Chem 28 – analytical chemistry
EQUILIBRIA AND EQUILIBRIUM CONSTANTS OF
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EQUILIBRIA AND EQUILIBRIUM CONSTANTS OF IMPORTANTCE TO ANALYTICAL CHEMISTRY: For the general reaction: 𝑤𝑊 + 𝑥𝑋 ↔ 𝑦𝑌 + 𝑧𝑍 𝐾 = [𝑌]
y [𝑍]
z [𝑊]
{ [𝑋]
3 Dissociation of H 2 O: 2𝐻 } 𝑂 ↔ 𝐻 • 𝑂 m + 𝑂𝐻
n 𝐾 { = [𝐻 • 𝑂 m ][𝑂𝐻
n ]
𝐴 3
y = 𝑥𝐴
ym + 𝑦𝐵
3n 𝐾 (X = [𝐴 ym ] 3 [𝐵 3n ] y
Weak Acids: 𝐻𝐴 + 𝐻
} 𝑂 ↔ 𝐻
• 𝑂 m + 𝐴 n 𝐾 e =
[𝐻 • 𝑂 m ][𝐴
n ] [𝐻𝐴] Weak Base: 𝐵 + 𝐻
} 𝑂 ↔ 𝐵𝐻 m + 𝑂𝐻
n 𝐾 € = [𝐵𝐻
m ][𝑂𝐻
n ] [𝐵] Complex Formation Equilibrium: e.g.
𝐴𝑔 m + 2𝑁𝐻 • ↔ [𝐴𝑔(𝑁𝐻 • )
] m
𝛽 = 𝐾 ‚ 𝐾 } =
[𝐴𝑔(𝑁𝐻 • ) } ] m [𝐴𝑔 m ][𝑁𝐻 • ] } Oxidation Reduction Equilibrium: e.g.
𝐹𝑒 }m + 𝐶𝑒 ƒm ↔ 𝐹𝑒
•m + 𝐶𝑒
•m
𝐾 *+/13 =
[𝐹𝑒 •m ][𝐶𝑒 •m ] [𝐹𝑒 }m ][𝐶𝑒
ƒm ]
solvents e.g.:
𝐼 }('f)
↔ 𝐼 }(1*K)
𝐾 / = [𝐼 } ] 1*K
[𝐼 } ] 'f Chemical Reactions used in Analytical Chemistry: ▪ Acid Base Reaction ▪ Precipitation, Gravimetric and Titration ▪ Redox Reactions ▪ Complex Formation
▪ Reaction should be stoichiometric ▪ Reaction should take place rapidly ▪ Reaction should be quantitative (reaction should be at least 99% complete); quantitative reaction with K eq
≥ 10 7
▪ Convenient method to follow progress of reaction to determine when it is complete ( for titration: with suitable indicator)
▪ Formation of precipitate ▪ Formation of un-ionized molecules ▪ Formation of chelates or gases e.g. strong acid + strong base reaction
▪ For ionic participants in equilibrium reactions ▪ Effect depends on ionic strength (ì) 𝜇 =
1 2 ‡ 𝐶 - 𝑍 - } Where C is the molar concentration and z is the charge Electrolyte Type ì/c
Examples 1:1
1 KI, NaClO 4
3 MgCl
2 , Na
2 SO 4 2:2
4 CaSO
4
3:2 or 2:3 15 Fe 2 (SO 4 ) 3
1:3 or 3:3 6 Na 3 PO 4 ; Al(NO 3 ) 3 Effect of Electrolytes on Ionic Equilibria: For solutions with ì of 0.1 or less, the electrolyte is independent of the kinds of ions and dependent upon the ionic strength e.g. soluble BaSO 4 is the same in solutions NaI, KNO 3 , or AlCl 3 provided the ì is the same. Source of salt effect/ electrolye effect is the electrostatic interaction and repulsive forces between electrolyte ions and ions involved in an equilibrium effective concentration of ions like Ba 2+
& SO 4 - lesser as ì of the reactions becomes greater. Activity and Activity Coefficient: 𝑎 3 = 𝛾 3 [𝑋] Where ã is the activity coefficient (which is a function of ionic strength), [X] is the molar concentration Equilibrium Calculations yield values in better agreement with experimental results than those using molar concentration
𝑎𝐴 + 𝑏𝐵 ↔ 𝑐𝐶 + 𝑑𝐷 𝐾 +f
𝑎 ‰ , 𝑎 Š / 𝑎 e ' 𝑎 € W 𝐾 +f = [𝐶 , ]𝛾 ‰ , [𝐴 ' ]𝛾 e ' ∙ [𝐷 / ]𝛾 Š / [𝐵 W ]𝛾 € W = [𝐶 , ][𝐷 / ] [𝐴 ' ][𝐵 W ] ∙ 𝛾 ‰ , 𝛾 Š / 𝛾 € W 𝛾 e ' As c i → 0, ì→0, ã i →1, and a i →[i] , Therefore K eq is in terms of concentration only in very dilute solutions e.g.
𝑋 = 𝑌 2 = 𝑚𝑋
2m + 𝑛𝑌
=m
𝐾 +f = 𝑎 L Œ• = 𝑎 Ž •• 2 𝐾 +f = [𝑋 2m ] = [𝑌 =m ] 2 𝛾 L Œ• = 𝛾 Ž •• 2 = 𝛾
L Œ• = 𝛾 Ž •• 2 ∙ 𝐾′
(X Where K’
sp is the concentration soluble product and K sp is the
thermodynamic equilibrium constant Debye-Huckel Equation – can calculate the ã theoretically − 𝑙𝑜𝑔 𝑙𝑜𝑔 (𝛾 3 ) = 0.51𝑍 3 } √𝜇 1 + 3.3𝑎
3 √𝜇
Where ã x is the activity coefficient of X, Z x the charge of x, ì the ionic strength of the solution and a x the effective diameter of hydrated ion X in nanometers (10 -9 M) Equilibrium Calculations to Complex Systems: ▪ Systematic approach for solving multiple-equilibrium problems ▪ Used to illustrate effect of pH ad complex formation on solubility where equilibria are involved
1. Keq expressions – develop n independent algebraic equations 2. Mass Balance Equations – containing n unknowns 3. A single charge-balance equation - & solve simultaneously A Systematic Method for solving Multiple-Equilibrium Problems: 1. Write the balance chemical equation (for all pertinent equilibria) 2. Set-up equation for unknown quantity ( in terms of equilibrium concentrations) 3. Write Keq expressions for all equilibria in step 1 4. Write mass-balance expressions for the system 5. Write charge-balance expressions for the system if possible 6. Count the number of equations and the number of unknowns; if the number of equations ≥unknowns, then go to step 7; if not STOP, problem unsolvable a. Make suitable approximations (to simplify algebra) and decide the number of unknowns 7. Solve equations for the unknown values 8. Check the validity using provisional answers→if valid, problem solved, if not try again and approximately recalculate *approx. can only be made in charge-balance and mass- balance equations can assume some terms negligible or use computer – several software packages available for solving multiple, nonlinear, simultaneous equations
various species in a solution to 1 another and analytical concentrations of various solutes Total or analytical concentration of a substance is equal to the equilibrium concentrations of its various species in a solution e.g. HNO
2 Solution 𝐻𝑁𝑂 }
} 𝑂 ↔ 𝐻
• 𝑂 m + 𝑁𝑂 } n 𝐶 •–—
˜ = [𝐻𝑁𝑂
} ] + 𝑁𝑂
} n ⋮ [𝐻 • 𝑂 m ] Charge-Balance Equation – apply Electroneutrality Principle (electrolyte solutions are electrically neutral) Total Concentration of (+) ions = total concentration of (-) ions Molar concentrations →molar charge concentration → multiply molar charge concentration of ion by it charge = molar charge concentration VOLUMETRIC ANALYSIS: Standard Solution (Titrant) – reagent of known concentration used in the titration Equivalence Point – point in titration when amount of the titrant is chemically equivalent to amount of analyte in sample: For any titration at equivalence point: #𝑒𝑞𝑢𝑖𝑣 𝑎𝑛𝑎𝑙𝑦𝑡𝑒 = #𝑒𝑞𝑢𝑖𝑣 𝑡𝑖𝑡𝑟𝑎𝑛𝑡 End Point – point in titration which estimates the equivalence point by observing some physical changes associated with the equivalence point ▪ Most common endpoint – color change due to titrant, analyte or indicator ▪ Can use instruments to detect endpoints, e.g. if physical property is potential or conductivity
solution is added to the analyte and excess amount of standard determined by titration with a 2 nd standard solution; required when rate of reaction between analyte and standard reagent is slow or when standard reagent lacks stability Requirements for Volumetric Chemical Reaction: ▪ Reaction must proceed according to a definite chemical reaction ▪ Reaction must be complete (K eq
7 ) ▪ Availability of a method to detect endpoint ▪ The reaction must be rapid Primary Standard – an ultrapure scompound that serves as the reference material for a titrimetric method of analysis
▪ High purity (~99.5% pure) ▪ Stability toward air ▪ Absence of hydrated H 2 O
▪ Reasonable solubility in titration medium ▪ Reasonably large molar mass or FW (minimize relative error in weighing) with required inc’s directly with FW
▪ Sufficiently stable ▪ Reacts rapidly with analyte ▪ Reacts completely with analyte ▪ Undergo selective reaction with analyte that can be described by a simple balanced equation Methods to establish concentration of standard solutions: 1. Direct Method – weighed quantity of a primary standard dissolved in suitable solvent and diluted to an exactly known volume 2. Standardization – titrant to be standardized is used to titrate: a. A weighed quantity of a primary standard b. Weighed quantity of a secondary standard (compound whose purity was determined by chemical analysis and serves as reference material for titration) c. Measured volume of another standard solution Secondary Standard Solution – titrant standardized against a 2” standard or against another standard solution Neutralization Titrations: Analytes – acids or bases that can be converted to such species by chemical treatment Standard Solutions – strong acids or strong bases (react more completely than their weaker counterparts Titration Curve: Plot some function of analyte or titrant concentration vs. V titrant
Stages of Titration: ▪ Initial point ▪ Pre-equivalence region ▪ Equivalence point ● Equivalence Point Region – large ÄpH for small ÄV
▪ Post equivalence region Effect of Concentration on Titration Curve: ÄpH at equivalence point region decreases as concentration of analyte or titrant decreases
undissociated form differs in color from its conjugate base/acid form.
𝐻𝐼𝑛 + 𝐻
} 𝑂 ↔ 𝐼𝑛 n + 𝐻
• 𝑂 m (acid color) (base color) Basic Indicator: 𝐼𝑛 + 𝐻
} 𝑂 ↔ 𝐼𝑛𝐻 m + 𝑂𝐻
n (base color) (acid color)
𝐾 ' = [𝐻 • 𝑂 m ][𝐼𝑛 n ] [𝐻𝐼𝑛] [𝐻 • 𝑂 m ] = 𝐾 ' [•š2]
[š2 › ] When [HIn]/[In - ]
When [HIn]/[In - ] ≤ 0.1: HIn exhibits its true base color [H 3 O + ] ≥ 10 K a for full acid color [H 3 O + ] ≤ 0.1 K a for full base color Indicator pH Range: 𝑝𝐻 (𝑎𝑐𝑖𝑑 𝑐𝑜𝑙𝑜𝑟) = − 𝑙𝑜𝑔 𝑙𝑜𝑔 (10 𝐾 ' ) = 𝑝𝐾
' − 1
𝑝𝐻 (𝑏𝑎𝑠𝑖𝑐 𝑐𝑜𝑙𝑜𝑟) = − 𝑙𝑜𝑔 𝑙𝑜𝑔 (0.1 𝐾 ' ) = 𝑝𝐾
' + 1
𝐼𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟 𝑝𝐻 𝑅𝑎𝑛𝑔𝑒 = 𝑝𝐾 ' ± 1
(approximate pH transition range of most acid-base indicators) Indicator Choice: ▪ Can use any indicator which could change color at the equivalence point of the titration ▪ Equivalence point region: pH 4-10; can use any indicator changing color in this region ▪ Smaller equivalence point region with dilution lessens choice of indicator
base or a weak base and its conjugate acid that resists changes in pH of a solution as a result of either dilution or small addition of acids or bases HA + A -
𝐻𝐴 + 𝐻 } 𝑂 ↔ 𝐻 • 𝑂 m + 𝐴 n 𝐻 • 𝑂 m = 𝐾 ' [𝐻𝐴] [𝐴 n ] 𝐾 ' = [𝐻 • 𝑂 m ][𝐴
n ] [𝐻𝐴] Henderson – Hasselbalch Equation: 𝑝𝐻 = 𝑝𝐾
' + 𝑙𝑜𝑔 𝑙𝑜𝑔 [𝐴 n
[𝐻𝐴]
▪ Essentially independent of dilution ▪ Resist pH change after addition of small amounts of strong acids or bases
▪ Addition of a strong base converts the acid into its conjugate base thus increasing the base and decreasing the acid leading to a small change in the ratio and a small ÄpH ▪ Addition of a strong acid converts the base into its conjugate acid thus increasing the acid and decreasing the base leading to a small change in the ratio and a small ÄpH
▪ number of moles of a strong acid or strong base that causes 1.00L of the buffer to undergo a 1.00 unit change in pH
▪ depends on the total concentration of its components and also on their concentration ratio ▪ at max when ratio = 1
Preparation of Buffers – a buffer solution of any derived pH can be prepared by combining calculated quantities of a suitable conjugate acid/base pair
Consider acidic buffer with HA + A - :
𝐶 ž = [𝐻𝐴] + [𝐴 n ] 𝛼 =
[𝐻𝐴] 𝐶 ž = [𝐻 • 𝑂 m ] [𝐻 • 𝑂 m ] + 𝐾
' 𝛼 ‚ = [𝐴 n ] 𝐶 ž = 𝐾 ' [𝐻 • 𝑂 m ] + 𝐾
' 𝛼
+ 𝛼 ‚ = 1 Titration Curve for Weak Acids: Consider the reaction of 50.00 mL 0.1000M HOAc (K a = 1.75 x 10 5 ) with 0.1000m NaOH 𝐻𝑂𝐴𝑐 + 𝑁𝑎𝑂𝐻 → 𝐻 } 𝑂 + 𝑁𝑎𝑂𝐴𝑐 1. Initial pH (V NaOH
= 0.00 mL) 𝐻𝑂𝐴𝑐 + 𝐻
} 𝑂 ↔ 𝐻
• 𝑂 m + 𝑂𝐴𝑐 n 𝐾 ' =
[𝐻 • 𝑂 m ][𝑂𝐴𝑐
n ] [𝐻𝑂𝐴𝑐] = ¡𝐾 ' [𝐻𝑂𝐴𝑐] pH = 2.88 2. Pre-equivalence Point [𝐻𝑂𝐴𝑐] = #𝑚𝑜𝑙𝑒𝑠
'; +f:-.. X; − # 𝑚𝑜𝑙𝑒𝑠 ;-;*'2; 𝑉
Use either K a expression or Henderson-Hasselbalch Equation to find pH pH = 4.16 3. Equivalence Point (all HOAc converted to OAc -
𝑂𝐴𝑐 n + 𝐻 } 𝑂 ↔ 𝐻𝑂𝐴𝑐 + 𝑂𝐻 n 𝐾
= [𝐻𝑂𝐴𝑐][𝑂𝐻 n ]
n ] = ¡𝐾 W [𝑂𝐴𝑐
n ] pOH = 5.27 pH = 8.73 4. Post Equivalence Point (excess NaOH) [𝑂𝐻 n
# 𝑚𝑜𝑙𝑒𝑠 ;-;*'2;
−#𝑚𝑜𝑙𝑒𝑠 '; +f:-.. X; 𝑉 ž1;'9
pOH = 4.00 pH = 10.00 Determination of K a or K b for weak acids or bases using potentiometric titration (pH meter + glass pH electrode) ▪ For weak acid, at half-neutralization: pH = pK a
b
Acids: ▪ Initial pH values are higher and equivalence point. pH is lower for more dilute concentrations of acid or titrant ▪ At intermediate titrant volumes, pH values differ only slightly due to buffering action
▪ The more complete a reaction between acid and base, the larger the ÄpH at equivalence point region ▪ The smaller K a is, the higher the pH at equivalence point and the smaller the ÄpH
Titration Curve for Weak Base: Derivation is analogous to that of a weak acid
COMPLEX ACID-BASE SYSTEMS Complex Acid-Base Systems – mixture of a strong acid and weak acid (K a
≤ 10 -4 ) Concentration of approximately same order of magnitude In early stages of titration (before 1 st equivalence point); titration curve identical to strong acid After 1
st equivalence point, remainder of titration curve identical to that of dilute solution of weak acid Polyfunctional Acids and Bases: pH of Polyfunctional Systems – determined using systematic approach to multiple equilibrium problem (solve simultaneous equations) Buffer Solutions involving Polyprotic Acids: 2 buffers can be prepared from weak acid H 2 A and its salts: 1. H 2 A + NaHA 2. NaHA + Na 2 A pH of (2) > pH of (1) estimate pH by assuming a single principal equilibrium and using the Henderson-Hasselbalch Equation Salts with both acidic and basic properties – formed during neutralization titration of polyfunctional acids and bases If Ka1>Kb2, solution is acidic, otherwise basic Titration curves for Polyfunctional Acids: Multiple endpoints observed For titration step to be distinct K a1 /K a2 > 10
3
Titration Curve for a Diprotic Acid: Initial pH – consider only 1 st dissociation step Before 1 st equivalence point – 1 st Buffer region 1 st
- ) After 1 st equivalence point but before 2 nd equivalence point (second buffer region) 2 nd equivalence point (with solution of Na2M) pH beyond equivalence point (with excess base/ NaOH) Titration Curves for Polyfunctional Acids and Bases: Titration of H3PO4 – with 2 well-defined endpoints like H2PO42-: Kb2>Kb1; can be titrated with standard acid but not with standard base Ttration of Carbonates and Alkali mixtures: Substance Relation between volumes
Mmoles substance present NaOH
V 2 = 0 M x V 1
Na 2 CO 3
V 1 = V
2
M x V 1
NaHCO 3
V 1 = 0
M x V 2
NaOH + Na 2 CO 3
V 1 >V 2 NaOH:
Na 2 CO 3 : V 1 2
NaHCO 3 : NaHCO 3 + Na 2 CO 3
Na 2 CO 3 :
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