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Monoprotic Acid-Base Equilibria Review of Fundamentals 1.)Acids and Bases are essential to virtually every application of chemistry Analytical procedures such as chromatography and electrophoresis Protein purification, chemical reactions, environmental issues Urban Stone Decay Pollutants Contribute to Acid Rain Forest Destruction Yellowstone Air Pollution (same view)

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Monoprotic Acid-Base Equilibria Review of Fundamentals 2.)Strong Acids and Bases Completely dissociates [H 3 O + ] or [OH - ] equals concentration of strong acid or base - What is the pH of a 0.1M solution of HCl? - What is the pH of a 0.1M solution of KOH?

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Monoprotic Acid-Base Equilibria Review of Fundamentals 2.)Strong Acids and Bases pH at other concentrations of a strong base Relationship between pH and pOH: [OH - ] (M)[H + ] (M)pH 1x x x x x x x x x x AcidKaKa HCl HBr HI HNO

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Monoprotic Acid-Base Equilibria Review of Fundamentals 2.)Strong Acids and Bases Dilemma: What is the pH of 1.0x10 -8 M KOH? How can a base produce an acidic solution? Wrong Assumption!!

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Monoprotic Acid-Base Equilibria Review of Fundamentals 2.)Strong Acids and Bases Wrong Assumption!! For large concentration of acid or base, [H + ] = [acid] or [OH - ] = [base] For small concentration, must account for water dissociation In pure water [OH - ] = 1.0x10 -7 M, which is greater than [KOH] = 1x10 -8 M Must Use Systematic Treatment of Equilibrium

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Monoprotic Acid-Base Equilibria Review of Fundamentals 2.)Strong Acids and Bases Systematic Treatment of Equilibrium Step 1: Pertinent reactions: KwKw Step 2: Charge Balance: Step 3: Mass Balance: All K + comes from KOH Completely dissociates, not pertinent

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Monoprotic Acid-Base Equilibria Review of Fundamentals 2.)Strong Acids and Bases Systematic Treatment of Equilibrium Step 4: Equilibrium constant expression (one for each reaction): Step 5: Count equations and unknowns: Three equations: Three unknowns: (1) (2) (3)

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Monoprotic Acid-Base Equilibria Review of Fundamentals 2.)Strong Acids and Bases Systematic Treatment of Equilibrium Step 6: Solve (Seeking pH [H + ]): Set [H + ] =x, and substitute mass balance equation into charge balance equation: From mass balance Substitute OH - equation into equilibrium equation:

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Monoprotic Acid-Base Equilibria Review of Fundamentals 2.)Strong Acids and Bases Systematic Treatment of Equilibrium Step 6: Solve (Seeking pH [H + ]): Solve the quadratic equation: Negative number is physically meaningless Use quadratic equation pH slightly basic, consistent with low [KOH]

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Monoprotic Acid-Base Equilibria Review of Fundamentals 2.)Strong Acids and Bases Systematic Treatment of Equilibrium Three Regions depending on acid/base concentrations High concentrations (≥10 -6 M), pH considered just from the added H +,OH - low concentrations (≤10 -8 M), pH=7 not enough H +,OH - added to change pH intermediate concentrations, ( M), H 2 O ionization ≈ H +,OH - systematic equilibrium calculation necessary

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Monoprotic Acid-Base Equilibria Review of Fundamentals 3.)Water Almost Never Produces M H + and OH - pH=7 only true for pure water Any acid or base suppresses water ionization - Follows Le Châtelier’s principal In M HBr solution, water dissociation produces only M OH - and H +

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Monoprotic Acid-Base Equilibria Review of Fundamentals 4.)Weak Acids and Bases Weak acid/base do not completely dissociate Dissociation K a for the acid HA: Base Hydrolysis constant K b pK is negative logarithm of equilibrium constant -As K a or K b increase pK a or pK b decrease - Smaller pK a stronger acid

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Monoprotic Acid-Base Equilibria Review of Fundamentals 4.)Weak Acids and Bases Conjugate acid-base pair – related by the gain or loss of a proton -Conjugate base of a weak acid is a weak base - Conjugate acid of a weak base is a weak acid -Conjugate base of a strong acid is a very weak base or salt Acid-base pair Formic acid (pK a 3.744) stronger acid than benzoic acid (pK a =4.202)

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Monoprotic Acid-Base Equilibria Weak Acid Equilibria 1.)General Systematic Treatment of Equilibrium Unlike concentrated strong acid, need to account for water ionization Find pH for a solution of a general weak acid HA Step 1: Pertinent reactions: KwKw KaKa Step 2: Charge Balance: Step 3: Mass Balance: F – formal concentration of acid Step 4: Equilibrium constant expression (one for each reaction):

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Monoprotic Acid-Base Equilibria Weak Acid Equilibria 1.)General Systematic Treatment of Equilibrium Find pH for a solution of a general weak acid HA Step 5: Count equations and unknowns: Four Equations: Four Unknowns: (1) (4) (2) (3) Step 6: Solve (Not easy to solve cubic equation results!): - Again, need to make assumptions to simplify equations - The goal is to determine [H + ], so we can measure pH

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Monoprotic Acid-Base Equilibria Weak Acid Equilibria 1.)General Systematic Treatment of Equilibrium Find pH for a solution of a general weak acid HA Step 6: Solve (Not easy to solve cubic equation results!): Make Some Initial Assumptions: For a typical weak acid, [H + ] from HA will be much greater than [H + ] from H 2 O If dissociation of HA is much greater than H 2 O, [H + ] >> [OH - ] Set [H + ]=x: substitute

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Monoprotic Acid-Base Equilibria Weak Acid Equilibria 1.)General Systematic Treatment of Equilibrium Find pH for a solution of a general weak acid HA Step 6: Solve (Not easy to solve cubic equation results!): Substitute into Equilibrium Equation: Rearrange: Solve quadratic equation:

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Monoprotic Acid-Base Equilibria Weak Acid Equilibria 1.)General Systematic Treatment of Equilibrium Find pH for a solution of a general weak acid HA Step 7: Verify Assumption: Was the approximation [H + ] ≈ [A - ] justified ([H + ] >>[OH - ])? Setting F = M and K a = 1.07x10 -3 for o-hydroxybenzoic acid: Determine [OH - ] from water dissociation: [H + ] >> [OH - ] 6.8x10 -3 M >> 1.5x M assumption is justified!

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Monoprotic Acid-Base Equilibria Weak Acid Equilibria 2.)Fraction of Dissociation Fraction of acid HA in the form A - ( ): Example: Percent dissociation increases with dilution What is the percent fraction dissociation for F = M and K a = 1.07x10 -3 for o-hydroxybenzoic acid?

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Monoprotic Acid-Base Equilibria Weak Base Equilibria 1.)Treatment of Weak Base is Very Similar to Weak Acid Assume all OH - comes from base and not dissociation of water Step 1: Pertinent reactions: KwKw KbKb Step 2: Charge Balance: Step 3: Mass Balance: F – formal concentration of base Step 4: Equilibrium constant expression (one for each reaction):

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Monoprotic Acid-Base Equilibria Weak Base Equilibria 1.)Treatment of Weak Base is Very Similar to Weak Acid Assume all OH - comes from base and not dissociation of water Step 6: Solve (Assume [BH + ] >> [H + ] [BH + ] ≈ [OH-]): Set [OH - ]=x and substitute into Equilibrium Equation: Rearrange: Solve quadratic equation:

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Monoprotic Acid-Base Equilibria Weak Base Equilibria 2.)Example What is the pH of cocaine dissolved in water? F = M and K b = 2.6x10 -6 for cocaine? x x x K b =2.6x10 -4

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Monoprotic Acid-Base Equilibria Weak Base Equilibria 2.)Example What is the pH of cocaine dissolved in water? F = M and K b = 2.6x10 -6 for cocaine? Because x=[OH - ], we need to solve for [H + ]

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Monoprotic Acid-Base Equilibria Weak Base Equilibria 4.)Fraction of Association Fraction of Base B in BH + form ( ): Example: What is the percent fraction dissociation of cocaine reacted with water? F = M and K b = 2.6x10 -6 for cocaine?

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Monoprotic Acid-Base Equilibria Weak Acid Base Equilibria 5.)Example A M solution of benzoic acid has a pH of Calculate pK a for this acid. What is the percent fraction dissociation?

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Monoprotic Acid-Base Equilibria Buffers 1.)A buffered solution resists changes in pH when acids or bases are added Buffer: is a mixture of a weak acid and its conjugate base - Must be comparable amounts of acid & base For an organism to survive, it must control the pH of each subcellular compartments - Enzyme-catalyzed reactions are pH dependent Thermophilic archaea Picrophilus oshimae and Picrophilus torridus grow at pH =0.7 (Stomach acid 1-3 pH) Nature (London) (1995), 375(6534), Bacteria growing in hot springs (acidic pH) Bacteria growing in lung tissues (neutral pH)

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Monoprotic Acid-Base Equilibria Buffers 2.)Mixing a Weak Acid and Its Conjugated Base Very little reaction occurs Very little change in concentrations Example: Consider a 0.10 M of acid with pK a of x x x

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Monoprotic Acid-Base Equilibria Buffers 2.)Mixing a Weak Acid and Its Conjugated Base Example: Consider adding 0.10 M of conjugate base with pK b of x x x HA dissociates very little and A - reacts very little with water

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Monoprotic Acid-Base Equilibria Buffers 3.)Henderson-Hasselbalch Equation Rearranged form of K a equilibrium equation: Take log of both sides: rearrange: pH pKa

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Monoprotic Acid-Base Equilibria Buffers 3.)Henderson-Hasselbalch Equation Determines pH of buffered solution - Need to know ratio of conjugate [acid] and [base] - If [A - ] = [HA], pH = pK a - All equilibria must be satisfied simultaneously in any solution at equilibrium - Only one concentration of H + in a solution Similar equation for weak base and conjugate acid pKa is for this acid [A - ]/[HA]pH 100:1pK a :1pK a + 1 1:1pKapKa 1:10pK a - 1 1:100pK a - 2

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Buffers 3.)Henderson-Hasselbalch Equation A strong acid and a weak base react “completely” to give the conjugate acid: Also, a strong base and a weak acid react “completely” to give the conjugate base: Monoprotic Acid-Base Equilibria Weak base Strong acid conjugate acid Weak acid Strong base conjugate base

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Monoprotic Acid-Base Equilibria Buffers 3.)Henderson-Hasselbalch Equation Example: Calculate how many milliters of M KOH should be added to 5.00 g of MOBS to give a pH of 7.40? What is the pH if an additional 5 mL of the KOH solution is added? FW = pK a = 7.48

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Monoprotic Acid-Base Equilibria Buffers 4.)Why Does a Buffer Resist Changes in pH? Strong acid or base is consumed by B or BH + Maximum capacity to resist pH change occurs at pH=pK a Buffer Capacity ( ): measure of a solutions resistance to pH change 5.)Choosing a Buffer Choose a buffer with pK a as close as possible to desired pH Useful buffer range is pK a ± 1 pH units Buffer pH depends on temperature and ionic strength activity coefficients where Ca and Cb are the number of moles of strong acid and strong base per liter needed to produce a unit change in pH

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When preparing a buffer, you need to monitor the pH. Can not assume the added HA and A - will yield the desired pH. pH dependent on: - activity - temperature - ionic strength

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Wide number of buffers available that cover an essential complete range of pHs. Choose a buffer with a pK a as close as possible to the desired pH.

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