WELCOME!! LABORATORY MATH PERCENT CONCENTRATION. Things to do ASAP: Concepts to deal with:

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1 WELCOME!! Things to do ASAP: Read the course syllabus; information regarding testing, homework, lecture schedules, expectations and course objectives are all there Read the weekly overview; lecture objectives are there Look at the study guides which are for EXAM STUDY GUIDING ONLY! These are NOT assignments! LABORATORY MATH Concepts to deal with: 1. Percent concentration 2. Molarity 3. Inverse proportions 4. Statistics!! PERCENT CONCENTRATION An expression of concentration that does not give molecule information; does not require mw info Described as parts per 100 parts; percent (%) is weight in grams per volume in 100 mls (w/v) or grams/100 To determine how much of a substance to add to a solvent, use a ratio equation: grams/100 mls = grams needed/volume needed

2 Problem: How much NaCl do you need to make 600 mls of 0.9% solution of NaCl? Answer: 0.9 = x = 100x 5.4 = x So add 5.4 grams of NaCl to 600 mls of solvent MOLARITY Describes the concentration of solute within a solution by stating the relative number of reactant particles tells the number of "moles" of solute in a specific amount of solution; this is the number of molecules available for interaction A mole contains 6.02 X particles; it is different for each element...this is also the molecular weight of the element A mole of an element is its molecular weight; for example, a mole of sodium is 23 grams A mole of a compound is the total of the molecular weights of each element in the compound; for example, a mole of NaOH is = 40 grams Molarity is expressed as mol/l or M; this refers to the number of moles in one liter of solvent

3 Thusly, one mole (1M) of NaOH in one liter of solvent is equal to 40 grams of solid NaOH dissolved in 1 liter (1 mol/l)...2 moles would be 80 grams of NaOH, etc. CALCULATING MOLARITY Quick and Simple (use this formula): Molarity = [grams/liter] / molecular weight or grams/liter = Molarity X molecular weight Problem: What is the molarity of a solution containing 24 grams H 2 SO 4 (MW = 98 gm) in 150 mls of buffer? Answer: 24 grams/0.15 liters = M X = M X = Molarity Problem: One liter of a solution is labeled 24 grams NaOH What is the molarity of this solution? Answer: 24 grams/1 liter = M X = Molarity

4 The Inverse Proportion Calculation Used in determining how to make solutions of lesser concentration from solutions of greater concentration Formula is: V1 X C1 = V2 X C2 where V is volume and C is concentration Both V units must be the same and both C units must be the same Problem: Make 500 mls of an 0.8M solution from a 15M solution. Solution: V1 X C1 = V2 X C2 500 mls X 0.8M = V2 X 15M 400 = 15X X = mls Add 26.7 mls of the 15M solution to a flask and add solvent up to 500 mls STATISTICS Statistics is the mathematical analysis and evaluation of collected data a statistic is a number summarizing data Used daily in clinical lab to evaluate quality control (QC) data QC statistical data must be kept on file for inspections and equipment maintenance

5 Two types of stats: 1. Descriptive: summarizes features of a single group of data or things; describes the relationship of each piece of data to a central value (usually the mean) 2. Inferential: allows one to infer findings from small groups to large populations using, in part, descriptive stats (mostly research) Descriptive Stats When data points are plotted in a specific way, they will form a symmetrical (bell-shaped) curve called the Normal Curve, Gaussian Distribution, or normal distribution To plot the normal curve, data is collected, the mean and the standard deviation are calculated; values are plotted on the curve If the distribution is normal, then 68.2% of values lie between ±1 standard deviation away from the mean, 95.5% lie between ±2 standard deviations away from the mean, and 99.7% are ±3 standard deviations away

6 Inferential Stats Compares certain features of two or more groups of data to determine similarities or differences usually looks at small samples and infers the findings of this group to large populations Used more in research designs Common Descriptive Stats Mean: the arithmetic average of a set of numbers...symbolized by x-bar Calculate mean by adding all values and then dividing that sum by the number of values Dispersion or range: a not very useful simple statistic that describes the spread of data around the mean obtained by subtracting the smallest value in a set of data from the largest value Standard deviation (SD or σ): A commonly used stat that describes the dispersion of groups around the mean...the square root of the variance; allows one to determine which values lie within certain deviations from the mean Where Σ is sum of, x is an individual value, x bar is the mean value of all the scores; and N is the population size

7 Calculate mean and standard deviation of the following values: 1, 2, 3, 4, 5 x bar equals = 15 5 = 3 (x x bar) 2 equals: 1 3 = -2, -2 2 = = -1, -1 2 = = 0, 0 2 = = 1, 1 2 = = 2, 2 2 = 4 Sum of (Σ) squared values = = 10 Sum of squared values = 10 N = 5 10/5 = 2, find the square root of 2 SD (or σ) = So 1 standard deviation is 1.41, what are 2 standard deviations? 3 standard devs? Coefficient of Variation: a statistic used to compare the relative variability in two sets of values not expressed in the same units; it relates the standard deviation to the mean and is expressed as a percentage Calculate the CV using this formula: SD X 100 = CV% mean Mode: the value in a set of data that occurs most frequently Median: the values that occurs in the middle of all of the values (least affected by outlier values) when values are arranged from high to low