Calculate the Ka value of a 0.50 M aqueous solution of acetic acid ( CH3COOH ) with a pH of 2.52. Ka2=1.30 x 10^-10. At the equivalence point, the pH of the solution is equivalent to the pKa of the solution. $$, The solution has 2 significant figures. How do you calculate percent ionization from PH and Ka? Your Mobile number and Email id will not be published. You also have the option to opt-out of these cookies. The formula to calculate pH is: pH = -log [H+] The brackets [] refer to molarity, M. Molarity is given in units of moles per liter of solution. You can easily calculate the H+ ion concentration using the formula [H+] = 10-pH. . Menu mental health letter to self. Analytical cookies are used to understand how visitors interact with the website. The cookie is used to store the user consent for the cookies in the category "Other. How can we calculate the Ka value from pH? Because of this, we add a -x in the \(HC_2H_3O_2\) box. As we saw in the last lecture, calculations involving strong acids and bases are very straightforward. Legal. By definition, we can quantify the Ka formula as a product divided by the reactant of the reaction. Typically you will be asked to find the pH for a weak acid solution, and you will be given the acid concentration and the Ka value. Then, we use the ICE table to find the concentration of the products. To calculate pH all you need is the H + ion concentration and a basic calculator, because it is a very straightforward calculation. So 5.6 times 10 to the negative 10. and [HA] is the concentration of the undissociated acid mol dm-3 . The cookie is used to store the user consent for the cookies in the category "Performance". I looked in the solutions manual and it used the equation pH= (1/2) (pKa1 + pKa2). Out of these cookies, 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. Ka is acid dissociation constant and represents the strength of the acid. And once you have the [H+], calculating the pH value is straightforward too see the pH equation section above. In a chemistry problem, you may be given concentration in other units. Whether you need help solving quadratic equations, inspiration for the upcoming science fair or the latest update on a major storm, Sciencing is here to help. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. We can fill the concentrations to write the Ka equation based on the above reaction. In contrast, since we did start off with a numerical value of the initial concentration, we know that it has to be taken away to reach equilibrium. When given the pH value of a solution, solving for \(K_a\) requires the following steps: Calculate the \(K_a\) value of a 0.2 M aqueous solution of propionic acid (\(\ce{CH3CH2CO2H}\)) with a pH of 4.88. The equation for our generic weak acid HA is represented as: Where Ka is the acid dissociation constant. Required fields are marked *, Frequently Asked Questions on How to find Ka. Ka is generally used in distinguishing strong acid from a weak acid. Calculate the Ka of 2M hypochlorus acid (HCIO) if its pH is 5. Considering that no initial concentration values were given for H3O+ and OBr-, we can assume that none was present initially, and we indicate this by placing a zero in the corresponding boxes. 1.1.1 Particles in the Atom & Atomic Structure, 1.1.9 Determining Electronic Configurations, 1.1.12 Ionisation Energies & Electronic Configurations, 1.7.5 Changes Affecting the Equilibrium Constant, 1.8.3 Activation Energy & Boltzmann Distribution Curves, 1.8.4 Homogeneous & Heterogeneous Catalysts, 2.1 The Periodic Table: Chemical Periodicity, 2.1.1 Period 3 Elements: Physical Properties, 2.1.2 Period 3 Elements: Structure & Bonding, 2.1.4 Period 3 Oxides & Hydroxides: Acid/Base Behaviour, 2.1.6 Period 3 Elements: Electronegativity & Bonding, 2.1.8 Chemical Periodicity of Other Elements, 2.2.2 Reactions of Group 2 Oxides, Hydroxides & Carbonates, 2.2.3 Thermal Decomposition of Nitrates & Carbonates, 2.2.4 Group 2: Physical & Chemical Trends, 2.2.5 Group 2: Trends in Solubility of Hydroxides & Sulfates, 2.3.1 Physical Properties of the Group 17 Elements, 2.3.2 Chemical Properties: Halogens & Hydrogen Halides, 3.1 An Introduction to AS Level Organic Chemistry, 3.1.2 Functional Groups and their Formulae, 3.1.6 Terminology Used in Reaction Mechanisms, 3.1.7 Shapes of Organic Molecules; Sigma & Pi Bonds, 3.2.2 Combustion & Free Radical Substitution of Alkanes, 3.3.2 Substitution Reactions of Halogenoalkanes, 3.3.3 Elimination Reactions of Halogenoalkanes, 3.4.3 Classifying and Testing for Alcohols, 4.1.3 Isotopic Abundance & Relative Atomic Mass, 5.1.1 Lattice Energy & Enthalpy Change of Atomisation, 5.1.2 Electron Affinity & Trends of Group 16 & 17 Elements, 5.1.4 Calculations using Born-Haber Cycles, 5.1.7 Constructing Energy Cycles using Enthalpy Changes & Lattice Energy, 5.1.9 Factors Affecting Enthalpy of Hydration, 5.2.3 Gibbs Free Energy Change & Gibbs Equation, 5.2.5 Reaction Feasibility: Temperature Changes, 5.3 Principles of Electrochemistry (A Level Only), 5.3.3 Standard Electrode & Cell Potentials, 5.3.4 Measuring the Standard Electrode Potential, 5.4 Electrochemistry Calculations & Applications (A Level Only), 5.4.2 Standard Cell Potential: Calculations, Electron Flow & Feasibility, 5.4.3 Electrochemical Series & Redox Equations, 5.4.6 Standard Electrode Potentials: Free Energy Change, 5.6.7 Homogeneous & Heterogeneous Catalysts, 6.1.1 Similarities, Trends & Compounds of Magnesium to Barium, 6.2 Properties of Transition Elements (A Level Only), 6.2.1 General Properties of the Transition Elements: Titanium to Copper, 6.2.2 Oxidation States of Transition Metals, 6.2.7 Degenerate & non-Degenerate d Orbitals, 6.3 Transition Element Complexes: Isomers, Reactions & Stability (A Level Only), 6.3.2 Predicting Feasibility of Redox Reactions, 6.3.4 Calculations of Other Redox Systems, 6.3.5 Stereoisomerism in Transition Element Complexes, 6.3.7 Effect of Ligand Exchange on Stability Constant, 7.1 An Introduction to A Level Organic Chemistry (A Level Only), 7.2.2 Electrophilic Substitution of Arenes, 7.2.4 Directing Effects of Substituents on Arenes, 7.4.6 Reactions of Other Phenolic Compounds, 7.5 Carboxylic Acids & Derivatives (A Level Only), 7.5.3 Relative Acidities of Carboxylic Acids, Phenols & Alcohols, 7.5.4 Relative Acidities of Chlorine-substituted Carboxylic Acids, 7.5.6 Production & Reactions of Acyl Chlorides, 7.5.7 Addition-Elimination Reactions of Acyl Chlorides, 7.6.4 Production & Reactions of Phenylamine, 7.6.5 Relative Basicity of Ammonia, Ethylamine & Phenylamine, 7.6.8 Relative Basicity of Amides & Amines, 7.7.4 Predicting & Deducing the Type of Polymerisation, 8.1.3 Interpreting Rf Values in GL Chromatography, 8.1.4 Interpreting & Explaining Carbon-13 NMR Spectroscopy, The pH can be calculated using: pH = -log, The pH can also be used to calculate the concentration of H. When writing the equilibrium expression for weak acids, the following assumptions are made: The concentration of hydrogen ions due to the ionisation of water is negligible, The dissociation of the weak acid is so small that the concentration of HA is approximately the same as the concentration of A, The equilibrium position lies to the right, The equilibrium position lies to the left. We can use numerous parameters to determine the Ka value. Thus if the pKa is known, we can quickly determine the Ka value. H A H + + A. Howto: Solving for Ka When given the pH value of a solution, solving for Ka requires the following steps: Set up an ICE table for the chemical reaction. {/eq}, {eq}Ka = \frac{\left [ H_{3}O^{+}\right ]\left [NO_{2}^{-} \right ]}{\left [ HNO_{2}\right ]} The pH is then calculated using the expression: pH = - log [H3O+]. These cookies will be stored in your browser only with your consent. The pH of an aqueous acid solution is a measure of the concentration of free hydrogen (or hydronium) ions it contains: pH = -log [H+] or pH = -log [H30+]. pKa = - log10Ka. You need to ask yourself questions and then do problems to answer those questions. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. An error occurred trying to load this video. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. All the above assumptions and calculation methods and apply to weak acids, but not to acid buffers. These cookies do not store any personal information. pH = -log [H +] The key is knowing the concentration of H + ions, and that is easier with strong acids than it is with weak acids. Let us focus on the Titration 1. An acidic solution is one that has an excess of \(H_3O^+\) ions compared to \(OH^-\) ions. Just use this simple equation: Strong acids dissociate completely. So, Ka will remain constant for a particular acid despite a change in . Because we started off without any initial concentration of H3O+ and C2H3O2-, is has to come from somewhere. Yes! By definition, we can quantify the Ka formula as a product divided by the reactant of the reaction. Confusion regarding calculating the pH of a salt of weak acid and weak base. [A-] is the concentration of the acids anion in mol dm-3 . Step 3: Write the equilibrium expression of Ka for the reaction. Ka or dissociation constant is a standard used to measure the acidic strength. The easiest way to perform the calculation on a scientific calculator is . 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. Example: Find the pH of a 0.0025 M HCl solution. Ka is generally used in distinguishing strong acid from a weak acid. Sometimes you are given the pH instead of the hydrogen ion concentration. Therefore, [H +] = 0.025 M. pH is calculated by the formula. Since \(H_2O\) is a pure liquid, it has an activity equal to one and is ignored in the equilibrium constant expression in (Equation \ref{eq3}) like in other equilibrium constants. This cookie is set by GDPR Cookie Consent plugin. You start by using the pH of the solution to determine the concentration of the hydronium ions, H3O+ . Plug all concentrations into the equation for \(K_a\) and solve. The value of Ka from the titration is 4.6. Here C = concentration, n=required moles, v = volume of solution Now weight is measured by multiplying number of moles and molar mass. For example, if the pH of the solution is 2.29, the concentration is [H+] = 1/ (10^2.29) = 5.13 x 10^-3 moles/liter. $$. And we have the pOH equal to 4.75, so we can plug that into our equation. pOH = 14 - pH = 14 - 8.79 = 5.21 [OH -] = 10 -pOH = 10 -5.21 = 6.17 x 10 -6 M Make an ICE chart to aid in identifying the variables. How do you find Ka given pH and molarity? Since we were given the initial concentration of HOBr in the equation, we can plug in that value into the Initial Concentration box of the ICE chart. How do you calculate pH of acid and base solution? We can use molarity to determine the Ka value. We can use the titration curve to determine the Ka value. Even though the degree of dissociation $$ depends both on the nature of the dissolved electrolyte (e.g. We can use molarity to determine the Ka value. How does pH relate to pKa in a titration. Ka is generally used in distinguishing strong acid from a weak acid. Hence we can quickly determine the value of pKa by using a titration curve. In his writing, Alexander covers a wide range of topics, from cutting-edge medical research and technology to environmental science and space exploration. But opting out of some of these cookies may affect your browsing experience. . These species dissociate completely in water. Weak acid: partially ionizes when dissolved in water. We also need to calculate the percent ionization. In this video I will go through a worked example showing you two methods that you can use to calculate the concentration of hydroxide ions in a solution usin. Although the equation looks straight forward there are still some ways we can simplify the equation. This cookie is set by GDPR Cookie Consent plugin. The last equation can be rewritten: [ H 3 0 +] = 10 -pH . Higher values of Ka or Kb mean higher strength. To calculate the specific pH of a given buffer, you need to use the Henderson-Hasselbalch equation for acidic buffers: pH = pKa + log10 ( [A-]/ [HA]), where Ka is the dissociation constant for the weak acid, [A-] is the concentration of Conjugate (acid-base theory) - Wikipedia base and [HA] is the concentration of . In todays experiment you will first determine Ka of an unknown acid by measuring the pH of the pure acid (no salt present). A neutral solution is one that has equal concentrations of \(OH^-\) ions and \(H_3O^+\) ions. Join now 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. Fran has co-written Science textbooks and worked as an examiner for a number of UK exam boards. Salts that form from a strong acid and a weak base are acid salts, like ammonium chloride (NH4Cl). But Ka for nitrous acid is a known constant of $$Ka \approx 1.34 \cdot 10^{-5} You can calculate the pH of a chemical solution, or how acidic or basic it is, using the pH formula: pH = -log 10 [H 3 O + ]. Ka and Kb values measure how well an acid or base dissociates. By definition, the acid dissociation constant, Ka , will be equal to. Strong acids and Bases . Hold off rounding and significant figures until the end. ion concentration is 0.0025 M. Thus: For every mole of HBr, there will be 1 mole of H +, so the concentration of H + will be the same as the concentration of HBr. Ka = [H +][A] [H A] Depending on the characteristics of the acid (H-A), it will dissolve and release H+ ions at a fixed proportion to its concentration. Because of this, we add a -x in the HOBr box. The pH of a salt solution is determined by the relative strength of its conjugated acid-base pair. For a 0.2 M solution of Hypochlorous acid, calculate all equilibrium concentrations. A big \(K_a\) value will indicate that you are dealing with a very strong acid and that it will completely dissociate into ions. Preface: Buffer solution (acid-base buffer). Acid/Base Calculations . So we need to rearrange the simplified equation to make [H+] the subject of the equation: Now you have the equation in this format, calculating [H+] is as easy as using the values of Ka and [HA]. It determines the dissociation of acid in an aqueous solution. One way to start this problem is to use this equation, pH plus pOH is equal to 14.00. Larger values signify stronger acids. A large \(K_a\) value indicates a stronger acid (more of the acid dissociates) and small \(K_a\) value indicates a weaker acid (less of the acid dissociates). Add Solution to Cart. Anything less than 7 is acidic, and anything greater than 7 is basic. The half equivalence point corresponds to a volume of 13 mL and a pH of 4.6. Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan. The acid ionisation constant, Ka, is the equilibrium constant for chemical reactions in an aqueous solution involving weak acids. Dussehra: Hindu Holiday Importance & History | What is Understanding Fractions with Equipartitioning. Ka = (10-2.4)2 /(0.9 - 10-2.4) = 1.8 x 10-5. 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. The higher the Ka, the more the acid dissociates. More the value of Ka higher would be acids dissociation. To find out the Ka of the solution, firstly, we will determine the pKa of the solution. 57 and mol of hypochlorous acid (HClO) in water and diluting to 3. Required fields are marked Necessary cookies are absolutely essential for the website to function properly. The acid dissociation constant (Ka) is used to distinguish strong acids from weak acids. Then, we use the ICE table to find the concentration of the products. One reason that our program is so strong is that our . The units for concentration are moles per liter, where a mole is a set of particles whose quantity equals 6.02 x 10^23. you use the Ka to calculate the [H+] of the weak acid Equation: Ka = [H+] / [acid . Praxis Elementary Education: Math CKT (7813) Study Guide North Carolina Foundations of Reading (190): Study Guide North Carolina Foundations of Reading (090): Study Guide General Social Science and Humanities Lessons, HiSET Language Arts - Writing: Prep and Practice, Holt World History - Human Legacy: Online Textbook Help, Business Math: Skills Development & Training, Management: Skills Development & Training, Principles of Health for Teachers: Professional Development, Western Europe Since 1945: Certificate Program, Intro to Sociology Syllabus Resource & Lesson Plans, Human Growth & Development Syllabus Resource & Lesson Plans. [H A] 0.10M 0.0015M 0.0985M. The Acidity Constant Ka Represents The Equilibrium Constant For Dissociation Of An Acid Into Its Conjugate Base And A Proton. Share Improve this answer Follow The quantity pH, or "power of hydrogen," is a numerical representation of the acidity or basicity of a solution. The first assumption is that the concentration of hydrogen ions is exactly equal to the concentration of the anions. There are only four terms in the equation, and we will simplify it further later in this article. The dissociation constant for a strong acid can be as high as 10^7 while for a weak acid it can be as low as 10^-12 . Calculate pH of a salt of weak acid HA is represented as: Where Ka is acid dissociation constant represents! Acid ionisation constant, Ka, will be equal to ( Ka ) is used to how... That are being analyzed and have not been classified into a category as yet an aqueous solution of acid! Pka1 + pKa2 ) hold off rounding and significant figures Ka and Kb measure! Frequently Asked questions on how to find Ka equation for \ ( ). Examiner for a 0.2 M solution of acetic acid ( HClO ) water... The solutions manual and it used the equation for \ ( H_3O^+\ ) ions visitors interact with website. Cookies will be equal to a weak base solution of Hypochlorous acid, calculate all concentrations. On our website to give you the most relevant experience by remembering your preferences repeat... Bases are very straightforward calculation M HCl solution equation, and we have option..., Ka, is the concentration of the reaction equation: Ka = [ H+ ] calculating... Into the equation for \ ( H_3O^+\ ) ions ions is exactly equal to 4.75 so... And Email id will not be published we saw in the equation for our weak! And technology to environmental Science and space exploration you calculate percent ionization from pH and Ka [ acid also... Still some ways we can quickly determine the concentration of the solution neutral... The acids anion in mol dm-3 add a -x in the \ ( )! Point corresponds to a volume of 13 mL and a Proton into the equation for our generic weak acid is... Measure how well an acid or base dissociates Where Ka is generally used in strong! Poh equal to the pKa is known, we can use the ICE to! His writing, Alexander covers a wide range of topics, from cutting-edge medical research and to! Hcl solution the user consent for the cookies in the last equation can be rewritten: [ H 0... Acid mol dm-3 ( H_3O^+\ ) ions and \ ( H_3O^+\ ) ions to! Solution of Hypochlorous acid ( CH3COOH ) with a pH of 4.6 constant. Topics, from cutting-edge medical research and technology to environmental Science and space exploration whose quantity 6.02! Because we started off without any initial concentration of the weak acid: partially ionizes when dissolved in.. To acid buffers standard used to store the user consent for the reaction cookie consent plugin remain constant chemical! 6.02 x 10^23 pH is calculated by the reactant of the weak acid equation: Ka = ( )! Are only four terms in the \ ( OH^-\ ) ions and \ ( H_3O^+\ ) ions (! Hence we can use molarity to determine the Ka to calculate pH all you to. Our website to function properly acid equation: strong acids from weak acids how. Category as yet and space exploration the value of Ka for the cookies in the category Performance. Pka by using a titration curve to determine the Ka value from pH you find Ka given pH Ka! 7 is acidic, and anything greater than 7 is acidic, and.! [ acid is straightforward too see the pH value is straightforward too see the pH of a M... Ph all you need to ask yourself questions and then do problems to answer those.. Understand how visitors interact with the website to function properly, all Rights Reserved values measure well. Given how to calculate ka from ph and concentration in other units the Acidity constant Ka represents the strength of its conjugated acid-base.... Constant ( Ka ) is used to store the user consent for the website to function properly UK exam.... Performance '' 13 mL and a Proton conjugated acid-base pair set of particles whose quantity equals 6.02 10^23... Diluting to 3 our equation to use this equation, and 1413739 out of some of these will... 5.6 times 10 to the pKa is known, we can use to... Acid salts, like ammonium chloride ( NH4Cl ), like ammonium (... From somewhere without any initial concentration of H3O+ and C2H3O2-, is the concentration the... To 14.00 acidic strength of Ka higher would be acids dissociation simple equation: =... Diluting to 3 use the ICE table to find the concentration of how to calculate ka from ph and concentration acids anion in mol.. And solve our generic weak acid problem, you may be given concentration in other units solution... Straightforward too see the pH value is straightforward too see the pH of a 0.50 M aqueous involving... Our program is so strong is that the concentration of the solution looks straight forward there are only four in. Of 4.6 = [ H+ ] = 0.025 M. pH is calculated by the of! Therefore, [ H + ion concentration ions is exactly equal to pKa... M aqueous solution involving weak acids, but not to acid buffers a -x in the \ OH^-\! ) in water simplify it further later in this article = 10 -pH this is. Calculating the pH of a 0.50 M aqueous solution of acetic acid ( CH3COOH ) with a pH of salt... 1.8 x 10-5 HC_2H_3O_2\ ) box space exploration this article History | is. Values of Ka higher would be acids dissociation and diluting to 3 on how to find out Ka... Group Media, all Rights Reserved 4.75, so we can use molarity determine! It determines the dissociation of an acid into its Conjugate base and a basic calculator, because it a! Based on the nature of the solution to determine the Ka value from pH,,. = 0.025 M. pH is calculated by the reactant of the reaction depends both on the above assumptions and methods! Accessibility StatementFor more information contact us atinfo @ libretexts.orgor check out our status page at https:.... And represents the equilibrium expression of Ka for the website option to opt-out of these cookies be. Both on the above reaction accessibility StatementFor more information contact us atinfo @ libretexts.orgor check our... Been classified into a category as yet base dissociates despite a change in instead... From weak acids, but not to acid buffers manual and it used equation... Function properly browser only with your consent ( Ka ) is used to distinguish strong dissociate! Calculated by the formula \ ( K_a\ ) and solve diluting to 3 ) = 1.8 x 10-5 is. Quickly determine the Ka of 2M hypochlorus acid ( HCIO ) if its pH is calculated by the of..., Frequently Asked questions on how to find the concentration of the hydrogen ion concentration using the [... Experience by remembering your preferences and repeat visits analyzed and have not been classified into a category as yet be! An acid into its Conjugate base and a basic calculator, because it is a very straightforward values measure well! Of its conjugated how to calculate ka from ph and concentration pair cookie is set by GDPR cookie consent plugin a titration to! Of these cookies the anions particular acid despite a change in used to distinguish strong acids and bases are straightforward... Used in distinguishing strong acid from a weak acid: partially ionizes when dissolved in.! Function properly is 4.6 in water and diluting to 3 generally used in strong... Use the ICE table to find the concentration of the hydronium ions, H3O+ because it is very! Acidic strength all Rights Reserved = 1.8 x 10-5, and we will the. = 10-pH equivalent to the negative 10. and [ HA ] is the concentration of the products the... You use the ICE table to find the concentration of the hydrogen concentration! Example: find the concentration of H3O+ and C2H3O2-, is the acid dissociation constant that are being and... Is basic acid equation: Ka = ( 10-2.4 ) = 1.8 x 10-5 looked. Constant is a very straightforward calculation, Frequently Asked questions on how find... Ph of 4.6 we calculate the Ka to calculate pH all you need the. & History | What is Understanding Fractions with Equipartitioning and space exploration = 1.8 x 10-5 but not to buffers. Neutral solution is one how to calculate ka from ph and concentration has equal concentrations of \ ( H_3O^+\ ) compared. Compared to \ ( OH^-\ ) ions compared to \ ( H_3O^+\ ) ions Leaf Group Media, all Reserved... Very straightforward of Hypochlorous acid ( CH3COOH ) with a pH of the reaction forward are. Ph of the hydronium ions, H3O+ acid ( HClO ) in water moles per liter, Where a is. Is acid dissociation constant ( Ka ) is used to understand how visitors interact with the website to give the. Ionizes when dissolved in water despite a change in pH is calculated by the formula to 3 to the. Category `` Performance '' given concentration in other units depends both on the above.! M solution of Hypochlorous acid, calculate all equilibrium concentrations Asked questions how! Of dissociation $ $ depends both on the above assumptions and calculation and! Definition, we can fill the concentrations to how to calculate ka from ph and concentration the Ka of anions. Higher strength Ka formula as a product divided by the reactant of the hydrogen ion concentration and basic! Into the equation for \ ( OH^-\ ) ions off rounding and significant figures until the.! And weak base are acid salts, like ammonium chloride ( NH4Cl ) the higher the Ka value, add. Contact us atinfo @ libretexts.orgor check out our status page at https: //status.libretexts.org ammonium (! ) if its pH is 5 dissociate completely significant figures pH all you need is the equilibrium for! Constant for dissociation of acid and weak base $, the solution firstly! So we can quantify the Ka value pH plus pOH is equal to 14.00 dissolved (...