is ammonia a strong electrolyte is ammonia a strong electrolyte

Example: soapy water pH 13 Concentration: 1/1,000,000. Nervous System Levels of Organization, 42. Bookshelf The general form of the strong electrolyte equation is: strong electrolyte (aq) cation+ (aq) + anion- (aq). \(\mathrm{Zn | Zn^{2+} || Cu^{2+}| Cu}\). It forms ammonium hydroxide (NH4OH), which is a base, and basic solutions are electrolytic. Examples of weak electrolytes include acetic acid (CH3COOH), carbonic acid (H2CO3), ammonia (NH3), hydrogen fluoride (HF), hydrogen cyanide (HCN), and pyridine (C2H5N), etc. The ionization or autoionization of pure water can be represented by the ionization equation, \(\mathrm{H_2O \rightleftharpoons H^+ + OH^-}\), \(\mathrm{\mathit K = \dfrac{[H^+] [OH^-]}{[H_2O]}}\). 2016;4:16041. Glucose, a sugar with the chemical formula C6H12O6, is a typical example of a nonelectrolyte. where we use [ ] to mean the concentration of the species in the [ ]. 2015 Apr 07;10(4):676-87. Clipboard, Search History, and several other advanced features are temporarily unavailable. The solute is one hundred percent (100%) ionized. false. Hypokalemia occurs when serum potassium levels under 3.6 mmol/Lweakness, fatigue, and muscle twitching present in hypokalemia. Which of the following is a strong electrolyte in aqueous solution ? Example: pure water (7) pH 8 Concentration: 1/10. Phosphate plays a crucial role in metabolic pathways. Am Fam Physician. The quantitative treatment of these effects was first worked out by P. Debye and W. Huckel in the early 1920's, and was improved upon by Ostwald a few years later. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. The fraction (often expressed as a %) that undergos ionization depends on the concentration of the solution. For pure water, \(\ce{[H2O]}\) is a constant (1000/18 = 55.6 M), and we often use the ion product, Kw, for water, \(\mathrm{\mathit K_w = \mathit K [H_2O] [H^+] [OH^-]}\). Sodium regulation occurs in the kidneys. Identification of strong, weak and non-electrolytes, predicting solubility based on "solubility rules" and identifying aqueous equations as general, total or net ionic. if you dissolve a substance into water and the substance conducts an electrical current through it, you can determine that the dissolved substance is an ___________. a high NH3 yield rate of ~70 g h-1 mgcat.-1 and a high Faradaic efficiency of ~26% at -0.5 V vs. RHE in an aqueous electrolyte. government site. Hypercalcemia is when corrected serum total calcium levels exceed 10.7 mg/dl, as seen with primary hyperparathyroidism. https://www.thoughtco.com/strong-and-weak-electrolytes-609437 (accessed March 4, 2023). Patients may present with headaches, confusion, nausea, delirium. The principal species in solution for weak electrolytes is the unionized electrolyte itself, Solutions containing a strong electrolyte will have high electrical conductivity, Solutions containing a weak electrolyte will have low electrical conductivity, Strong acids, strong bases, and salts (except some) are strong electrolytes, Weak acids and weak bases are weak electrolytes, HCl, NaCl, NaOH are some examples of strong electrolytes. They get immediately converted into ammonia and water. For strong electrolytes, a single reaction arrow shows that the reaction occurs completely in one direction, in contrast to the dissociation of weak electrolytes, which both ionize and re-bond in significant quantities.[1]. Strong electrolytes conduct electricity only when molten or in aqueous solutions. FOIA Copyright 2022, StatPearls Publishing LLC. Weak electrolytes include weak acids, weak bases, and a variety of other compounds. NaHCO3 (Sodium hydrogen carbonate/baking soda), C12H22O11 (lactose) (lactose and sucrose have the same formula??? These ions are used in maintaining protein structure and in cell communication, and generally can help maintain water balances throughout the body. Unable to load your collection due to an error, Unable to load your delegates due to an error. Chapter 9: The Lymphatic System and Immunity, 53. Most molecular compounds are non-electrolytes.----- Definitions ------ Strong Electrolyte: completely dissociate in solution and conducts electricity. This work represented one of the major advances in physical chemistry in the first half of the 20th Century, and put the behavior of electrolytic solutions on a sound theoretical basis. A solution is neutral if its pH is equal to 7.0. The kidneys are the primary avenue of phosphorus excretion. Disclaimer. The solution will contain only ions and no molecules of the electrolyte. Retrieved from https://www.thoughtco.com/strong-and-weak-electrolytes-609437. This means that the principal species in solution for strong electrolytes are ions, while the principal species in solution for weak electrolytes is the un-ionized compound itself. Federal government websites often end in .gov or .mil. A nonelectrolyte is a type of substance that does not ionize in either a molten state or in solution. . Introduction to the Integumentary System, 24. (c) Glucose C 6 H 12 O 6 is non electrolyte. When the heart stops pumping in a heart attack, the life ends quickly. It is mostly present in the extracellular fluid. When the ions are indifferent of each other, there is no reaction. This site needs JavaScript to work properly. KCl is a strong electrolyte and the bulb is very bright. glycerol ammonia iron (III) This problem has been solved! The proximal tubule is where the majority of sodium reabsorption takes place. pH 0 Concentration: 10,000,000. Find the state of plane stress at point CCC located 8in8\ \mathrm{in}8in. While NH3 will dissolve in water (it is soluble in water) it only partially dissociates into its ions. Explain ion movement in a solution of electrolytes. Soluble ionic compounds and strong acids are electrolytes.- Weak Electrolyte: partially dissociate in solution and poorly conduct electricity.- Non-Electrolytes: do not dissociate into ions and do not conduct electricity. To the extent that ions having opposite charge signs are more likely to be closer together, we would expect their charges to partially cancel, reducing their tendency to migrate in response to an applied potential gradient. , No Comment, February 6, 2023 Instead, new counter-ions are continually acquired on the leading edge of the motion, while existing ones are left behind on the opposite side. These studies revealed that the equivalent conductivities of electrolytes all diminish with concentration (or more accurately, with the square root of the concentration), but they do so in several distinct ways that are distinguished by their behaviors at very small concentrations. -, Gumz ML, Rabinowitz L, Wingo CS. Organ Systems, The Whole Body, and Populations, VI. Legal. Here's some extreme examples of what can happen with an imbalance of electrolytes: elevated potassium levels may result in cardiac arrhythmias; decreased extracellular potassium produces paralysis; excessive extracellular sodium causes fluid retention; and decreased plasma calcium and magnesium can produce muscle spasms of the extremities. It exists as molecule in water and to some extent get dissociated as ion. Aldosterone increases potassium secretion. Please rate this article: Why Do Aqueous Solution Conduct Electricity? Answer. Strong electrolytes are good conductors of electricity, but only in aqueous solutions or in molten form. Getting the heart restarted as soon as one can is crucial in order to maintain life. These ions are good conductors of electric current in the solution. These are nutritionally called macrominerals. You can help Wikipedia by expanding it. Ammonia is an electrolyte because it produces ions by the following reaction: NH 3 (aq) + H 2 O = NH 4+ (aq) + OH - (aq) Ammonia is a weak rather than strong electrolyte because this reaction runs both ways; ammonia reacts with water to produce ammonium and hydroxide ions, while hydroxide ions react with ammonium ions to produce ammonia and water. You can generalize the definition of K here to give the equilibrium constant expression for any weak electrolyte. Helmenstine, Anne Marie, Ph.D. "Strong Electrolyte Definition and Examples." Eighty-five percent of the total body phosphorus is in the bones and teeth in the form of hydroxyapatite; the soft tissues contain the remaining 15%. Some of the examples of strong electrolyte are sodium nitrate, sodium chloride and sodium sulphate and one example for weak a electrolytes is ammonia solution. Reproductive Structures and Functions. As the ions exist as such, the solution of HCl will have ample ions to conduct electricity and hence acts as a strong electrolyte. Introduction to the Respiratory System, 70. , Jessica Damian Legal. But for the \(\ce{Cu}\) electrode, \(\ce{CuSO4}\) or \(\ce{CuCl2}\) is commonly used. Examples: acid rain (5.6), black coffee (5) pH 6 Concentration: 10. In practice, only a few strong acids are commonly encountered: HCl, HBr, HI, HNO 3, HClO 4, and H 2 SO 4 (H 3 PO 4 is only moderately strong). The cation and anion that are formed to conduct electricity will not stay back as such. Since the pH scale is an inverse scale, the concentration of protons is high at low pH and low at high pH. A strong electrolyte is a substance that splits water into hydrogen and oxygen by electrolysis. A strong electrolyte is a solute or solution that is an electrolyte that completely dissociates in solution . . Cardiovascular Integration of Systems, XII. This page titled 8.10.9C: Weak and Strong Electrolytes is shared under a CC BY 3.0 license and was authored, remixed, and/or curated by Stephen Lower via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. The substances which ionize up to a small extent into ions are called weak electrolytes. But it is still a strong electrolyte and the solution's electrical conductance is a separate . Carbonic acid (CH2O3), Ammonia (NH3), and Phosphoric acid (H3PO4) act as weak electrolytes. Ann Clin Lab Sci. The zinc atoms have a tendency to become ions, leaving the electrons behind. Because C is a non-metal and H, O is a. Note that only at 298 K is the pH of water = 7. Is HF (Hydrofluoric Acid) a Strong Acid or a Weak Acid? In terms of child health, oral electrolyte is need when a child is dehydrated due to diarrhea. The more ionization, the stronger the electrolyte. A strong electrolyte consists of a solute that dissociates into free ions in large quantity while a weak electrolyte does not release much of the free ions. will shift to the left as the concentration of the "free" ions increases. Skill: Dr. Helmenstine holds a Ph.D. in biomedical sciences and is a science writer, educator, and consultant. Skill: February 9, 2023 NH4 is the conjugate acid of the weak base ammonia, and reacts with water to a small extent to form H,0 . A substance whose aqueous solution or molten state decomposed into ions by passing electricity is known as electrolytes. In: StatPearls [Internet]. The reactants (molecular form) and the products (ionic form) will be in equilibrium. But this ideal behavior is never observed; instead, the conductivity of electrolytes of all kinds diminishes as the concentration rises. When a patient is dehydrated, a carefully prepared (commercially available) electrolyte solution is required to maintain health and well being. When muscle contracts, calcium re-uptake by the calcium-activated ATPase of the sarcoplasmic reticulum is brought about by magnesium. , Syed Hasan The pH is the negative logarithm (-log) of the proton concentration:pH = log (H+). Difference Between Strong Electrolyte and Weak Electrolyte Importance Substances that form a high degree of ions in solution are classified as strong electrolytes, substances that form a small percentage of ions in solution are weak electrolytes and those that form no ions in solution are nonelectrolytes. This electrochemistry-related article is a stub. [Electrolyte and acid-base balance disorders in advanced chronic kidney disease]. Salts much have high solubility in the solvent to act as strong electrolytes. The light will glow dimly for each solution since each is a weak electrolyte. Even though NH3 is an base, it is a weak base and therefore a weak electrolyte. Electrolyte balance is crucial to many body functions. An electrolyte is any fluid that contains free ions. Extensions and connections A more quantitative approach to equilibria uses weak acids and weak bases as important examples. D. A strong electrolyte is any ionic substance. (d) Ammonia N H 3 is weak electrolyte. \(\mathrm{Cu^{2+}_{\large{(aq)}} + 2 e^- \rightarrow Cu_{\large{(s)}}}\). Why cant pure water be used as an electrolyte? Most of the chloride, which is filtered by the glomerulus, is reabsorbed by both proximal and distal tubules (majorly by proximal tubule) by both active and passive transport. Unlike the weak electrolytes, the equation for the ionization of strong electrolytes is not represented with double-headed arrows, such as. 2016 Apr;27(4):981-9. Some other ionic solids are \(\ce{CaCl2}\), \(\ce{NH4Cl}\), \(\ce{KBr}\), \(\ce{CuSO4}\), \(\ce{NaCH3COO}\) (sodium acetate), \(\ce{CaCO3}\), and \(\ce{NaHCO3}\) (baking soda). official website and that any information you provide is encrypted The beam has a cross section of 612in.6 \times 12\ \text{in. From everyday experience you are probably aware that table sugar (sucrose), C12H22O11, is soluble in water. Accessibility Treasure Island (FL): StatPearls Publishing; 2022 Jan. Aqueous solutions containing electrolytes conduct electricity. Electrolytes are essential for life, but many people get too much (like too much sodium from salt in processed food), which can also disrupt proper physiological function. below the top of the beam and 0.5ft0.5\ \mathrm{ft}0.5ft to the right of support AAA. This is because strong electrolyte solutions have more free-charged species (ions). Why can't pure water be used as an electrolyte? They exist as molecules as well as dissociate back into ions. Since \(\ce{NaCl}\) is an ionic solid (s), which consists of cations \(\ce{Na+}\) and anions \(\ce{Cl-}\), no molecules of \(\ce{NaCl}\) are present in \(\ce{NaCl}\) solid or \(\ce{NaCl}\) solution. MeSH Example: household ammonia (11.9) pH 12 Concentration: 1/100,000. The .gov means its official. Sodium, potassium, and chloride are the significant electrolytes along with magnesium, calcium, phosphate, and bicarbonates. . Potassium channels and potassium-chloride cotransporters at the apical membrane also secrete potassium. In: StatPearls [Internet]. Depending upon the extent or degree of ionization, the electrolytes are divided into two types: Strong electrolytes are the chemical substances that ionize completely when dissolved in water, whereas weak electrolytes only ionize partially. Hypochloremia presents in gastrointestinal losses like vomiting or excess water gain like congestive heart failure. This work not only exemplifies the first stable preparation and practical . Most molecular compounds are non-electrolytes.----- Helpful Resources -----Metals, Non-Metals on the Periodic Table: https://youtu.be/OoooStZQHdAIonic, Covalent, \u0026 Polar Covalent: https://youtu.be/OHFGXfWB_r4Solubility Table: https://youtu.be/b0pDquyGSdk)Solubility Rules: https://youtu.be/zffVKN6tm7k---www.Breslyn.org Ammonia, NH3, is a weak electrolyte. Abstracts of Presentations at the Association of Clinical Scientists 143. Electrolyte is a solution and a medium that consists of free ions which help in the conduction of electricity. It is of course impossible to measure the conductance of an electrolyte at vanishingly small concentrations (not to mention zero! { "Acids_and_Bases_-_Conjugate_Pairs" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Balance_Reduction_and_Oxidation_(Redox)_Reactions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Chemical_Reactions_Overview : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Conjugate_Acids_of_Bases_-_Ka_Kb_and_Kw" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Electrolytes : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Features_of_Chemical_Reaction : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Half_Reactions : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Metathesis_Reactions : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Oxidation_States : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Revealing_the_Dates_of_Buffalo_Nickels_(Demo)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Solutions : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Solution_Stoichiometry : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { Chemical_Reactions_Examples : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Limiting_Reagents : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Properties_of_Matter : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Reactions_in_Solution : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Stoichiometry : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Stoichiometry_and_Balancing_Reactions : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "cations", "anions", "Electrolytes", "bases", "equilibrium constant", "acid", "base", "salt", "ionic solid", "electrolyte", "neutralization", "showtoc:no", "weak electrolytes", "strong electrolytes", "salts", "aqueous solutions", "Body Fluids", "Macrominerals", "Solid formation", "Gas formation", "license:ccbyncsa", "licenseversion:40" ], https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FInorganic_Chemistry%2FSupplemental_Modules_and_Websites_(Inorganic_Chemistry)%2FChemical_Reactions%2FChemical_Reactions_Examples%2FElectrolytes, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), status page at https://status.libretexts.org. Glucose (commonly known as sugar) dissolves readily in water, but because it does not dissociate inside the solution into ions, it is considered a nonelectrolyte. For example, \(\ce{NH4OH}\) (ammonia), \(\ce{H2CO3}\) (carbonic acid), \(\ce{CH3COOH}\) (acetic acid), and most organic acids and bases are weak electrolytes. Electrolytes dissociate into ions when added to water. The diet is the predominant source of calcium. Magnesium is mainly involved in ATP metabolism, contraction and relaxation of muscles, proper neurological functioning, and neurotransmitter release. Unauthorized use of these marks is strictly prohibited. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Strong electrolytes completely ionize when dissolved, and no neutral molecules are formed in solution. , No Comment, February 8, 2023 NCI CPTC Antibody Characterization Program, Palmer LG, Schnermann J. Help us improve. Examples: liquid drain cleaner, caustic soda. Treasure Island (FL): StatPearls Publishing; 2022 Jan. Would you like email updates of new search results? Hypernatremia presents when the serum sodium levels are greater than145 mmol/L. Example: tomato juice (4.1) pH 5 Concentration: 100. These electrolytes can have an imbalance, leading to either high or low levels. Types of Electrolytes. NITRO-3D is an unmatched, supercharged intra-workout formulated to help you push harder and further than ever during your workouts. Chung (Peter) Chieh (Professor Emeritus, Chemistry @University of Waterloo). Calcium has a significant physiological role in the body. Even so, the, 8.10.9B: The nature of ions in aqueous solution, Conductivity diminishes as concentrations increase, Not all Electrolytes Totally Dissociate in Solution, Weak electrolytes are dissociated only at extremely high dilution, source@http://www.chem1.com/acad/webtext/virtualtextbook.html, status page at https://status.libretexts.org. Some substances, when dissolved in water, undergo either a physical or a chemical change that results in constituent cations and anions in the solution. , Dr. Romisa, No Comment, February 24, 2023 Examples: baking soda (8.4), seawater, eggs pH 9 Concentration: 1/100. . Important ions in physiology include sodium, potassium, calcium, chloride and phosphate. Soluble ionic compounds and strong acids are electrolytes.- Weak Electrolyte: partially dissociate in solution and poorly conduct electricity.- Non-Electrolytes: do not dissociate into ions and do not conduct electricity. \(\mathrm{Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu}\). Parathyroid hormone also regulates calcium secretion in the distal tubule of kidneys. Hydrochloric acid is also a strong acid, because when it completely dissociates it also completely donates all of its protons. Join AUS-e-TUTE! The non-ideality of electrolytic solutions is also reflected in their colligative properties, especially freezing-point depression and osmotic pressure. If a parent provides an oral electrolyte maintenance solution at the very start of the illness, dehydration can be prevented. order now. Ammonia is such a substance. . Electrolytes come from our food and fluids. Phosphate is regulated simultaneously with calcium by Vitamin D3, PTH, and calcitonin. It can present with alcohol use disorder and gastrointestinal and renal lossesventricular arrhythmias, which include torsades de pointes seen in hypomagnesemia. Example: battery acid pH 1 Concentration: 1,000,000. A list of further examples is provided in the lower section of this article. Strong electrolytes examples: Hydrochloric acid (HCl), Sulfuric acid (H2SO4), sodium hydroxide (NaOH), and potassium hydroxide (KOH). Solutions in which water is the dissolving medium are called aqueous solutions. Since the weak electrolytes have fewer ions in the solution, it acts as weak conductor of electricity. You have already learned about ions and ionic properties. Symptoms of hypernatremia include tachypnea, sleeping difficulty, and feeling restless. ThoughtCo. Answer the following question to test your understanding of the preceding section: 2022 Jun 21. Match the following modalities with the appropriate classification. A strong electrolyte is a solution/solute that completely, or almost completely, ionizes or dissociates in a solution. Glycerol, C3H8O3, is a nonelectrolyte; ammonia, NH3, is a weak electrolyte; and iron (III) sulfate, Fe2 (SO4)3, is a strong electrolyte. The same goes for weak bases used as ammonia - in combination with pure water, you get a basic solution and very little ammonium, but when dissolved in a solution maintaining a neutral pH, ammonia forms the ammonium ion almost quantitatively. HCl is a strong electrolyte as it is a strong acid. N Engl J Med. Depending on the extent of ionization in water, the electrolyte can be regarded as strong or weak. Any salt can be used for the \(\ce{Zn}\)-electrode. February 28, 2023 A strong electrolyte is a solution/solute that completely, or almost completely, ionizes or dissociates in a solution. Helmenstine, Anne Marie, Ph.D. "Chemistry Examples: Strong and Weak Electrolytes." Strong acids, strong bases and soluble ionic salts that are not weak acids or weak bases are strong electrolytes. Electrolytes is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.