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A comprehensive introduction to chemical analysis, covering key concepts such as errors, significant figures, and descriptive statistics. It delves into the types of errors encountered in experimental data, including random, systematic, and gross errors. The document also explains the rules for significant figures in calculations and explores various measures of descriptive statistics, such as measures of frequency, dispersion, position, and inferential statistics. It is a valuable resource for students and researchers seeking a foundational understanding of chemical analysis principles.
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Interference: An effect which alters or obscures the behavior of an analyte in an analytical procedure (Sources contaminants, reagents, instrumentation used for the measurements) Standards: Materials containing a known concentration of a substance. They provide a reference to determine unknown concentrations or to calibrate analytical instruments. Primary Standard: A substance whose purity and stability are particularly well-established and with which other standards may be compared. It is a pure substance which reacts in a quantitative and known stoichiometric manner with the analyte or a reagent. Primary standard is a reagent that is extremely pure, stable, has no waters of hydration, and has a high molecular weight. Criteria:
Equivalent: That amount of a substance which, in a specified chemical reaction, produces, reacts with, or can be indirectly equated with one mole (6.023 x 1022) of hydrogen ions. This confusing term is obsolete, but its use is still to be found in some analytical laboratories. Selecting and Handling Reagents and other Chemical Purity of reagents - The purity of reagents influences the accuracy of analysis. Reagent grade : conform to the minimum standards set forth by the Reagent Chemical Committee of the American Chemical Society (ACS). EXAMPLE: Tollens reagent The reagent consists of a solution of silver nitrate, ammonia and some sodium hydroxide (to maintain a basic pH of the reagent solution). Primary-standard carefully analyzed by the supplier. The National Institute of Standards and Technology (NIST) is an excellent source. EXAMPLE: Standardization of silver nitrate. Sodium chloride is used as the primary standard for this purpose. Some Examples: Sodium carbonate (Na2CO3) Potassium hydrogen phthalate (KHP): C8H5KO4, mol wt.= 204.23 g/mol, Potassium hydrogen iodate: KH(IO3)2, mol wt. = 389. g/mol Sodium tetraborate Na2B4O7, Special-purpose reagent chemicals are prepared for a specific application such as solvents spectrophotometry and for high- performance liquid chromatography. Rules for Handling Reagents and Solutions 1: Select the best grade of chemical available. Pick the smallest bottle that is sufficient to do the job. 2: Replace the top of every container immediately after removing reagent 3: Hold the stoppers of reagent bottles between your fingers. Never set a stopper on a desktop 4: Unless specifically directed otherwise, never return any excess reagent to a bottle. 5: Never insert spatulas, spoons, or knives into a bottle that contains a solid chemical. Instead, shake the capped bottle vigorously or tap it gently against a wooden table to break up an encrustation. Then pour out the desired quantity. 6: Keep the reagent shelf and the laboratory balance clean and neat. Clean up any spills immediately. 7: Follow local regulations concerning the disposal of surplus reagents and solutions. Cleaning and marking of laboratory ware 1: Each vessel that holds a sample must be marked. Special marking Inks are available for porcelain surfaces. A saturated solution of iron (III) chloride can also be used for marking. 2: Every apparatus must be thoroughly washed with a hot detergent solution and then rinsed, initially with large amounts of tap water and finally with several small portions of deionized water 3: Properly cleaned glassware will be coated with a uniform and unbroken film of water. Do not dry the interior surfaces of glassware. 4: An organic solvent, such as methyl ethyl ketone or acetone, may be effective in removing grease films. Evaporating Liquids
Error – defined as the difference between the true result (or accepted true result) and the measured result. Precise
Significant Figures are the digits of a number that are meaningful in terms of accuracy or precision. The importance of significant figures in reporting measurement is the number of significant figures corresponds to all digits that are certain in a measurement plus one uncertain digit. VALUES SF 1.) 45 TWO 2.) 0. TWO 3.) 7.4220 FIVE 4.) 5002 FOUR 5.) 3800 FOUR Determining the number of significant figures RULES FOR SIGNIFICANT FIGURES
⚫ natural variations in real world or experimental contexts. ⚫ imprecise or unreliable measurement instruments. ⚫ individual differences between participants or units Systematic error (Determinate) are those errors that are known and controllable errors. Error affects the accuracy of data sets. TYPES OF SYSTEMATIC ERROR OFFSET ERRORS occurs when a scale isn’t calibrated to a correct zero point. It’s also called an additive error or a zero-setting error. EXAMPLE: When measuring participants’ wrist circumferences, you misread the “2” on the measuring tape as a zero-point. All of your measurements have an extra 2 centimeters added to them. SCALE FACTOR ERROR is when measurements consistently differ from the true value proportionally (e.g. by 10%). It’s also referred to as a correlational systematic error or a multiplier error. EXAMPLE: A weighing scale consistently adds 10% to each weight. A true weight of 10 kg is recorded as 11 kg, while a true weight of 40 kg is recorded as 44 kg CLASSIFICATION OF SYSTEMATIC ERROR Instrumental error are errors caused by poor instrument condition and calibration. Method error are caused by poor outcomes caused by substandard conditions of chemicals and reactions. Example: In volumetric analysis, the use of improper indicator leads to wrong results. Personal error are caused by personal limitations of the analyst such as failing to follow procedures properly, among others. Example: Parallax Error The error/displacement caused in in the apparent position of the object due to the viewing angle that is other than the angle that is perpendicular to the object. DETECTION OF SYSTEMATIC ERROR Systematic errors can be detected by: Analysis of reference standards reference standards are chemicals of known concentration and purity Example: pH buffer solution Analysis of blank samples blank samples contain all reagents used in the analysis other than the sample. Third Party Analysis allows other chemists to analyze the sample. Variation of sample size to check for constant or proportional errors. ⚫ Constant error - an average of the errors over the range of all data. Errors that do not change in magnitude as sample size increases. ⚫ Proportional Error - an error that is dependent on the amount of change in a specific variable. Errors that increase in magnitude as sample size increase. Example: Titration GROSS ERRORS causes large errors leading to outlier data. These are errors that are so serious (i.e. large in magnitude) that they cannot be attributed to either systematic or random errors associated with the sample instrument, or procedure. Example: When the contents of a mixture is spilled when it is being boiled. The loss brought about by spilling causes an error in the amount of the analyte present in the sample being boiled. 02: A. INTRODUCTION TO STATISTICS WHAT IS STATISTICS? A branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data. The science that deals with the collection, classification, analysis, and interpretation of numerical facts or data, and that, by use of mathematical theories of probability, imposes order and regularity on aggregates of more or less disparate elements. WHAT IS VARIABLE? a variable is a characteristics or condition that can change or take on different values. most research begins with a general question about the relationship between two variables for a specific group of individuals. 03: TYPES OF VARIABLES DISCRETE VARIABLE - a variable that may assume only a countable, and usually finite, number of values (such as
class size). It consists of indivisible categories. No values can exist between two neighboring categories. Example: Number of planets around the Sun or Number of students in a class CONTINUOUS VARIABLE - Continuous variables would take forever to count (such as time or weight) are infinitely divisible into whatever units a researcher may choose. Example: time can be measured to the nearest minute, second, half-second or Age (you can’t count “age”, you could be: 25 years, 10 months, 2 days, 5 hours, 4 seconds, 4 milliseconds, 8 nanoseconds, 99 picosends…and so on) REAL LIMIT - To define the units for a continuous variable, a researcher must use real limits which are boundaries located exactly half-way between adjacent categories. Example: a test score of 95 has the lower real limit of 94. and the upper real limit of 95.4 since any value within that range will equal 95 when rounded to a whole number. MEASURING VARIABLE - To establish relationships between variables, researchers must observe the variable and recorded their observations. This requires that the variables be measured.
categories called a scale of measurement and a process that classifies each individual into one category. 04: TYPES OF MEASURING VARIABLE NOMINAL SCALE - is an unordered set of categories identified only by name. Nominal measurements only permit you to determine whether two individuals are the same or different. Example: blood type ORDINAL SCALE - is an ordered set of categories. Ordinal Measurement tell you the direction of difference between two individuals. Example: satisfaction rating (“extremely dislike”, “dislike”, “neutral”, “like”, “extremely like”) INTERVAL SCALE - is an ordered series of equal sized categories. Interval measurement identify the direction and magnitude of a difference. The zero point is located arbitrarily on an interval scale. Variables that have familiar, constant, and computable differences are classified using the Interval scale. Example: in the temperature, there is no point where the temperature can be zero. Zero degrees F does not mean the complete absence of temperature. INTERVAL SCALE - is an interval scale where a value of zero indicates none of the variable. Ratio measurements identify the direction and magnitude of difference and allow ratio comparison of measurements. Example: the temperature outside is 0-degree Celsius. 0 degree doesn’t mean it’s not hot or cold, it is a value. 05: DATA TYPES NOMINAL (CATEGORICAL) - No comparison is defined. Example: Gender (male & female) ORDINAL - Comparable but the difference is not defined Example: socio economic status (“low income”, “middle income”,” high income”) INTERVAL - Deduction and addition is define but not division Example: calculate intelligence score in an IQ test. RATIO - a form of numerical data which is quantitative in nature. Example: HEIGHT (What is your height in feet and inches?) -Less than 5 feet. -5 feet 1 inch – 5 feet 5 inches -5 feet 6 inches- 6 feet -More than 6 feet EXPERIMENTS
EXAMPLE: Data set: 46, 69, 32, 60, 52, 41 Step 1: Find the mean x̅ = ∑ x / n = (46 + 69 + 32 + 60 + 52 + 41) ÷ 6 = Step 2: Find each score’s deviation from the mean. Score Deviation from the mean 46 46 – 50 = - 69 69 – 50 = 19 32 32 – 50 = - 60 60 – 50 = 10 52 52 – 50 = 2 41 41 – 50 = - VARIANCE EXAMPLE: Data set: 46 69 32 60 52 41 Step 5: Divide the sum of squares by n – 1 or N Variance σ = 886 ÷ (6 – 1) = 886 ÷ 5 = 177 CONFIDENCE INTERVAL is a specific interval estimate of a parameter determined by using data obtained from a sample. The confidence interval is the preferred method for describing the range of uncertainty in a value. The confidence interval is expressed as a range of uncertainties at a stated percent confidence. This percent confidence reflects the percent certainty that the value is within the stated range.
You can calculate confidence intervals for many kinds of statistical estimates, including: Proportions Population means Differences between population means or proportions Estimates of variation among groups
4. MEASURES OF POSITION Use this when you need to compare scores to a normalized score Describe how scores fall in relation to one another. Relies on standardized scores Use percentile ranks, quartile rank to measure position PERCENTILE RANKS - the percentage of scores in its frequency distribution that are equal to or lower than it.
EXAMPLE: a test score that is greater than 75% of the scores of people taking the test is said to be at the 75th percentile, where 75 is the percentile rank. QUARTILE RANKS - a type of quantile which divides the number of data points into four parts, or quarters, of more- or-less equal size. FORMULA FOR QUARTILE: Lower Quartile (Q1) = (N+1) * 1 / 4 Middle Quartile (Q2) = (N+1) * 2 / 4 Upper Quartile (Q3)= (N+1) * 3 / 4 INFERENTIAL STATISTICS - Are methods for using sample data to make general conclusions (inferences) about populations Inferential statistics have two main uses: making estimates about populations. Example: the mean SAT score of all 11th graders testing hypotheses to draw conclusions about populations. Example: the relationship between SAT scores and family income 09: TYPES OF INFERENTIAL STATISTICS