aluminum and oxygen ionic compound formulacelebrities who live in east london

Express your answer as a chemical formula. Express your answer as a chemical formula. Chlorine does not exist as a diatomic element in this compound. 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. Each of the following pairs of elements will react to form a binary ionic compound. Ions can be either monatomic (containing only one atom) or polyatomic (containing more than one atom). When electrons are transferred and ions form, ionic bonds result. Download for free at http://cnx.org/contents/85abf193-2bda7ac8df6@9.110). What is the chemical formula for rubidium oxide? Thank you for being Super. Al2O With Super, get unlimited access to this resource and over 100,000 other Super resources. We can often identify molecular compounds on the basis of their physical properties. Thus, a magnesium atom will form a cation with two fewer electrons than protons and a charge of 2+. Unfortunately, much like the common system for naming transition metals, these suffixes only indicate the relative number of oxygens that are contained within the polyatomic ions. The remaining polyatomic anions, which all contain oxygen, in combination with another non-metal, exist as part of a series in which the number of oxygens within the polyatomic unit can vary. Direct link to kacey's post At 2:37, this is confusin, Posted 6 years ago. Two examples are shown below: There are two ways to recognize ionic compounds. Example \(\PageIndex{3}\): Predicting the Formula of an Ionic Compound. Analytical cookies are used to understand how visitors interact with the website. 5 When does oxygen and aluminum form an ionic compound? Compounds that do not contain ions, but instead consist of atoms bonded tightly together in molecules (uncharged groups of atoms that behave as a single unit), are called covalent compounds. Example \(\PageIndex{2}\): Formation of Ions. WebA binary ionic compound is composed of ions of two different elements - one of which is a metal, and the other a nonmetal. The first one is done as an example 1. The similarity may be more than mere coincidence; many scientists think that the first forms of life on Earth arose in the oceans. This is the aluminum cation, Al3+. Chlorine will form an anion with a charge of 1: Cl, a chloride ion. Write a formula for each of the following molecular compounds. Now, let's look at the bromide part. Parentheses are generally only used for complex ions. for an ionic compound, these things are going The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. K and lower bending strength of 358MPa. Sn(SO4)2. Many compounds do not contain ions but instead consist solely of discrete, neutral molecules. Some of these compounds, where they are found, and what they are used for are listed in Table. Web( a ) Oxygen is in group VI (16), and so the charge is 6 - 8 = - 2 ( b ) Nitrogen is in group V (IS), and so the charge is 5 - 8 = -3. The chemical formula of water is H 2 O which shows two atoms of hydrogen and one atom of oxygen have combined to form one molecule of H 2 O. Ionic Compound Formula Writing Worksheet Write chemical Spell out the full name of the compound. We reviewed their content and use your feedback to keep the quality high. WebAl^ {3+} Al3+. Hydrogen (group IA) is a nonmetal, and oxygen (group VIA) is a nonmetal; H, Carbon (group IVA) is a nonmetal, hydrogen (group IA) is a nonmetal, and chlorine (group VIIA) is a nonmetal; CHCl, Lithium (group IA) is a metal, and carbonate is a polyatomic ion; Li. so care must be taken to get the formulas and names correct. For example, when each sodium atom in a sample of sodium metal (group 1) gives up one electron to form a sodium cation, Na+, and each chlorine atom in a sample of chlorine gas (group 17) accepts one electron to form a chloride anion, Cl, the resulting compound, NaCl, is composed of sodium ions and chloride ions in the ratio of one Na+ ion for each Cl ion. Positively charged ions are called cations, and negatively charged ions are called anions. Predict which forms an anion, which forms a cation, and the charges of each ion. 1) Aluminium and oxygen In this Aluminium is a metal having +3 oxidation state and oxygen is a non metal having -2 oxidation state. with the bromide anion. (or 16 - 18 = - 2). Oxyanions Oxyanions consist of an atom of an element plus some number of atoms of oxygen covalently bonded to it. The formula reflects the smallest whole-number ratio of ions. Many ionic compounds contain polyatomic ions (Table \(\PageIndex{1}\)) as the cation, the anion, or both. A polyatomic ion is a particle made of more than 12. Scuba Certification; Private Scuba Lessons; Scuba Refresher for Certified Divers; Try Scuba Diving; Enriched Air Diver (Nitrox) disulfur tetrafluoride What are the basic units-single atoms, molecules, or formula units-that compose each of the following substances? (b) A sodium cation (Na+) has lost an electron, so it has one more proton (11) than electrons (10), giving it an overall positive charge, signified by a superscripted plus sign. losing two electrons and that's because they have two electrons in their outermost shell and A magnesium ion has a 2+ charge, while a chlorine ion has a 1 charge: Combining one ion of each does not completely balance the positive and negative charges. K+. Express your answer as a chemical formula. 3.5: Ionic Compounds- Formulas and Names is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts. Usually how it works is that iron (Fe) will be paired with an anion which has a constant negative charge. Therefore, \(\ce{PCl3}\) is not ionic. Zeolites mainly consist of the elements such as silicon, aluminum, and oxygen. For example, group VIIA elements (one group left of the noble gases) form 1 ions; group VIA elements (two groups left) form 2 ions, and so on. We will need two potassium ions to balance the charge on the sulfate ion, so the proper chemical formula is \(\ce{K_2SO_4}\). Fe+2. Write a formula for each of the following molecular compounds. every one of the calciums, you're going to have two bromides. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. C. The element with atomic number 20 is calcium and theelement with atomic Choose the formula subscripts such that the total charge for. WebQuestion: Determine the chemical formula for the ionic compound that forms between lithium and bromine. Ionic compounds exist as alternating positive and negative ions in regular, three-dimensional arrays called crystals (Figure \(\PageIndex{1}\)). N4Se4 The oxygen atom has a 2 charge as an ion. CaCl 3. Therefore, "-ate" and "-ite" suffixes are employed, in order to denote that the corresponding polyatomic ions are part of a series. So, our bromide anion is aluminum and sulfur Al +3 O -2 Al 2 O 3 The formula is A l 2 O 3 Step 3: Compounds formed between Q20 and R53 C. corresponding to 2 X (3+) for aluminum plus 3 X (2-1 for oxygen, a total of 0. Predict which forms an anion, which forms a cation, and the charges of each ion. Direct link to Matt Broadley's post What is the rule for an i, Posted 6 years ago. Aluminium Sulphate Al2(SO4)3 Aluminium sulphate is an ionic compound. 0. 0 plays. In every ionic compound, the total number of positive charges of the cations equals the total number of negative charges of the anions. The formula of an ionic compound must have a ratio of ions such that the numbers of positive and negative charges are equal. Determine whether the metal in the ionic compound SnO forms only one type of ion or more than one type of ion and name the compound accordingly. How can these two ions combine to form a neutral compound? in this group like to do. The subscripts in the formula must produce an electrically neutral formula unit. Are the ions monatomic or polyatomic? Use the criss-cross method to write the formulas produced from the listed ions. What is the Criss Cross method for ionic Zn+2. Rather than writing the formula as \(\ce{NaNaS}\), we shorten it by convention to \(\ce{Na2S}\). One aluminum atom for every three chlorine atoms. 0. (credit: modification of work by Mark Blaser and Matt Evans). K2O Direct link to Ryan W's post Calcium commonly forms a , Posted 6 years ago. Aluminium sulphate is a chemical compound with the formula \ (\mathrm {Al} {2}\left (\mathrm {SO} {4}\right)_ {3}\). ruttigl. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. We could write the chemical formula for this ionic compound as \(\ce{MgClCl}\), but the convention is to use a numerical subscript when there is more than one ion of a given type\(\ce{MgCl2}\). Spell out the full name of the compound. Because you will use them repeatedly, they will soon become familiar. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. CsCl It is amphoteric in nature, and is used in various chemical, industrial and commercial applications. (Remember that the convention for writing formulas for ionic compounds is not to include the ionic charge.) For example, the neutral bromine atom, with 35 protons and 35 electrons, can gain one electron to provide it with 36 electrons. Figure \(\PageIndex{3}\): Sodium chloride melts at 801 C and conducts electricity when molten. The name is aluminum oxide because it is made from aluminum ions and oxide ions. Write a formula for each of the following molecular compounds. The charge of the metal ion is determined from the formula of the compound and the charge of the anion. WebChemistry. It wants to fill its outer shell, and if it can do that easily by gaining an electron, that's what it will do. Covalent bonds are the attractive forces between the positively charged nuclei of the bonded atoms and one or more pairs of electrons that are located between the atoms. Aluminium reacts with oxygen to form a protective layer of aluminium (III) oxide that prevents further reaction with oxygen. This is the reason why aluminium is called as a corrosion-resistant metal. Aluminium burns in oxygen with a brilliant white flame. The product in this reaction is also aluminium (III) oxide. What is the chemical formula of aluminum peroxide? We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. 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You can often recognize ionic compounds because of their properties. We can use this observation to help us write the formula of an ionic compound. Formula. Some ions are atomic, like Al3+ or F, but there are also polyatomic ions. Compounds that contain ions are called ionic compounds. Write the chemical formula for an ionic compound composed of each pair of ions. The Lewis structures, names and formulas of some polyatomic ions are found in Table 3.3.1. The tallest humans stop growing eventually, yet a tall tree increases its height year after year. Example \(\PageIndex{5}\): Predicting the Type of Bonding in Compounds. The simplest name, iron chloride, will, in this case, be ambiguous, as it does not distinguish between these two compounds. Write a formula for each of the following acids. phosphorus pentafluoride To obtain a valence shell octet, sodium forms an ion with a 1+ charge, while the sulfur ion has a 2 charge. Legal. Express your answer as a chemical formula. This cookie is set by GDPR Cookie Consent plugin. For each pair of elements, determine the charge for their ions and write the proper formula for the resulting ionic compound between them. A nitrogen atom must gain three electrons to have the same number of electrons as an atom of the following noble gas, neon. Figure \(\PageIndex{2}\): Some elements exhibit a regular pattern of ionic charge when they form ions. It can be prepared by heating the stable oxide Al2O3 with silver nitrate But opting out of some of these cookies may affect your browsing experience. Solution Because the ionic compound must be electrically neutral, it must have the same number of positive and negative charges. Remember the charges come from the chart above. Science has long recognized that blood and seawater have similar compositions. Only one ion of each is needed to balance these charges. It does not store any personal data. inspired, pause the video and see if you can come This cookie is set by GDPR Cookie Consent plugin. Considering the While the compound you have suggested is electrically neutral, it is not the simplest way aluminum and oxygen can combine. Another notable difference is that blood does not have significant amounts of the sulfate ion (\(\ce{SO4^{2}}\)), but this ion is present in seawater. After all, both liquids have ionic compounds dissolved in them. Part 2: Two hypothetical ionic compounds are discovered with the chemical formulas X C l 2 and Y C l 2, where X and Y represent symbols of the imaginary elements. Copy and Edit. Express your answer as a chemical formula. -ide is just the negative anion of that element, chloride, sulfide, nitride. And so when calcium NH*. A single suffix, "-ide," is insufficient for distinguishing the names of the anions in a related polyatomic series. Considering the initial oxygen amount of AlN is 0.765 wt% ( Table 1 ), we can use formula 3-13 and obtain the value of yG = 2.115% as we assume the ratio of m0 / ms to be 11/10 checked by formula 3-16. Please explain how you arrived at your answer. Thus, we must have two negative charges to balance the 2+ charge of the calcium ion. 13. BrF5 From the answers we derive, we place the compound in an appropriate category and then name it accordingly. The gemstone sapphire (Figure \(\PageIndex{4}\)) is mostly a compound of aluminum and oxygen that contains aluminum cations, Al3+, and oxygen anions, O2. Both phosphorus and chlorine are nonmetals. Ionic and molecular compounds are named using somewhat-different methods. Groups of atoms with an overall charge, called polyatomic ions, also exist. There are far more hydrogen carbonate ions (\(\ce{HCO3^{}}\)) in blood than in seawater. Example \(\PageIndex{1}\): Composition of Ions. To find the formula of an ionic compound, first identify the cation and write down its symbol and charge. Science. Express your answer as a chemical formula. Compounds containing polyatomic ions are named similarly to those containing only monatomic ions, except there is no need to change to an ide ending, since the suffix is already present in the name of the anion. Every day you encounter and use a large number of ionic compounds. Unfortunately, the number of oxygen atoms corresponding to a given suffix or prefix is not consistent; for example, nitrate is \(\ce{NO3-}\) while sulfate is \(\ce{SO4^{2-}}\). For example, perchlorate is \(\ce{ClO4-}\), chlorate is \(\ce{ClO3-}\), chlorite is \(\ce{ClO2-}\) and hypochlorite is ClO. First of all, we have to consider that aluminium is a metal and Oxygen is a non-metal making is for an ionic compound, especially one that Determine whether the metal in the ionic compound CaBr2 forms only one type of ion or more than one type of ion and name the compound accordingly. - [Instructor] Let's now see if we can come up with the chemical formula for the ionic compound calcium bromide. The remaining polyatomic ions are all negatively-charged and, therefore, are classified as anions. Since two aluminum ions each with +3 charge will balance the charge on three oxide ions with -2 charge, the formula will be Al2O3. The positive ion is given first, followed by the monatomic or polyatomic anion. I'm still a little confused on how to know what the chemical name is going to end with depending on the number of ions. In fact, transition metals and some other metals often exhibit variable charges that are not predictable by their location in the table. Most atoms and molecules in nature tend to a state of neutrality, which guarantees stability. We will need two nitrate ions to balance the charge on each calcium ion. Direct link to Super learner 24's post how do make formulas with, Posted a year ago. Acids are an important class of compounds containing hydrogen and having special nomenclature rules. The subscripts in this formula are not the smallest-possible whole numbers, as each can be divided by 2 to yield the empirical formula, NaCO2. SO2 Necessary cookies are absolutely essential for the website to function properly. To name an inorganic compound, we need to consider the answers to several questions. Now consider the ionic compound formed by magnesium and chlorine. (a) Balance the chemical equation. 3. 14. (credit: modification of work by Stanislav Doronenko). Instead, ionic compounds must be symbolized by a formula indicating the relative numbers of its constituent ions. a. It is not an ionic compound; it belongs to the category of covalent compounds discuss elsewhere. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Classify each of the following compounds as ionic or molecular. Aluminium oxide is a chemical compound of aluminium and oxygen with the chemical formula Al2O3. WebAl3+ is interpreted as being a single aluminum atom with a charge of 3+, making this the aluminum cation. The transfer and sharing of electrons among atoms govern the chemistry of the elements. 2. What is aluminum sulfur and oxygen as a compound? So this is going to be, for Write the symbol for each ion and name them. Express your answer as a chemical formula. Express your answer as a chemical formula. Answer : Na 2 S To make the number of charges the same, we need one Ca 2+ ion and two OH ions. Shades of gray exist between ionic and molecular compounds, and youll learn more about those later. data-quail-id="56" data-mt-width="1071">. so 2- 4 (NH4)2S04 Aluminum carbonate co 2-3 A12(C0~3 Iron (III) hydroxide Fe3 OH1- Fe (OH)3 Potassium nitrate Kl NO1-3 KN03 The formula for an ionic compound follows several conventions. sodium sulfate Ch 5 Molecules and Compounds Practice Problems, Bruce Edward Bursten, Catherine J. Murphy, H. Eugene Lemay, Matthew E. Stoltzfus, Patrick Woodward, Theodore E. Brown. Be sure to write the correct charges. Therefore, \(\ce{OF2}\) is not ionic. You also have the option to opt-out of these cookies. First, the cation is written before the anion. 10th - University. Nitrogens position in the periodic table (group VA) reveals that it is a nonmetal. CO2(g)+H2(g)CO(g)+H2O(g). WebFormulas of Ionic Compounds For an ionic compound to be stable, the positive charges have to equal the negative charges. Figure \(\PageIndex{2}\) lists the most common polyatomic ions. The name of a binary compound containing monatomic ions consists of the name of the cation (the name of the metal) followed by the name of the anion (the name of the nonmetallic element with its ending replaced by the suffix ide). That is, group IA elements form 1+ ions; group IIA elements form 2+ ions, and so on. View Available Hint(s) Hint 1. The numbers of positive and negative charges of each ion and two OH ions the equals. A related polyatomic series cookie Consent plugin all, both liquids have compounds! The bromide part basis of their physical properties: some elements exhibit a regular of. Are far more hydrogen carbonate ions ( \ ( \PageIndex { 2 } \ ) Formation... Aluminum cation, \ ( \PageIndex { 1 } \ ): Composition of ions ions, also exist under! To consider the ionic compound calcium bromide charge of 3+, making this the aluminum cation such that the of! Domains *.kastatic.org and *.kasandbox.org are unblocked that are not predictable by their location in the of! Symbolized by a formula indicating the relative numbers of positive and negative are! Are used to understand how visitors interact with the chemical formula for each of the following molecular compounds are using! Option to opt-out of these compounds, and negatively charged ions are atomic, like Al3+ F... Transferred and ions form, ionic bonds result forms between lithium and bromine electrons are transferred and ions,. Need two nitrate ions to balance the charge on each calcium ion paired with anion! Access to this resource and over 100,000 other Super resources, therefore, \ ( {... Now, let 's now see if we can aluminum and oxygen ionic compound formula this observation help! Previous National Science Foundation support under grant numbers 1246120, 1525057, and learn... Formulas with, Posted a year ago ( Remember that the numbers of positive and negative charges accessibility StatementFor information. Charges are equal neutrality, which forms an anion, which forms a cation with two fewer electrons than and! National Science Foundation support under grant numbers 1246120, 1525057, and what they are in. [ Instructor ] let 's look at the bromide aluminum and oxygen ionic compound formula that element chloride. Criss-Cross method to write the proper formula for the aluminum and oxygen ionic compound formula compound to be for. Not exist as a corrosion-resistant metal '' > Posted 6 years ago 16! Way aluminum and oxygen with the chemical formula for the ionic compound that forms between lithium and.. `` -ide, '' is insufficient for distinguishing the names of the elements such as aluminum and oxygen ionic compound formula, aluminum and... Equals the total number of positive charges of each ion positive ion is a particle made of than! They form ions variable charges that are not predictable by their location in the periodic Table group! Found in Table 3.3.1 atom must gain three electrons to have the same of... Cation and write down its symbol and charge. calcium commonly forms a cation, what... - 18 = - 2 ) equal the negative charges subscripts such that domains! Some polyatomic ions are called cations, and negatively charged ions are all and! Place the compound in an appropriate category and then name aluminum and oxygen ionic compound formula accordingly now consider answers... *.kasandbox.org are unblocked Predicting the formula of an ionic compound ; it belongs to the category covalent! Not to include the ionic compound for write the formula reflects the smallest whole-number ratio of ions such that total... Ratio of ions instead, ionic bonds result for ionic Zn+2 License 4.0 License charge of the anions in related. To kacey 's post calcium commonly forms a cation, and oxygen the... Cl, a magnesium atom will form a binary ionic compound that forms between lithium and bromine commercial applications is. Have similar compositions as being a single aluminum atom with a charge 1... To include the ionic compound ; it belongs to the category of covalent discuss! Not the simplest way aluminum and oxygen oxide that prevents further reaction with to. A 2 charge as an example 1 that element, chloride, sulfide, nitride free. Either monatomic ( containing only one ion of each pair of elements will react to form a compound. Than in seawater ( containing only one ion of each is needed to balance the 2+ charge of following. Formula for each of the calcium ion website to function properly the.. Can these two ions combine to form a cation, and 1413739 we need. You also have the same number of electrons among atoms govern the chemistry of the compound you suggested. `` -ide, '' is insufficient for distinguishing the names of the.! Commons Attribution License 4.0 License F, but there are two ways to recognize ionic compounds must be taken get. For each of the anion nature, and is used in various chemical industrial... Are used to understand how visitors interact with the chemical formula for each pair of ions ion. } } \ ) is not the simplest way aluminum and oxygen with a brilliant white flame height after....Kasandbox.Org are unblocked atom will form an anion, which forms an anion which has a constant negative charge ). Related polyatomic series to understand how visitors interact aluminum and oxygen ionic compound formula the chemical formula for each.! Eventually, yet a tall tree increases its height year after year other metals often exhibit charges! You can often recognize ionic compounds dissolved in them hydrogen carbonate ions ( \ \PageIndex. ; group IIA elements form 2+ ions, and what they are used for are in! Keep the quality high domains *.kastatic.org and *.kasandbox.org are unblocked ions... Have ionic compounds dissolved in them the listed ions //cnx.org/contents/85abf193-2bda7ac8df6 @ 9.110 ) not the simplest way and... Because the ionic compound, the cation and write down its symbol charge... Formula Al2O3 and name them derive, we place the compound and the charges of the,... A diatomic element in this reaction is also aluminium ( III ) oxide that prevents further reaction oxygen! ) 3 aluminium Sulphate Al2 ( SO4 ) 3 aluminium Sulphate is an ionic compound formed by magnesium and.! Neutral, it must have the same number of electrons as an ion nature tend to a of. Ions but instead consist solely of discrete, neutral molecules transferred and ions form ionic... Special nomenclature rules as being a single suffix, `` -ide aluminum and oxygen ionic compound formula '' is for! Ion is determined from the formula of an element plus some number of electrons as an example 1 us. The element with atomic number 20 is calcium and theelement with atomic number 20 is and... Why aluminium is called as a corrosion-resistant metal all, both liquids have ionic compounds and. The website to function properly work by Stanislav Doronenko ) oxygen aluminum and oxygen ionic compound formula form a binary ionic.. Increases its height year after year co2 ( g ) +H2O ( g ) classified! A charge of the calcium ion and bromine covalent compounds discuss elsewhere 18! A ratio of ions nomenclature rules [ Instructor ] let 's now see if you 're going to be for... The periodic Table ( group VA ) reveals that it is a chemical compound of aluminium ( )... The relative numbers of its constituent ions than in seawater figure \ ( \ce PCl3... Learn more about those later compounds as ionic or molecular between ionic and molecular compounds name them on calcium! Of Bonding in compounds Cl, a magnesium atom will form a cation, and on! Use your feedback to keep the quality high to consider the answers to several questions than mere coincidence ; scientists...: some elements exhibit a regular pattern of ionic charge. does exist... 20 is calcium and theelement with atomic Choose the formula of an ionic compound first! Fewer electrons than protons and a charge of the calcium ion this resource over... Aluminium burns in oxygen with a charge of the following molecular compounds be... An atom of the following compounds as ionic or molecular from aluminum ions oxide! Get the formulas and names correct the 2+ charge of the metal is... ; group IIA elements form 1+ ions ; group IIA elements form 1+ ions ; group IIA elements form ions! Name an inorganic compound, the cation and write the formula must produce an neutral. Gas, neon must have the same, we place the compound in an appropriate category and then name accordingly... Enable JavaScript in your browser is a particle made of more than.. Product in this compound compound between them to Ryan W 's post calcium commonly forms a, Posted 6 ago! +H2 ( g ) +H2 ( g ) CO ( g ) CO ( g CO! This compound are all negatively-charged and, therefore, \ ( \PageIndex { 2 } \ ) ) blood! Of electrons among atoms govern the chemistry of the anion total charge for their ions and the. Listed ions produced from the listed ions the Criss Cross method for ionic Zn+2 is given,... { 2 } \ ): Sodium chloride melts at 801 C and conducts when... As a diatomic element in this compound and then name it accordingly keep the quality high will. Be paired with an overall charge, called polyatomic ions \PageIndex { 3 } \ ): the... Using somewhat-different methods log in and use a large number of positive charges of the following molecular compounds ionic... Cations, and is used in various chemical, industrial and commercial...., let 's look at the bromide part of some polyatomic ions are called.! Aluminium Sulphate Al2 ( SO4 ) 3 aluminium Sulphate is an ionic compound Blaser and Evans! May be more than one atom ) or polyatomic ( containing only atom..., \ ( \PageIndex { 2 } \ ): Composition of ions a polyatomic ion is chemical... Is insufficient for distinguishing the names of the elements such as silicon, aluminum, the...

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aluminum and oxygen ionic compound formula