chem 26.1 - midterms reviewer.pdf
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UPD Chem 26.1 Midterms ReviewerTRANSCRIPT
Chem 26.1 Midterms Reviewer /steffigatdula/ 1
CHEM 26.1 – MIDTERMS REVIEWER Experiment 1: Application of Statistical Concepts in the Determination of Weight Variation in Samples Sample and Population • population – collection of all measurements of interest
o parameter – quantity that describes a property of the population
• sample – refers to the subset of a population that is representative of the population from which it was collected
o statistic – quantity that describes a property of the sample; in the absence of determinate errors, it is considered as a good estimate of the parameter; reliability increases with the number of measurements taken
Measures of Central Tendency • mean – average of the values measured from the
sample; use a calculator to get this (x)
x = (x! + x! + x!+ . . . x!)
n
• median – middle value in a set of data that has been
arranged in increasing or decreasing order; if the set of values is even, the median is the average of the 2 midpoints
Measures of Accuracy • absolute error, E – difference between the
experimental value and true value
E = x! − x! • relative error, Er – absolute error divided by the true
value; expressed in percent
E! = x! − x!x!
x 100
Measures of Precision • variance, s2 -‐ measure of how far each value in the data
set is from the mean; use a calculator to get this (xσn-‐1); unit2
s! = (x! − x)!!
!!!
n − 1
• standard deviation, s – square root of variance use a
calculator to get this (square of xσn-‐1); same unit
s = (x! − x)!!
!!!n − 1
!
• relative standard deviation, RSD -‐ absolute value of the
coefficient of variation; unit is ppt
RSD = sx x 1000
• coefficient of variation, CV – RSD expressed in percent; unit is %
CV = sx x 100
• pooled standard deviation, spooled – used when there
are several data sets (n!); same unit
s!""#$% = (x! − x!)!
!!!!! + (x! − x!)!
!!!!!
n! + n!+ . . . − n!
!
= s!! n! − 1 + s!! n! − 1
n! + n!+ . . . − n!
!
• range, R – difference between highest and lowest
values in a set of measurements; same unit
R = x!"#!$%& − x!"#$%& • relative range, RR – range expressed in relative terms;
unit is ppt
RR = Rx x 1000
Confidence Interval • provides a range of values within which the population
mean is expected to lie at a specified confidence level • uses n − 1 in the table for values of t
CI = x ± tsn
Grubbs Test • used to detect outliers; can only detect 1 outlier per
data set • arrange data set from lowest to highest then calculate
|x! − x| for both extremes, calculate gexp for the value with a higher |x! − x|
• if gtab > gexp then the value is accepted, otherwise it is rejected
o if gexp is rejected, calculate the new s and x for the data set with the outlier removed
• uses n in the table of critical values
g = max!!!..!
|x! − x|
s
3 Types of Errors • gross errors
o outliers → Grubbs test o e.g.
§ arithmetic mistake § reading a scale backward § using a wrong scale § spilling a solution
• systematic/determinate Errors o have a definite value o assignable cause o affects accuracy
Chem 26.1 Midterms Reviewer /steffigatdula/ 2
1. instrumental § faulty calibration § instrument used is under
inappropriate condition 2. method
§ non-‐ideal chemical/physical behavior of the chemicals
• side reactions • impurities in the product • slight solubility of the
precipitate • incomplete reaction
§ minimize by: • blank determination • standard reference material • independent analysis
3. personal § prejudice in estimation
• random/indeterminate o affects precision o sources: cannot be determined
Experiment 2: Solution Preparation and Standardization Expressions of Concentration
Molarity M = moles soluteL solution
Molality m = moles solutekg solvent
Mole Fraction, X = moles solutemoles solution
Dilution
𝑀!𝑉! = 𝑀!𝑉!
Dilution Factor,DF = total volume of solution
volume of aliquot
→M!"#!$#%&'%$( = M!"#$%&! x DF
Aliquot Factor,AF = volume of aliquot
total volume of solution=
1DF
→M!"#$%&! = M!"#!$#%&'%$( x AF Experiment 3: Chemical Kinetics – The Iodine Clock Reaction Chemical Kinetics • how fast or slow a reaction occurs Factors • nature of reactants • concentration • temperature • presence of a catalyst • surface area
Rate Law A + B → C + D
rate = k[A]m[B]n where: k = rate constant m & n = rate orders m + n = overall reaction order Graphical Method of Determining Rate Law
Zero First Second
Rate Law
R = k
R = k[A]
R = k[A]!
Int. Rate Law
[A]! = −kt + [A]!
ln[A]! = −kt + ln[A]!
1[A]!
= kt + 1[A]!
Units of k
Ms
1s
1M ∙ s
Linear Plot [A]t vs. t ln[A]t vs. t
![!]!
vs. t
Slope -‐k -‐k k
Half-‐life
𝑡!!=[A]!2k
𝑡!!=ln (2)k
𝑡!!=
1k[A]!
Initial Rate Method
rate 1rate 2
= k[A!]![B!]!
k[A!]![B!]!
Elementary Steps Method • include only the slow reaction and the steps before it
ex. A + B → C fast C + B → D slow D → E fast
rate = k[A][B]2
Arrhenius Equation E! = Activation Energy A = Arrhenius Constant ln k = !!!
!∙ !!+ ln (A) [in the form y = mx + b]
where: R = 8.3124 !!"#
& T is in Kelvin linear regression on a calculator (Casio) • STAT → A+BX → enter x & y values
o x = !! (!"#$%&)
o y = ln (k) • press SHIFT + STAT → go to Reg
o A = y − intercept = b = ln A → A = e! o B = slope = m = !!!
! → E! = mR
o r! = linearity = approaching 1
Chem 26.1 Midterms Reviewer /steffigatdula/ 3
Experiment starch and iodine create a blue complex: • S!O!
!! + 2I! → 2SO!!! + I!
• persulfate + iodide → sulfate + iodine addition of thiosulfate creates a clock reaction: • 2S!O!
!! + I! → S!O!!! + 2I!
• thiosulfate + iodine → tetrathionate + iodide maintaining a constant ionic strength for all set-‐ups: • addition of KCl and K!SO! Experiment 4: Common Ion Effect and Buffers Acid-‐Base Indicators
Indicator pH values Color
Methyl Orange pH < 3.1 Red
3.1 < pH < 4.5 Salmon Pink pH > 4.5 Yellow
Phenolphthalein
pH < 8.3 Colorless 8.3 < pH < 10.0 Very Light Pink
pH > 10.0 Red Buffers • resists appreciable change in pH upon the addition of
small amounts of strong acid or strong base • composed of weak acid/base + conjugate ion
o HA & A-‐ or BH+ & B • buffer capacity – amount of acid or base the buffer can
neutralize before pH begins to change to an appreciable level
o 𝑝𝐻 = 𝑝𝐾! ± 1 or 𝑝𝑂𝐻 = 𝑝𝐾! ± 1 Determining the pH/pOH of Weak Acids/Bases • remember that:
o 𝐻𝐴 → 𝐻! + 𝐴! o 𝐵 + 𝐻!𝑂 → 𝐵𝐻! + 𝑂𝐻!
• use ICE table to determine equilibrium concentrations o when 𝐾! ≤ 10!! , x is negligible in addition
and subtraction operations o change values if strong acid/base is added to
weak acid/base (addition of initial amount present or calculation of limiting/excess reactant when salt is formed)
𝐾! 𝑜𝑟 𝐾! = [𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠][𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠]
pK! = − logK! & pK! = − logK! → K!K! = K! = 1.00 x 10!!"
pH = − log H! & pOH = −log [OH!]
→ 14 = pH + pOH
Henderson-‐Hasselbalch Equation
pH = pK! + log[base][acid]
addition of SA: pH = pK! + log!!"# !"#$!!!"# !! !"".!!"# !"#$!!!"# !! !"".
addition of SB: pH = pK! + log
!!"# !"#$!!!"# !"! !"".!!"# !"#$!!!"# !!! !"".
pOH = pK! + log[acid][base]
addition of SB: pOH = pK! + log
!!"# !"#$ !!!"# !"! !"".!!"# !"#$!!!"# !!! !"".
addition of SA: pOH = pK! + log!!"# !"#$!!!"# !! !"".!!"# !"#$!!!"# !! !"".
Titration (For E5 & E6) titrimetric analysis • quantitative • aims to determine concentration of analyte • uses a titrant of known concentration requirements ü fast ü complete ü known reaction ü has a way to detect equivalence point 2 parts • standardization of titrant concentration using a
primary standard with o high % purity o high molecular weight o high stability o known reaction
• sample analysis o known titrant concentration and volume o known analyte volume o determine: analyte concentration
Experiment 5: Determination of the Solubility Product Constant of Calcium Hydroxide Solubility Product Constant
for a reaction: A!B!(!) → xA!! + yB!! → K!" = [A!!]![B!!]!
• K!" is the product solubility constant • [A!!]![B!!]! is the ion-‐product, IP, or reaction
quotient, Q, when the concentration used are initial concentrations
• solids do not appear as a denominator in the K!" expression because the activity of any solid is 1
• K!" is temperature dependent When A!! ions were added to a solution with B!! ions:
Chem 26.1 Midterms Reviewer /steffigatdula/ 4
• resultant solution is unsaturated if IP < K!" • reaction mixture is saturated if IP = K!" • precipitation is observed if IP > K!" Other Factors Affecting 𝐊𝐬𝐩 • common ion – identical ion is added to solution
o lowers s -‐ based on Le Chatelier’s principle, the CI will shift the reaction backward
• diverse-‐ion / ionic strength – ion from a substance containing no common ion is added to a solution
o 𝑠 increases with ionic strength (shielding)
µμ = 12
𝐶!(𝑍!)! where: C! = concentration of ion
Z! = charge of the ion Calculations
Ca(OH)! ! ⇋ Ca!! + 2OH! K!" = Ca!! [OH!]!
• [OH!] is calculated from HCl titration • Ca!! is OH! / 2 • compute 𝑠 using an ICE table • use 1:1 ratio for HCl standardization (only PH is used)
Experiment 6: Quantitative Determination of Soda Ash Composition by Double Indicator Titration Soda Ash Components ü 𝑁𝑎!𝐶𝑂! -‐ sodium carbonate ü 𝑁𝑎𝐻𝐶𝑂! -‐ sodium bicarbonate ü 𝑁𝑎𝑂𝐻 -‐ sodium hydroxide
Indicators • NaOH – phenolphthalein • NaHCO! – methyl orange • Na!CO! – phenolphthalein + methyl orange Relationship of VPH and VMO
Substance Present
mmol of Substance
VMO = 0 NaOH M!"#V!" VPH = 0 NaHCO! M!"#V!" VPH = VMO Na!CO! M!"#V!"
M!"#V!" VPH > VMO Na!CO! M!"#V!"
NaOH M!"#(V!" − V!") VPH < VMO Na!CO! M!"#V!"
NaHCO! M!"#(V!" − V!")
Factors in the Experiment • use of boiled 𝑑H!O
o removes CO! that can lead to carbonate error (only present in sample with NaOH)
o CO! + 2OH! → CO!!! + H!O
§ instead of needing 2 moles H! to neutralize 2 moles OH! , you only need 1 mole H! to neutralize 1 mole CO!
!! § carbonate error leads to a lower VPH
• boiling near MO endpoint o to obtain a sharper endpoint o to disrupt
• NaHCO! + NaOH → Na!CO! + H!O
o impossible to determine original composition o NaHCO! as the LR: Na!CO! + H!O + NaOH o NaOH as the LR: Na!CO! + H!O + NaHCO!
Calculations
%Na!CO! = mg Na!CO!sample
x 100
%NaHCO! = mg NaHCO!sample
x 100
%NaOH = mg NaOHsample
x 100
%inert = 100 − %Na!CO! − %NaHCO! − %NaOH *use AF or DF as needed Error Propagation Addition and Subtraction • R = A + B − C • r = a! + b! + c! • final result: R ± r
o R follows the decimal place of r o r should only have 1 significant figure
Multiplication and Division • R = AB C
• r = R !!
!+ !
!
!+ !
!
!
• final result: R ± r o R follows the decimal place of r o r should only have 1 significant figure
Multiple Operations • ex. 1.5 ± 0.1 + 2.6 ± 0.2 / (1.4 ± 0.3)
o addition: R = 4.1 and r = 0.2236067977
o division: r = !.!!.!
!!
!+ !.!
!.!
!
o final result: 2.9 ± 0.6
CO!!! + 𝐻! → 𝐻𝐶𝑂!!
𝐻𝐶𝑂!! + 𝐻! → 𝐻!𝐶𝑂!
𝐻! 𝑂 + 𝐶𝑂!(𝑔)
⇋
8.3
3.9
𝐕𝐌𝐎 𝐕𝐏𝐇
𝐻𝐶𝑂!! + 𝐻! → 𝐻!𝐶𝑂!
𝐻! 𝑂 + 𝐶𝑂!(!)
⇋