ion is a very weak base.Simple S N 2 reaction; S N 1 and S N 2; Substrate structure controls substitution mechanism S N 1 or S N 2; Stability and structure of carbocations; S N 2 examples; S N 2 Reaction: Allyl Chloride with HS – S N 2 Reaction: Benzyl Chloride with HS – S N 2 Reaction: 2 o Benzyl Chloride with HS – S N 2' Mechanism; Mitsunobu Reaction ... Jul 19, 2020 ... 376K views · 6:26 · Go to channel · Lewis Structure of SO4(2-) (Sulfate) CORRECT. chemistNATE•618K views · 28:30 · Go to channel...When it comes to decorating your home, lighting is one of the most important elements. A table lamp can be a great way to add a touch of style and personality to any room. At John ...John Lewis is one of the UK’s leading retailers, offering a wide range of products from fashion to home furnishings. With so many products available, it can be difficult to find th...The SO4 2- (Sulfate Ion), comprised of one sulfur atom and four oxygen atoms, presents a captivating example of a chemical species with intriguing properties. At the heart of comprehending the characteristics and reactivity of SO4 2- …6 Steps to Draw the Lewis Structure of CO3 2-Step #1: Calculate the total number of valence electrons. Here, the given ion is CO3 2- ion. In order to draw the lewis structure of CO3 2- ion, first of all you have to find the total number of valence electrons present in the CO3 2- ion. (Valence electrons are the number of electrons present in the …Science Chemistry What is the Lewis structure of SO4-2 and OH-? What is the Lewis structure of SO4-2 and OH-? BUY. Introductory Chemistry: A Foundation. 9th Edition. ISBN: 9781337399425. Author: Steven S. Zumdahl, Donald J. DeCoste. Publisher: Cengage Learning. expand_lessThe formal charge on sulfur in SO 4 2- is where the Lewis structure of the ion is: +2 + 4 -4 0 -2 For resonance forms of a molecule or ion, one always corresponds to the observed structure the observed structure is an average of the resonance forms there cannot be more than two resonance structures for a given species the same atoms need not be.The SO4 2- (Sulfate Ion), comprised of one sulfur atom and four oxygen atoms, presents a captivating example of a chemical species with intriguing properties. At the heart of comprehending the characteristics and reactivity of SO4 2- lies the exploration of its Lewis structure. Through a combination of explanations, visual aids, and frequently asked questions, The SO4 2- (Sulfate Ion), comprised of one sulfur atom and four oxygen atoms, presents a captivating example of a chemical species with intriguing properties. At the heart of comprehending the characteristics and reactivity of SO4 2- lies the exploration of its Lewis structure. It’s the quintessential human emotion, says New Brunswick, N.J., psychologist Michael Lewis, Ph.D., in his w It’s the quintessential human emotion, says New Brunswick, N.J., psycho...6 Steps to Draw the Lewis Structure of CO3 2-Step #1: Calculate the total number of valence electrons. Here, the given ion is CO3 2- ion. In order to draw the lewis structure of CO3 2- ion, first of all you have to find the total number of valence electrons present in the CO3 2- ion. (Valence electrons are the number of electrons present in the …PO4 3- structure showing Phosphorous at central position. C. Placing the Remaining Atoms. After identifying the central atom, we need to place the remaining atoms around it. In the case of PO4 3-, we have 4 oxygen atoms.Since oxygen needs 2 electrons to complete its octet, we can form a single bond between each oxygen atom and the …A Lewis structure for sulfate (SO 2 2) is shown below, however, its formal charges are not minimized. Starting from this structure, complete the correct structure with minimized formal charges. Starting from this structure, complete the correct structure with minimized formal charges.Oct 29, 2015 · SO4 2-. Sulfate ion has two ways of drawing its lewis structure. One is to follow the octet rule and having single bond for each oxygen each perfectly satisfies the octet rule. However, since sulfate can hold more than 8 electrons, it is better to draw the lewis structure with 2 double bond oxygens and 2 single bond oxygens around the sulfur ... Jan 25, 2016 · (O=)_2S(-O^-)_2 There are 5xx6+2 = 32 electrons to distribute over 5 centres (why? because all of the atoms are from Group VI, and thus each has 6 valence electrons, + 2 electrons for the negative charges). Of course this is a resonance structure, in that ALL the sulfur oxygen bonds are equivalent. If we keep (arbitrarily) to the given resonance structure, around each doubly bound oxygen there ... Nov 19, 2023 · The Lewis structure for SO4 2- is a central sulfur atom bonded to four oxygen atoms. The sulfur atom has 6 valence electrons, and each oxygen atom has 6 valence electrons. The sulfur atom also has an additional two electrons in its outermost shell, giving it a total of 6+2=8 valence electrons. The oxygen atoms each have a lone pair of electrons ... For sulfuric acid, computational analysis (with natural bond orbitals) confirms a clear positive charge on sulfur (theoretically +2.45) and a low 3d occupancy. Therefore, the representation with four single bonds is the optimal Lewis structure rather than the one with two double bonds (thus the Lewis model, not the Pauling model). Step-by-Step Guide to Drawing the SO3 2- Lewis Structure. 1. Count Valence Electrons. Begin by determining the total number of valence electrons in the SO3 2- ion. In this molecule, there is one sulfur (S) atom and three oxygen (O) atoms, along with the two additional electrons due to the -2 charge. Oxygen has six valence electrons, while ...Jan 6, 2021 · Lewis Structure for sulphate includes an expanded octet for the central sulphur atom.0:00 Lewis structure2:10 Shape and angles3:13 Dipoles5:16 Formal charges... Connect each atom to the central atom with a single bond (one electron pair). Subtract the number of bonding electrons from the total. Distribute the remaining electrons as lone pairs on the terminal atoms (except hydrogen), completing an octet around each atom. Place all remaining electrons on the central atom. John Lewis is one of the UK’s leading retailers, offering a wide range of products from fashion to home furnishings. With so many products available, it can be difficult to find th...Sep 4, 2022 · How to Draw a Lewis Structure. Step 1: Find the Total Number of Valence Electrons. …. Step 2: Find the Number of Electrons Needed to Make the Atoms “Happy” …. Step 3: Determine the Number of Bonds in the Molecule. …. Step 4: Choose a Central Atom. …. Step 5: Draw a Skeletal Structure. …. Step 6: Place Electrons Around Outside Atoms. Lewis Dot Structure of SO4 2- (Sulfate Ion) kentchemistry.com 25K subscribers Subscribe Subscribed 363 Share 196K views 12 years ago Every Video I quickly take you through …Draw the best lewis structure for the sulfate ion ( SO4^2-) that has the least possible formal charge. Here’s the best way to solve it. Learn the steps of drawing the lewis structure of SO4 2- ion, a sulfate ion with a sulfur atom and four oxygen atoms. Find out the valence electrons, the central …The SO4 2- (Sulfate Ion), comprised of one sulfur atom and four oxygen atoms, presents a captivating example of a chemical species with intriguing properties. At the heart of comprehending the characteristics and reactivity of SO4 2- …The sulphate ion is mainly composed of sulphur and oxygen atoms. Here, sulphur is the central atom, and it is surrounded by four oxygen atoms that are located at equal distances in the plane. For the bonding, 2 of the oxygen atoms form S=O bonds and the other two form S-O- bonds. The oxygen atoms are responsible for the negative charge (-2) of ... A step-by-step explanation of how to draw the HSO4- Lewis Dot Structure (Bisulfate ion or Hydrogen sulfate ion).When we have an H (or H2) in front of a polya... If you’re a history buff or just love exploring the great outdoors, a Lewis and Clark river cruise should definitely be on your bucket list. A river cruise is an excellent way to e...Solution for Lewis structure of SO4^2-Quantum Mechanical Treatment of the Valence Bond Theory. Quantum mechanical treatment of valence bond theory refers to the relationship established between the quantum mechanical theory and the valence bond theory to describe the chemical bonding in a particular molecule.(a) C O C l 2 (b) P O F 3 (c) H 2 O (d) A s ; Draw the Lewis structures for each of the following ions or molecules. For each, give (i) the molecular shape, (ii) the electron pair geometry at the central atom, and (iii) the hybridization of the central atom. (a) C O C l 2 (b) P O F 3 (c) H 2 O ; Draw the Lewis structure for BCl3.Draw the Lewis structures for the following molecules and ions: H2S, SiCl4, BeF2, CO3^2-, HCOOH. asked Jan 24, 2020 in Chemistry by Nishu03 ( 64.8k points) chemical bondingChemistry learning made easy.This tutorial will help you deal with the lewis structure and moleculargeometry of sulfate ion (SO4 2-)Sulphur cannot form more than four traditional 2-electron-2-centre bonds (double bonds counting as two bonds, triple bonds as three bonds) due to a lack of available orbitals. On a very basic, general and simplified level, such a (localised) 2e2c bond is formed when an orbital of each atom overlap, resulting in a bonding and an antibonding orbital.PO4 3- structure showing Phosphorous at central position. C. Placing the Remaining Atoms. After identifying the central atom, we need to place the remaining atoms around it. In the case of PO4 3-, we have 4 oxygen atoms.Since oxygen needs 2 electrons to complete its octet, we can form a single bond between each oxygen atom and the …Lewis Structure Examples. The Lewis electron dot structures of a few molecules are illustrated in this subsection. 1. Lewis Structure of CO2. The central atom of this molecule is carbon. Oxygen contains 6 valence electrons which form 2 lone pairs. Since it is bonded to only one carbon atom, it must form a double bond.Following steps are required to draw NO 3- lewis structure and they are explained in detail in this tutorial. Find total number of electrons of the valance shells of nitrogen and oxygen atoms and including charge of the …The 'octet' rule is based upon available n s and n p orbitals for valence electrons (2 electrons in the s orbitals, and 6 in the p orbitals). Beginning with the n=3 principle quantum number, the d orbitals become available ( l =2). The orbital diagram for the valence shell of phosphorous is: Hence, the third period elements occasionally …Downloads expand_more. Download Page (PDF) Download Full Book (PDF) Resources expand_more. Periodic Table. Physics Constants. Scientific Calculator. Reference expand_more. Reference & Cite.You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Choose the best Lewis structure for SO_4^2. Only one resonance structure is shown (formal charges not shown). Which of the following elements can form expanded octet compounds? The Lewis dot structure for Cl2, the chemical formula for chlorine gas, is written with two Cl symbols, each of which is surrounded by three pairs of dots, connected by a single li...SO4-2 PO4-3 For each of the. For each of the following examples draw the charge minimized Lewis dot structure, assign the formal charge to each atom in the structure and then determine the overall charge on the oxygen. SO4-2. PO4-3. For each of the following examples show all possible resonance structure that structure that contribute to the ...For the HSO4- Lewis structure, we have a total of 32 valence electrons. That includes this one up here. We'll put a pair of electrons between atoms to form chemical bonds--we've used 8 and 10. Then we'll go around and fill the octets for the Oxygen; 12, 14, and 32. So we've used all 32 valence electrons. Sulfur has 8 valence electrons, each of ...

Draw the electron dot structure for: propanone. (d) Draw the electron dot structure for: F 2. View Solution. Q 3. Assertion :Structure of SO2− 4 is identical to S2O2− 3. Reason: Sulphur atoms in S2O2− 3 are in different oxidation states.. Ugly monkey

so4 2- lewis structure

Re: Lewis Structure of SO4^2- and Formal Charge. We are supposed to calculate formal charge when drawing every Lewis structure and try to minimize it as much as possible. I don't think you have to draw multiple resonance structures unless the question specifically asks for them.Which of the following statement are correct about C O − 2 3? (a) The hybridisation of central atom is s p 3 (b) Its resonance structure has one C - O single bond and two C = 0 double bonds (c) The average formal charge on each oxygen atom is 0.67 units (d) All C - O bond lengths are equalJun 22, 2023 · This overall -2 charge on the SO4 molecule is represented in the image given below. In the above lewis dot structure of SO4 2- ion, you can also represent each bonding electron pair (:) as a single bond (|). By doing so, you will get the following lewis structure of SO4 2- ion. I hope you have completely understood all the above steps. Re: Lewis Structure of SO4^2- and Formal Charge. We are supposed to calculate formal charge when drawing every Lewis structure and try to minimize it as much as possible. I don't think you have to draw multiple resonance structures unless the question specifically asks for them.What is usually the first step when drawing a Lewis dot structure? Q. Draw the Lewis structure for CO2− 3. Q. Draw the Lewis dot structure of SN F 3 , consistent with V SEP R . Q. Draw the Lewis dot structure of the following. CO2− 3, HClO4, HN O3. Q. Draw lewis structures for the following molecules HCOOH.CO2− 2.A step-by-step explanation of how to draw the HSO4- Lewis Dot Structure (Bisulfate ion or Hydrogen sulfate ion).When we have an H (or H2) in front of a polya... If you’re in the market for new curtains, there’s no better time to shop than during a John Lewis curtains sale. Known for their high-quality and stylish home decor, John Lewis off...Step 1: Figure out how many electrons the molecule must have, based on the number of valence electrons in each atom. When drawing the structure of an ion, be sure to add/subtract electrons to account for the charge. Step 2: Connect the atoms to each other with single bonds to form a “skeleton structure.”.Sep 23, 2020 ... QUIMICA Estructura de Lewis Sulfato SO4(-2) Expansión Octeto Resonancia AULAEXPRESS. 22K views · 3 years ago ...more ...The Lewis structure of SO3 2- represents the arrangement of atoms and valence electrons in the sulfite ion. It shows one sulfur (S) atom bonded to three oxygen (O) atoms, with an overall -2 charge on the ion. The Lewis structure illustrates the distribution of electrons, including lone pairs and bonding pairs. 2.N2O, or nitrous oxide, has many Lewis dot structures since both nitrogen and oxygen can act as the center atom. In total, there are three valid Lewis dot structures for nitrous oxi...In questo video vi spiego come fare la struttura di Lewis dello ione solfato.Se ti stai preparando per superare il TEST, vai a vedere i corsi che organizzo d...Learn how to draw the Lewis structure of SO4 2-, the sulfate ion, using the octet rule and the lone pair rule. Find out the valence electrons, the central atom, the bonding and lone …Lewis Structure. The formal charge of an atom in a Lewis structure is a way to determine the distribution of electrons and the stability of the molecule. To calculate the formal charge, we use the formula:. Formal Charge = Valence Electrons – Lone Pairs – 1/2 * Bonded Electrons. In the SO3 Lewis structure, the formal charge of the sulfur …Question: Below are Lewis structures for the SO42− ion including resonance structures with expanded the octet on the central atom. Which of them is the least plausible Lewis structure? There are 2 steps to solve this one.Science. Chemistry. Chemistry questions and answers. lewis structure for SO4 2- ion?.

Popular Topics