how to calculate ksp from concentration

root of the left side and the cube root of X cubed. of calcium two plus ions raised to the first power, times the concentration Educ. Given: Ksp and volumes and concentrations of reactants. In this case, each formula unit of CaCO 3 yields one Ca 2+ ion and one CO 3 2 ion. of calcium fluoride that dissolves. So we're going to leave calcium fluoride out of the Ksp expression. Calculate the molar solubility of calcium hydroxide (Ks,-6.0% 106) in pure water and in a solution with a pH of 13.3. How do you calculate enzyme concentration? Before any of the solid Mass percent composition (also called mass percent or percent composition) is the easiest way to express the concentration of a solution because no unit conversions are required. What is the solubility, in mol/L, of MgCO3 in a 0.65 mol/L solution of MgCl2 if the Ksp of MgCO3 is 2.5 x 10-5? Check out Tutorbase! What is the solubility (in m) of PBCL2 in a 0.15 m solution of HCL? Example #3: Determine the Ksp of mercury(I) bromide (Hg2Br2), given that its molar solubility is 2.52 x 108 mole per liter. From the balanced dissolution equilibrium, determine the equilibrium concentrations of the dissolved solute ions. Insert the appropriate values into the solubility product expression and calculate the molar solubility at 25C. The next step is to set up an ICE table, where I stands for initial concentration, C stands for the change in concentration, and E stands for First, we need to write out the dissociation equation: $K_s_p$=$ [Ag^{+}]^2$ $[SO_4^2]$. The adolescent protagonists of the sequence, Enrique and Rosa, are Arturos son and , The payout that goes with the Nobel Prize is worth $1.2 million, and its often split two or three ways. To do this, simply use the concentration of the common The concentration of Cl^-(aq) in seawater is 0.54 M. i. Calcul, Calculate the molar solubility of FeF2 in: (a) pure water (b) 0.150 M solution of NaF. Direct link to Shariq Khan's post What would you do if you , Posted 7 years ago. From this we can determine the number of moles that dissolve in 1.00 L of water. In this section, we explain how to write out $K_s_p$ chemistry expressions and how to solve for the value of $K_s_p$. The more soluble a substance is, the higher the Ksp value it has. Ksp for BaCO3 is 5.0 times 10^(-9). Below is a chart showing the $K_s_p$ values for many common substances. Looking for other chemistry guides? make the assumption that since x is going to be very small (the solubility What does molarity measure the concentration of? The solubility of CaC2O4 is 0.00081 g/100 mL at 25 degrees Celsius. 1) Write the chemical equation for the dissolving of barium phosphate in water: 2) Write the Ksp expression for barium phosphate: 4) Put values into and then solve the Ksp expression: 5) Note that the formula weight of Ba3(PO4)2 is not involved at any point. [6] In our example, C = (10 g)/ (1,210 g) = 0.00826. The College Entrance Examination BoardTM does not endorse, nor is it affiliated in any way with the owner or any content of this site. Also, the key thing to be aware of with these equations is that each concentration (represented by square brackets) is raised to the power of its coefficient in the balanced $K_s_p$ expression. of the ions that are present in a saturated solution of an ionic compound, It applies when equilibrium involves an insoluble salt. and calcium two plus ions. it will not improve the significance of your answer.). concentration of fluoride anions. How do you know when to make the initial concentration for OH- 0 versus making it 1.0x10^-7? Example: 25.0 mL of 0.0020 M potassium chromate are mixed in a solution that contains a common ion, Determination whether a precipitate will or will Inconsolable that you finished learning about the solubility constant? The concentration of Ba2+ when the solutions are mixed is the total number of moles of Ba2+ in the original 100 mL of BaCl2 solution divided by the final volume (100 mL + 10.0 mL = 110 mL): Similarly, the concentration of SO42 after mixing is the total number of moles of SO42 in the original 10.0 mL of Na2SO4 solution divided by the final volume (110 mL): C We now compare Q with the Ksp. Direct link to Reda's post Why is X expressed in Mol, Posted 4 years ago. So the equilibrium concentration All rights reserved. 2-] will go up by 1.31 x 10-4 moles/L: x 1/1 -1.31 x 10-4 moles/L > + 1.31 x 10-4 M. The solubility product constant, Ksp, is the equilibrium constant for a solid substance dissolving in an aqueous solution. Solution: 5.5 M x V 1 = 1.2 M x 0.3 L These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. Calculate the concentration of OH, Pb 2+ and the K sp of this satured solution. If there are coefficients in front of any of the products, it is necessary to raise the product to that coefficient power(and also multiply the concentration by that coefficient). Calculate the concentration of all species in a 0.15 M HF solution and K_a (HF) = 6.3 \times 10^{-4}. The equation for the Ksp of Ca (OH)2 is the concentration [Ca2+] times the concentration [OH-] taken to the second power, since the OH- has a coefficient of 2 in the balanced equation. 2.3 \cdot 10^{-6} b. (b) Find the concentration (in M) of iodate ions in a saturat. The more soluble a substance is, the higher its $K_s_p$ chemistry value. Neither solid calcium oxalate monohydrate nor water appears in the solubility product expression because their concentrations are essentially constant. What is the molar concentration of scandium ions in a 0.260 mol/L solution of scandium sulfate? For the fluoride anions, the equilibrium concentration is 2X. And since it's a one-to-two mole ratio for calcium two plus Clark, Roy W.; Bonicamp, Judith M. " Solubility and Solubility Products (about J. Chem. Now, since in this problem we're solving for an actual value of $K_s_p$, we plug in the solubility values we were given: $K_s_p$ = (5.71 x $10^{}^7$) (5.71 x $10^{}^7$) = 3.26 x $10^{}^13$, The value of $K_s_p$ is 3.26 x $10^{}^13$. When you have a solid grasp of $K_s_p$, those questions become much easier to answer! If they asked for the concentration of the chloride anion during equilibrium would you just multiply the molar solubility by two? Question: 23. At the bottom of this guide, we also have a table with the $K_s_p$ values for a long list of substances to make it easy for you to find solubility constant values. It represents the level at which a solute dissolves in solution. What SAT Target Score Should You Be Aiming For? Both contain $Cl^{-}$ ions. Direct link to Brett Kramer's post If they asked for the con, Posted 6 years ago. symbol Ksp. Direct link to tyersome's post Concentration is what we . Direct link to Richard's post Jay misspoke, he should h, Posted 7 years ago. Pure solids are not included in equilibrium constant expression. Euler, William B.; Kirschenbaum, Louis J.; Ruekberg, Ben. The solubility product constant, Ksp , is the equilibrium constant for a solid substance dissolving in an aqueous solution. The 5 Strategies You Must Be Using to Improve 160+ SAT Points, How to Get a Perfect 1600, by a Perfect Scorer, Free Complete Official SAT Practice Tests. The cookie is used to store the user consent for the cookies in the category "Performance". Let's do an example: The solubility of Ag2CrO4 in water is 1.31 x 10-4 moles/L. Image used with permisison from Wikipedia. To calculate the solubility product constant, youll first need to write out the dissociation equation and balanced $K_s_p$ expression, then plug in the molar concentrations, if youre given them. We begin by setting up an ICE table showing the dissociation of CaCO 3 into calcium ions and carbonate ions. This converts it to grams per 1000 mL or, better yet, grams per liter. First, we need to write out the two equations. Calculate the molar solubility of BaSO_{4} in: a) Water b) A solution containing 1.0 M SO_{4}^{2-} ions c) Explain the difference in solubilities. Write the solubility product expression (Ksp) for the decomposition of Ag2CO3. $K_s_p$ represents how much of the solute will dissolve in solution, and the more soluble a substance is, the higher the chemistry $K_s_p$ value. The value of $K_s_p$ varies depending on the solute. Educ. Relating Solubilities to Solubility Constants. Ksp for sodium chloride is 36 mol^2/litre^2 . 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. However, the molarity of the ions is 2x and 3x, which means that [PO43] = 2.28 107 and [Ca2+] = 3.42 107. Such a solution is called saturated. How do you convert molar solubility to Ksp? It applies when equilibrium involves an insoluble salt. 1. How do you find equilibrium constant for a reversable reaction? Calculate the molar solubility of strontium chloride (Ksp 3.0 x 10) in pure water and in a solution of 0.10 M NaCI. ACT Writing: 15 Tips to Raise Your Essay Score, How to Get Into Harvard and the Ivy League, Is the ACT easier than the SAT? You do this because of the coefficient 2 in the dissociation equation. The concentration of Mg2+ ion in the solution was found to be 2.34 x 10-4 M. Calculate the Ksp for MgF2. In like manner, there is a 1:1 molar ratio between dissolved AgBr and Br in solution. The solubility product of barium fluoride (BaF2) is 2 x 10-6 at 25 C. From the balanced dissolution equilibrium, determine the equilibrium concentrations of the dissolved solute ions. The common ion effect states that when two solutions that share a common ion are mixed, the solute with the smaller $K_s_p$ value will precipitate first. This would mean the $K_s_p$ unit would be different for every problem and would be difficult to solve, so in order to make it simpler, chemists generally drop $K_s_p$ units altogether. Its easier for the solvent to surround smaller molecules, so those molecules can be dissolved faster than larger molecules. Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. In the case of a simple 1:1 solid such as AgCl, this would just be the concentration of Ag + or Cl - in the saturated solution. Will barium sulfate precipitate if 10.0 mL of 0.0020 M Na2SO4 is added to 100 mL of 3.2 104 M BaCl2? What is the Ksp of Cupric Carbonate (aqueous solution) if molar solubility is 1.52 x 10-5 M? 1998, 75, 1179-1181 and J. Chem. Get the latest articles and test prep tips! The values given for the Ksp answers are from a reference source. Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. Small math error on his part. This can be flipped to calculate pH from hydronium concentration: pH = log[H3O +] An acidic solution is one that has an excess of H3O + ions compared to OH ions. The solubility product (Ksp) is used to calculate equilibrium concentrations of the ions in solution, whereas the ion product (Q) describes concentrations that are not necessarily at equilibrium. write the Ksp expression from the balanced equation. The cookie is used to store the user consent for the cookies in the category "Analytics". Click, We have moved all content for this concept to. You need to ask yourself questions and then do problems to answer those questions. How do you calculate pH from hydrogen ion concentration? Our goal was to calculate the molar solubility of calcium fluoride. Createyouraccount. What is the pH of a saturated solution of Mn(OH)2? of an ionic compound. Calcium carbonate, CaCO3 has a Ksp value of 1.4 10^-8 . Putting the values into the Ksp expression, we obtain: Example #4: Calculate the Ksp for Ce(IO3)4, given that its molar solubility is 1.80 x 104 mol/L. Using this equation, Ksp values can be calculated if the concentrations of the ions are known. How can Ksp be calculated? Ag_{2}CO_{3}, K_{sp} = 8.5*10^{-12} 4. to just put it in though to remind me that X in fluoride will dissolve, and we don't know how much. Silver nitrate (AgNO3) has Ksp = 1.8 x 10 I. Ksp of PbCl2 was found to be 1.59 105. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. concentration of calcium two plus and 2X for the equilibrium Plug in your values and solve the equation to find the concentration of your solution. Example: Estimate the solubility of barium sulfate in a 0.020 Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. For the reaction $A_aB_b$(s) $aA^b^{+}$(aq) + $bB^a^{-}$ (aq), The solubility expression is $K_s_p$= $[A^b^{+}]^a$ $[B^a^{-}]^b$. Convert the solubility of the salt to moles per liter. - [Instructor] Let's calculate the molar solubility of calcium fluoride if the Ksp value for calcium fluoride is 3.9 times 10 to the negative $K_s_p$ is known as the solubility constant or solubility product. So we can go ahead and put a zero in here for the initial concentration In this case, we treat the problem as a typical equilibrium problem and set up a table of initial concentrations, changes in concentration, and final concentrations (ICE Tables), remembering that the concentration of the pure solid is essentially constant. The general equilibrium constant for such processes can be written as: Since the equilibrium constant refers to the product of the concentration Convert the solubility of the salt to moles per liter. For dilute solutions, the density of the solution is nearly the same as that of water, so dissolving the salt in 1.00 L of water gives essentially 1.00 L of solution. By clicking Accept, you consent to the use of ALL the cookies. The F concentration is TWICE the value of the amount of CaF2 dissolving. negative 11th is equal to X times 2X squared. Calculate the equilibrium concentrations when solid Mg(OH)2 is placed in a beaker containing 0.050 M NaOH solution. Direct link to Nada Youssef's post At 4:55 while he was solv, Posted 6 years ago. It represents the level at which a solute dissolves in solution. The larger the negative exponent the less soluble the compound is in solution. of ionic compounds of relatively low solubility. An basic (or alkaline) solution is one that has an excess of OH ions compared to H3O + ions. The molar solubility of Pbl_2 is 1.5 \times 10^{-3} mol/L. Whereas Ksp describes equilibrium concentrations, the ion product describes concentrations that are not necessarily equilibrium concentrations. Need more help with this topic? ADVERTISEMENT MORE FROM REFERENCE.COM of calcium two plus ions. How to calculate number of ions from moles. Yes! of calcium two plus ions. This would mean the $K_s_p$ unit would be different for every problem and would be difficult to solve, so in order to make it simpler, chemists generally drop $K_s_p$ units altogether. a. of the fluoride anions. copyright 2003-2023 Homework.Study.com. First, determine How to calculate solubility of salt in water. Calculate the value of Ksp . This cookie is set by GDPR Cookie Consent plugin. Its solubility product is 1.08 1010 at 25C, so it is ideally suited for this purpose because of its low solubility when a barium milkshake is consumed by a patient. Solubility product constants are used to describe saturated solutions 3. Next we need to solve for X. In order to write $K_s_p$ expressions correctly, you need to have a good knowledge of chemical names, polyatomic ions, and the charges associated with each ion. Write the solubility product expression (Ksp) for the decomposition of Ag2CO3. The next step is to liter. 2 times 2 is 4 and x times x is x^2, so 2x times 2x equals 4x^2. How to calculate concentration in mol dm-3. The concentration of magnesium increases toward the tip, which contributes to the hardness. To calculate exactly how much dissolves, you use K sp, the solubility product constant, along with an expression derived from the solubility equilibrium reaction for the substance. Calcite, a structural material for many organisms, is found in the teeth of sea urchins. Write the balanced equilibrium equation for the dissolution reaction and construct a table showing the concentrations of the species produced in solution. b. Concentration is what we care about and typically this is measured in Molar (moles/liter). These cookies ensure basic functionalities and security features of the website, anonymously. So to solve for X, we need Simply use a scale to measure the mass of the solute and the final solution and express the ratio as a percentage. Calculate the value for K sp of Ca(OH) 2 from this data. When a transparent crystal of calcite is placed over a page, we see two images of the letters. In our calculation, we have ignored the reaction of the weakly basic anion with water, which tends to make the actual solubility of many salts greater than the calculated value. For highly soluble ionic compounds the ionic activities must be found instead of the concentrations that are found in slightly soluble solutions. (b) If the K_{ sp} for copper(II) carbonate is 1.4 times 10^{-10}, determine the concentration of Cu^{2+} in a saturated solution. Will a precipitate of This page will be removed in future. The solubility product constant, \(K_{sp}\), is the equilibrium constant for a solid substance dissolving in an aqueous solution. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. Answer 4.5 10 9 The reaction of weakly basic anions with H 2 O tends to make the actual solubility of many salts higher than predicted. Martin, R. Bruce. Therefore, if we know the Ksp of the reaction, we can calculate the x, molar solubility of the reaction. hbspt.cta.load(360031, '4efd5fbd-40d7-4b12-8674-6c4f312edd05', {}); Have any questions about this article or other topics? Our vetted tutor database includes a range of experienced educators who can help you polish an essay for English or explain how derivatives work for Calculus. concentration of fluoride anions. Video transcript. Calculate the concentration of NH_3 required to just dissolve 0.022 mol of NiC_2O_4 (K_sp = 4.0 x 10^-10) in 1.00 L of solution. So if we're losing X for the concentration of calcium fluoride, we must be gaining X for the concentration of Actually, it doesnt have a unit! 33108g/L. H2O] is a sparingly soluble salt that is the other major component of kidney stones [along with Ca3(PO4)2]. (Hint: Use pH to get pOH to get [OH]. The $K_s_p$ values are for when the substances are around 25 degrees Celsius, which is standard. Legal. Are solubility and molarity the same when dealing with equilibrium? with 75.0 mL of 0.000125 M lead(II) nitrate. What ACT target score should you be aiming for? Direct link to Sophie Butt's post At around 4:53, why do yo, Posted 7 years ago. The Ksp of La(IO3)3 is 6.2*10^-12. Recall that NaCl is highly soluble in water. All Modalities Calculating Ksp from Solubility Loading. calcium two plus ions, and since there's a coefficient of one in the balanced equation, that's the concentration Temperature affects the solubility of both solids and gases but hasnt been found to have a defined impact on the solubility of liquids. Necessary cookies are absolutely essential for the website to function properly. He is using a calculator simulator, so it might be a bit different from a normal graphing calculator. \[Ag_2CrO_{4(s)} \rightleftharpoons 2Ag^+_{(aq)} + CrO^{2-}_{4(aq)}\nonumber \], \[K_{sp} = [Ag^{+}]^2[CrO_4^{2-}]\nonumber \]. Example #5: Calculate the Ksp for Mg3(PO4)2, given that its molar solubility is 3.57 x 10-6 mol/L. Solving K sp Problems I: Calculating Molar Solubility Given the K sp. In order to determine whether or not a precipitate What is the concentration of OH- ions in 0.125M Ba(OH)2 solution? As summarized in Figure \(\PageIndex{1}\) "The Relationship between ", there are three possible conditions for an aqueous solution of an ionic solid: The process of calculating the value of the ion product and comparing it with the magnitude of the solubility product is a straightforward way to determine whether a solution is unsaturated, saturated, or supersaturated. a common ion must be taken into account when determining the solubility Example: Calculate the solubility product constant for Looking back over my notes that I took over the Khanacademy MCAT prep videos I don't see any examples with this, but doing just a little research you can confirm that the coefficients are incorporated when determining any equilibrium expression (even if it is just 1). our salt that dissolved to form a saturated As a reminder, a solute (what is being dissolved) is considered soluble if more than 1 gram of it can be completely dissolved in 100 ml of water. Click, SCI.CHE.916 (Calculating Ksp from Solubility - Chemistry). What is concentration in analytical chemistry? Ion. This is shown below: Note that the reactant, aA, is not included in the \(K_{sp}\) equation. that occurs when the two soltutions are mixed. For what it's worth, my "Handbook of Chemistry and Physics" gives the Ksp as 9.86 x 1025. are combined to see if any of them are deemed "insoluble" base on solubility Direct link to Seth Sturgill's post You actually would use th, Posted 7 years ago. Determine the molar solubility. This website uses cookies to improve your experience while you navigate through the website. There is a 1:1 ratio between Hg2Br2 and Hg22+, BUT there is a 1:2 ratio between Hg2Br2 and Br. The K_{sp} of Ag_2SO_3 is 1.50 times 10^{-14}. In finding the \, K_{sp}\, of the dissociation of \, \text{PbCl}_2\, to \, \text{Pb}\, and \, 2\text{Cl},\, why does the equation for \, K_{sp}\, have the form \qquad K_{sp} = \lbrack x\rbrack \lbrack 2x\rbrack^2 \, (and not of the form \, K_{sp} =. We saw that the Ksp for Ca3(PO4)2 is 2.07 1033 at 25C. See Answer. we need to make sure and include a two in front Our experts can answer your tough homework and study questions. A compound's molar solubility in water can be calculated from its K. What would you do if you were asked to find the ppm of the cu2+ ion or the OH- ion? M sodium sulfate solution. Calculate the solubility of Au(OH)3 in water (Ksp=5.5x10^46). To log in and use all the features of Khan Academy, please enable JavaScript in your browser. How do you find molar solubility given Ksp and molarity? Given that the K_{sp} of MgCO_3 is 4.00 \times10^{-5}, what mass of MgCO_3 is needed to make a saturated1.00 L solution? Tabulated values of Ksp can also be used to estimate the solubility of a salt with a procedure that is essentially the reverse of the one used in Example \(\PageIndex{1}\). Example: Estimate the solubility of Ag2CrO4 The winners are: Princetons Nima Arkani-Hamed, Juan Maldacena, Nathan Seiberg and Edward Witten. { An_Introduction_to_Solubility_Products : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Calculations_Involving_Solubility_Products : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Common_Ion_Effect : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Pressure_Effects_On_the_Solubility_of_Gases : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Relating_Solubility_to_Solubility_Product : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Solubility : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Solubility_and_Factors_Affecting_Solubility : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Solubility_Product_Constant,_Ksp" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Solubility_Rules : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Temperature_Effects_on_Solubility : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Temperature_Effects_on_the_Solubility_of_Gases : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "Acid-Base_Equilibria" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Chemical_Equilibria : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Dynamic_Equilibria : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Heterogeneous_Equilibria : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Le_Chateliers_Principle : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Physical_Equilibria : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Solubilty : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "showtoc:no", "license:ccby", "solubility product constant", "licenseversion:40", "author@Kathryn Rashe", "author@Lisa Peterson" ], https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FPhysical_and_Theoretical_Chemistry_Textbook_Maps%2FSupplemental_Modules_(Physical_and_Theoretical_Chemistry)%2FEquilibria%2FSolubilty%2FSolubility_Product_Constant%252C_Ksp, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), Solubility and Factors Affecting Solubility, status page at https://status.libretexts.org.