��02 �~]���R�!ͻgU*��SM���d�^��d�?��� (f.w. The convention is that the cation is written first in a formula, followed by the anion. 0000002824 00000 n startxref From, this we can say, \([Na^+ ] = 0.30\, M\), \([PO_4^{3–}] = 0.10\, M\), and the concentration of all ions (both cations and anions) is \(0.40\, M\). We will delay that topic until later. This worksheet has 4 problems to solve. Thus, oxidation numbers are Cl = -1, H = +1 Notice that oxidation numbers are written as +1 vs. 1+ to distinguish them from charges. Some of the worksheets displayed are Work oxidation numbers name, Work 25, Oxidation number exercise, Work 1 determination of oxidation number or valence, Chapter 20 work redox, Work 25, , Redox practice work. 2. 0000000966 00000 n 0000030504 00000 n <<49E2DCE38265AE47975CA8C9A5646046>]>> For each, assume that the first species is the analyte and the second species is the titrant. Overall, the most electronegative elements are in the upper right, and the least electronegative elements are in the lower left of the periodic table. Watch the recordings here on Youtube! 3. The sum of the oxidation numbers of all of the atoms in a polyatomic ion is always equal to the charge A reaction in which one species transfers electrons to another is called an oxidation-reduction reaction, also called a redox reaction. For each millimole of analyte, how many millimoles of titrant are needed for complete reaction in each case? 0000002326 00000 n The Oxidation Number Of A Monatomie Ion Equals That Charge On The Ion 3. 43 17 Save or instantly send your ready documents. Oxidation Number - Displaying top 8 worksheets found for this concept. The number of moles of solute in the aliquot of the concentrated solution can be calculated from M × V. Regardless of the dilution, this will be the number of moles in the new solution. For example, if the analyte is a monoprotic acid and the titrant is a standard solution of NaOH(aq), the millimoles of acid initially present will be equal to the millimoles of NaOH(aq) added to reach the equivalence point, because the stoichiometry between moles of analyte and moles of titrant is 1:1. If the analyte is polyprotic (n = 2, 3, ...), \(n\) millimoles of titrant will be required for every millimole of analyte to reach the equivalence point: \[mmol \,titrant = n \times mmol\, analyte\], For example, in the titration of a sample of \(H_2SO_4 (aq)\) with \(NaOH(aq)\), the titration equation is, \[2 NaOH(aq) + H_2SO_4 (aq) \rightarrow Na_2SO_4 (aq) + 2 H_2O(l)\], and at the equivalence point for consuming all the \(H_2SO_4\) we would have, \[M_{NaOH} V_{NaOH} = 2 \times M_{H_2SO_4 } V_{H_2SO_4 }\]. For example, suppose we make a \(0.10\, M\, NaCl\) aquous solution; i.e., \(C = 0.10\, M\). The situation is different with electrolytes, because they break up to some extent to give ions in solution. The indicator is chosen so that it will undergo a pronounced color change very near the equivalence point. Complete Oxidation Numbers Worksheet online with US Legal Forms. Hydrogen –usually +1, except when bonded to Group I or Group II, when it forms hydrides, -1. Describe how you would go about making exactly 500 mL of 0.100 M NaNO3 (aq) solution, using reagent grade NaNO3 (s) (f.w. If the analyte is a weak or strong base, the titrant will be a standard solution of a strong acid, such as hydrochloric acid, HCl(aq). Students determine whether an element is oxidized or reduced in the given reactions. Turtle Meat For Sale, Pmp Exam Simulator 6000 Questions, Missed 2nd Dose Of Rabies Vaccine, Plantlets Malayalam Meaning, Best Point And Shoot Camera For Wildlife Photography, Certified Surgical Assistant Verification, Anastasia Name Meaning, Wella Thermal Image Spray, Villa Le Lac Plan, Mens Kashmiri Shawls, Samsung Stove Turning On By Itself, Dill Meaning In Punjabi, Transcriptionist Resume With No Experience, Cost Of Dentures For Pensioners Nsw, " /> ��02 �~]���R�!ͻgU*��SM���d�^��d�?��� (f.w. The convention is that the cation is written first in a formula, followed by the anion. 0000002824 00000 n startxref From, this we can say, \([Na^+ ] = 0.30\, M\), \([PO_4^{3–}] = 0.10\, M\), and the concentration of all ions (both cations and anions) is \(0.40\, M\). We will delay that topic until later. This worksheet has 4 problems to solve. Thus, oxidation numbers are Cl = -1, H = +1 Notice that oxidation numbers are written as +1 vs. 1+ to distinguish them from charges. Some of the worksheets displayed are Work oxidation numbers name, Work 25, Oxidation number exercise, Work 1 determination of oxidation number or valence, Chapter 20 work redox, Work 25, , Redox practice work. 2. 0000000966 00000 n 0000030504 00000 n <<49E2DCE38265AE47975CA8C9A5646046>]>> For each, assume that the first species is the analyte and the second species is the titrant. Overall, the most electronegative elements are in the upper right, and the least electronegative elements are in the lower left of the periodic table. Watch the recordings here on Youtube! 3. The sum of the oxidation numbers of all of the atoms in a polyatomic ion is always equal to the charge A reaction in which one species transfers electrons to another is called an oxidation-reduction reaction, also called a redox reaction. For each millimole of analyte, how many millimoles of titrant are needed for complete reaction in each case? 0000002326 00000 n The Oxidation Number Of A Monatomie Ion Equals That Charge On The Ion 3. 43 17 Save or instantly send your ready documents. Oxidation Number - Displaying top 8 worksheets found for this concept. The number of moles of solute in the aliquot of the concentrated solution can be calculated from M × V. Regardless of the dilution, this will be the number of moles in the new solution. For example, if the analyte is a monoprotic acid and the titrant is a standard solution of NaOH(aq), the millimoles of acid initially present will be equal to the millimoles of NaOH(aq) added to reach the equivalence point, because the stoichiometry between moles of analyte and moles of titrant is 1:1. If the analyte is polyprotic (n = 2, 3, ...), \(n\) millimoles of titrant will be required for every millimole of analyte to reach the equivalence point: \[mmol \,titrant = n \times mmol\, analyte\], For example, in the titration of a sample of \(H_2SO_4 (aq)\) with \(NaOH(aq)\), the titration equation is, \[2 NaOH(aq) + H_2SO_4 (aq) \rightarrow Na_2SO_4 (aq) + 2 H_2O(l)\], and at the equivalence point for consuming all the \(H_2SO_4\) we would have, \[M_{NaOH} V_{NaOH} = 2 \times M_{H_2SO_4 } V_{H_2SO_4 }\]. For example, suppose we make a \(0.10\, M\, NaCl\) aquous solution; i.e., \(C = 0.10\, M\). The situation is different with electrolytes, because they break up to some extent to give ions in solution. The indicator is chosen so that it will undergo a pronounced color change very near the equivalence point. Complete Oxidation Numbers Worksheet online with US Legal Forms. Hydrogen –usually +1, except when bonded to Group I or Group II, when it forms hydrides, -1. Describe how you would go about making exactly 500 mL of 0.100 M NaNO3 (aq) solution, using reagent grade NaNO3 (s) (f.w. If the analyte is a weak or strong base, the titrant will be a standard solution of a strong acid, such as hydrochloric acid, HCl(aq). Students determine whether an element is oxidized or reduced in the given reactions. Turtle Meat For Sale, Pmp Exam Simulator 6000 Questions, Missed 2nd Dose Of Rabies Vaccine, Plantlets Malayalam Meaning, Best Point And Shoot Camera For Wildlife Photography, Certified Surgical Assistant Verification, Anastasia Name Meaning, Wella Thermal Image Spray, Villa Le Lac Plan, Mens Kashmiri Shawls, Samsung Stove Turning On By Itself, Dill Meaning In Punjabi, Transcriptionist Resume With No Experience, Cost Of Dentures For Pensioners Nsw, " />
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redox assigning oxidation numbers worksheet

Balance electron loss and gain by adding coefficients to the reactants. This leads to the following definitions: Oxidizing agent (oxidant) a substance that causes another substance to be oxidized and is itself reduced. Report a problem. 2. An important application of the relationships \(MV_L = mol\) and \(MV_{mL} = mmol\) is volumetric analysis, which uses precise measurement of the volume of a solution of known concentration, called a standard solution, as a means of carrying out chemical analysis. Oxidizing something must cause something else to be reduced and vice versa. When electrons are transferred from one chemical species to another oxidation and reduction are said to have occurred. If the solute can be obtained in high purity ("analytical reagent grade"), the needed amount can be weighed on an analytical balance and then quantitatively transferred (no loss) to the volumetric flask. \(Zn(s) + 2 HCl(aq) \rightarrow ZnCl_2(aq) + H_2(g)\), \(Fe_2O_3(s) + 2 Al(s) \rightarrow 2 Fe(s) + Al_2O_3(s)\), \(14 HNO_3 + 3 Cu_2O \rightarrow 6 Cu(NO_3)_2 + 2 NO + 7 H_2O\), \(I^– + 2 MnO_4^– + H_2O \rightarrow IO_3^– + 2 MnO_2 + 2 OH^–\). Thus the oxidation number of Cl in the Cl- ion is -1, that for Mg in the Mg2+ ion is +2. How many milliliters of 0.0250 M CuSO4 solution contain 1.75 g of solute? The titrant and analyte react with one another according to a known stoichiometry. In which substance is the oxidation number of nitrogen zero? Updated: Jan 15, 2013. docx, 770 KB. All of the \(NaCl(s)\) breaks up to dissolve as \(Na^+ (aq)\) and \(Cl^– (aq)\) ions: From this we can say, \([Na^+ ] = 0.10\, M\), \([Cl^– ] = 0.10 \,M\), and the concentration of all ions (both cations and anions) is 0.20 M. Consider the same analytical concentration of \(Na_3PO_4\). To talk about the concentrations of ions in weak electrolyte solutions, we will need to have some way of assessing the extent of dissociation of the solute. The volume at which the stoichiometrically correct amount of titrant has been delivered to completely consume the analyte is called the equivalence point. Adding the scaled reactants and scaled products results in. Therefore, the substance oxidized is seen to be the agent of the other substance's reduction, and the substance reduced is seen to be the agent of the other substance's oxidation. Easily fill out PDF blank, edit, and sign them. How many grams of precipitate were formed? • Rule 5: The oxidation number of oxygen in a compound is usually –2. Example: Assign oxidation numbers to each atom \[\mathrm{H_2SO_4}\] Start with what you know: H and O. H: +1; O: –2; To assign the oxidation number to sulfur, take note of Rule 4. A. NH3 B. N2 C. NO2 D. N2O 2. Worksheet 25 - Oxidation/Reduction Reactions Oxidation number rules: Elements have an oxidation number of 0 Group I and II – In addition to the elemental oxidation state of 0, Group I has an oxidation state of +1 and Group II has an oxidation state of +2. Many chemists call the number of moles of solute dissolved per liter of solution the analytical concentration of solute, given the symbol \(C\). The worksheet contains 20 examples that cover all of the oxidation number rules discussed in class. Ideally the end point and the equivalence point should be the same, but in most real situations there is a small difference between the two, which introduces a small error into the measurement. Worksheet 25 - Oxidation/Reduction Reactions. The oxidation number of a monatomic ion equals the charge on the ion. In essence, the Fe "pushes" electrons and the Cl2 "pulls" electrons, thereby effecting electron transfer. = 278.1 u) are produced by the reaction, \[Pb(NO_3 )_2 (aq) + 2 NaCl(aq) \rightarrow PbCl_2 (s) + 2 NaNO_3 (aq)\]. We will discuss electronegativity in more detail later. The sum of the oxidation number of all of the atoms in a compound is always equal to 0. A 25.00-mL sample of an unknown monoprotic acid is titrated to an equivalence point with 32.42 mL of 0.1000 M NaOH solution. The transfer of electrons from one species to another changes the electron count and distribution about the atoms in both. Legal. The advantage of knowing solution concentration in molarity is the direct relationship between the volume of a sample of the solution and the number of moles of solute it contains. Step 1:Assign the oxidation numbers to all atoms on both sides of the equation to determine which are oxidized and which are reduced. �DK�P�фM���e�R:�(���C���1RGћ8����0� R��H0��;��ѣeܢ1�@�s�c We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Oxidation numbers and redox worksheet. Assign oxidation numbers to the elements in the following species using the oxidation number rules. Titration is often used to determine the concentration of a solution of an acid or base, employing the stoichiometry of a neutralization reaction. The More Electronegative Clement In A Binary Compound Is Assigned The Number Oqual To The Charge It Would Have If It Were An Ion. xref changes 4. 0000002901 00000 n BUNDLE: REDOX (Oxidation and Reduction) Practice Worksheets All 4 REDOX Practice Worksheets at a DISCOUNTED PRICE!! Oxidation numbers are bookkeeping numbers. The sum of all oxidation numbers for a neutral compound is zero; the sum is the charge on the species for a complex ion. From the changes in O.N., identify the oxidized and reduced species 3. Redox reactions can be balanced by the use of oxidation numbers. For example, in the reaction between metallic iron and gaseous chlorine, the oxidation state of Fe goes from 0 to +3, making this an oxidation, and the oxidation number of each Cl goes from 0 to –1, making this a reduction. The number of millimoles of titrant added to the analyte to reach the equivalence point is given by the product of the concentration of the standard solution in molarity times the volume delivered from the buret in milliliters: \[\text{millimol titrant} = M_t \times V\], At the equivalence point, the stoichiometric relationship between the millimoles of titrant added and the millimoles of analyte initially present, based on the balanced neutralization equation, can be used to find the solution concentration of the sample. x�b```f``:������� �� �@����Ł��\��D�u��9氪30D˼�r�*s���t� Redox practice worksheet Name: Date: 1. Which of the following has the highest concentration of sodium ion: \(0.20\, M\, NaCl\), \(0.13\, M \,Na_2SO_4\), \(0.080\, M\, Na_3PO_4\)? What was the original concentration of acid in the sample? If we take the product of a solution's molarity times its volume in liters, we can see by dimensional analysis that the resulting units will be moles of solute: \[ M V_l= \left( \dfrac{\text{mol solute}}{ \cancel{\text{L solution}}} \right) ( \cancel{\text{L solution}}) = \text{mol solute} \]. %PDF-1.4 %���� Oxygen – usually -2, except when it forms a O-O single bond, a … It is based on the quantitative relationships between volume and the mole-based solution concentration molarity. For example, in the titration of a sample of HCl(aq) with NaOH(aq) titrant, the titration equation is, \[NaOH(aq) + HCl(aq) \rightarrow NaCl(aq) + H_2O(l)\], and at the equivalence point we would have. 2Fe0 + 3Cl0 2 + 6e + → 2Fe3 + + 6e − + 2Cl −. Oxidation number increases Redox Reduction + Oxidation at the same time Redox reaction: change in ON ... B. Solution concentration is a statement of the amount of solute present in a solution relative to either the amount of solvent or the amount of solution. Work in groups on these problems. Some of the worksheets below are Redox Reactions Worksheets, useful trick to help identify oxidation and reduction, step by step guide to balance any Redox Equations, explanation of Oxidation, reduction, oxidizing agent, reducing agent and rules for assigning an oxidation number, … Once you find your worksheet(s), you can either click on the pop-out icon or download button to print or download your desired worksheet… If you get stuck, try asking another group for help. 0000001799 00000 n View US version. 3. 4.2: Oxidation Numbers, Redox Reactions, Solution Concentration, and Titrations (Worksheet), [ "article:topic", "worksheet", "Author: Robert Carter", "Guided Inquiry", "authorname:carterr", "transcluded:yes", "source-chem-81595" ], Associate Professor and Chair (Chemistry), 4.3: Balancing Redox Equations (Worksheet), Analytical Concentration vs. Actual Species Concentration, Understand the rules for assigning oxidation numbers, Understand the concepts of oxidation and reduction in terms of oxidation numbers, Understand solution concentration in terms of molarity, Know the connection between molarity, volume, and moles or millimoles of solute, Understand the difference between analytical concentration and actual species concentration, Understand the techniques of titration and the quantitative relationships on which it is based, Be able to assign oxidation numbers to elements in chemical species, Be able to identify when a species is being oxidized or reduced, Be able to calculate molarity of a solution, Be able to convert between molarity, volume, and moles or millimoles, Be able to assess the actual ion concentrations in a strong electrolyte solution, Be able to carry out stoichiometry calculations using molarities and volumes of solutions, Be able to carry out titration calculations, All simple monatomic ions have oxidation numbers equal to their charges. What is the oxidation number of carbon in ... oxidation numbers of element X are A. The volume of the analyte is usually measured and dispensed into a reaction flask with a pipet. Oxidation numbers and redox worksheet. The overall charge of the molecule is zero. 0000001177 00000 n For example, consider the reaction of metallic iron with chlorine gas to form ionic iron(III) chloride: \[2 Fe(s) + 3 Cl_2(g) \rightarrow 2 FeCl_3(s) º 2 [Fe^{3+}][Cl^–]_3\]. In addition to metathetical reactions, electron transfer reactions often occur in solutions. Oxidation numbers are usually written with the sign first, then the magnitude, to differentiate them from charges. The LibreTexts libraries are Powered by MindTouch® and 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. The following represent skeletal reaction equations for some possible titrations. 0000000016 00000 n Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Another way of preparing a solution of a certain molarity is to start with a measured volume (an aliquot) of a more concentrated solution of known molarity and dilute to the desired concentration. What was the concentration of \(Cl^–\) ion in the original sample? Therefore, we can write, \[ \dfrac{M_{initial}}{V_{initial}} = M_{final}V_{final}\]. Assign the oxidation numbers of each element in the following chemical species: HCl, H2O, NH3, NO3–, K2Cr2O7, Hg2Cl2, HgCl2, Al(OH)3, Na3PO4. Then, determine if each equation is a redox reaction. How many milliliters of 0.1200 M \(\ce{HCl}\) solution are needed to completely neutralize 50.00 mL of 0.1012 M \(\ce{Ba(OH)2}\) solution? Assign oxidation numbers to all elements and identify those that are oxidized and reduced. To become skilled at finding oxidation numbers you need lots of practice. Titrant in buret standard solution = known concentration Analyte in reaction flask known volume, unknown concentration, In most cases, the stoichiometric relationship between the analyte and titrant is 1:1, or less frequently 1:2 or 1:3. An oxidation number is a positive or negative number assigned to an atom according to a set of rules. Sum over the oxidation numbers and solve for the missing one. Have questions or comments? Therefore, when convenient, we can define the molarity of a given solution alternatively as, \[ \text{Molarity} = M = \dfrac{\text{millimoles of solute}}{\text{milliliters of solution}}\]. �f4J3 iu�R!à�mWan��TћoK�4j,ZMBK4�k���+=*��X`h&���N,��ыi��o&���\�C���+���z�DLA�z�4��8�a��D��"�� o����f�C��&0Aa�&�۪��db���h�Y28��8|*ЇzF�8q�ק0��@���qmZv�P�ij��D������&J��HDt��iby��$��� Created: Oct 11, 2012. 4. Compute the number of electrons lost in the oxidation and gained in the reduction from the O.N. 3. Oxidation numbers are real or hypothetical charges on atoms, assigned by the following rules: When a species is oxidized, one of its atoms goes to a higher (more positive or less negative) oxidation number. Oxidation number rules: Elementshave an oxidation number of 0 Group Iand II– In addition to the elemental oxidation state of 0, Group I has an oxidation state of +1and Group II has an oxidation state of +2. Indicate the concentrations of all ions in a solution prepared by mixing 45.0 mL of \(0.200\, M\, Na_2SO_4\) and 65.0 mL of \(0.300\, M Al_2(SO_4)_3\) . 2Fe(s) + 3Cl2(g) → 2Fe3 + + 6Cl −. Therefore, there is never oxidation without reduction and vice versa in a redox reaction. 0000005295 00000 n In this past live tutoring session I focused on Oxidation and Reduction Reactions, Oxidation Numbers and Periodic trends. the amount of electrolyte that is dissolved, whether the solute is a strong or weak electrolyte, and, \(HC_2H_3O_2 (aq) + NaOH(aq) \rightarrow H_2O(l) + NaC_2H_3O_2 (aq)\), \(Ca(OH)_2 (aq) + HCl(aq) \rightarrow H_2O(l) + CaCl_2 (aq) \), \(H_3PO_4 (aq) + KOH(aq) \rightarrow H_2O(l) + K_3PO_4 (aq)\). How many grams of \(PbCl_2\) (f.w. This BUNDLE contains the Assigning Oxidation Numbers worksheet, Identifying the Oxidizing and Reducing Agents worksheet, Writing Half Reactions worksheet, and Balancing REDOX Reactions worksheet. These kinds of reactions are very important in natural and synthetic processes. Balancing Redox Equations Method 1: Oxidation number method 1. In this reaction worksheet, students assign the oxidation numbers to all the atoms in the given compounds and ions. About this resource. CuSO4 = 159.6 u), No molecular dissociation occurs when a nonelectrolyte is dissolved in water. By either definition, the numerical value of the molarity of a particular solution is the same. Solvent, usually water, is then added until the level reaches the calibration mark for the flask's volume. We will indicate the actual concentration of a species X by writing its symbol in square brackets, \([X]\), meaning moles per liter of solution. �f~�➦N,>��02 �~]���R�!ͻgU*��SM���d�^��d�?��� (f.w. The convention is that the cation is written first in a formula, followed by the anion. 0000002824 00000 n startxref From, this we can say, \([Na^+ ] = 0.30\, M\), \([PO_4^{3–}] = 0.10\, M\), and the concentration of all ions (both cations and anions) is \(0.40\, M\). We will delay that topic until later. This worksheet has 4 problems to solve. Thus, oxidation numbers are Cl = -1, H = +1 Notice that oxidation numbers are written as +1 vs. 1+ to distinguish them from charges. Some of the worksheets displayed are Work oxidation numbers name, Work 25, Oxidation number exercise, Work 1 determination of oxidation number or valence, Chapter 20 work redox, Work 25, , Redox practice work. 2. 0000000966 00000 n 0000030504 00000 n <<49E2DCE38265AE47975CA8C9A5646046>]>> For each, assume that the first species is the analyte and the second species is the titrant. Overall, the most electronegative elements are in the upper right, and the least electronegative elements are in the lower left of the periodic table. Watch the recordings here on Youtube! 3. The sum of the oxidation numbers of all of the atoms in a polyatomic ion is always equal to the charge A reaction in which one species transfers electrons to another is called an oxidation-reduction reaction, also called a redox reaction. For each millimole of analyte, how many millimoles of titrant are needed for complete reaction in each case? 0000002326 00000 n The Oxidation Number Of A Monatomie Ion Equals That Charge On The Ion 3. 43 17 Save or instantly send your ready documents. Oxidation Number - Displaying top 8 worksheets found for this concept. The number of moles of solute in the aliquot of the concentrated solution can be calculated from M × V. Regardless of the dilution, this will be the number of moles in the new solution. For example, if the analyte is a monoprotic acid and the titrant is a standard solution of NaOH(aq), the millimoles of acid initially present will be equal to the millimoles of NaOH(aq) added to reach the equivalence point, because the stoichiometry between moles of analyte and moles of titrant is 1:1. If the analyte is polyprotic (n = 2, 3, ...), \(n\) millimoles of titrant will be required for every millimole of analyte to reach the equivalence point: \[mmol \,titrant = n \times mmol\, analyte\], For example, in the titration of a sample of \(H_2SO_4 (aq)\) with \(NaOH(aq)\), the titration equation is, \[2 NaOH(aq) + H_2SO_4 (aq) \rightarrow Na_2SO_4 (aq) + 2 H_2O(l)\], and at the equivalence point for consuming all the \(H_2SO_4\) we would have, \[M_{NaOH} V_{NaOH} = 2 \times M_{H_2SO_4 } V_{H_2SO_4 }\]. For example, suppose we make a \(0.10\, M\, NaCl\) aquous solution; i.e., \(C = 0.10\, M\). The situation is different with electrolytes, because they break up to some extent to give ions in solution. The indicator is chosen so that it will undergo a pronounced color change very near the equivalence point. Complete Oxidation Numbers Worksheet online with US Legal Forms. Hydrogen –usually +1, except when bonded to Group I or Group II, when it forms hydrides, -1. Describe how you would go about making exactly 500 mL of 0.100 M NaNO3 (aq) solution, using reagent grade NaNO3 (s) (f.w. If the analyte is a weak or strong base, the titrant will be a standard solution of a strong acid, such as hydrochloric acid, HCl(aq). Students determine whether an element is oxidized or reduced in the given reactions.

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