UNIT II: MATHEMATICS in CHEMISTRY Earland

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1 Quantitative analysis used in Chemistry is not difficult, but it requires you to be able to toggle between different units and be accurate in your calculation. In other words, you must become extremely fluent in UNIT CONVERSIONS and SIGNIFICANT FIGURES. You can do practice either from the website, or from your Hebden Workbooks. Good Luck I. Unit Conversions: Unit Conversion: a mathematical used to or more different. Conversion Factor: a used to convert the unit to the unit. Example: There are 1000mL in 1L of water. How many liters are there in 345mL of hydrochloric acid? Expressed Mathematically: 1) Cross Multiplication: = a little algebra 2) Unit Conversion Method: X CONVERSION FACTOR Since in a conversion factor the top part = bottom part, then the ratio is equal to 1 AND since multiplying any value by 1, doesn t change it, the value remains equal however the units change. (Read p9. Hebden) This method is the most useful mathematical tool you will have for chemistry 11 and 12. Please do NOT feel tempted to use other methods though they may look similar and easier. Eventually, they will fail you. Example: There are 60 seconds in 1 minute. How many seconds are there in 3.6 minutes?

2 A. Solving Problems using Unit Conversions: UNIT II: MATHEMATICS in CHEMISTRY Earland In any unit conversion problems, the following things must be identified before you proceed: 1) The amount and its. 2) The unit(s). 3) The which the unit(s) to the unit(s). 4) NEVER NEVER FORGET TO INCLUDE UNITS IN ALL YOUR UNIT CONVERSIONS!! Example: One pound of a substance is equal to 454g. How many grams are there in 2.75lbs of apples? Given Amount: Desired Unit: Conversion Factor: NOTE: Unit conversions serve to out the unwanted units to get to the desired unit. Having units throughout your equation makes this process extremely easy to do and avoids silly errors. DESIRED UNIT = (GIVEN UNIT) x (CONVERSION FACTOR) Example: If ml of Au has a mass of 3.86 g, what is the mass of 5.00 ml of Au? Given amount: Desired Unit: Conversion Factor: WORKSHEET: Single Unit Conversion Worksheet online Or Hebden p14 #2 a-j

3 B. Multiple Unit Conversions: The process is the same as for Single Unit Conversions, but with or more conversion factors involved. Example: If eggs are $1.44 / dozen, and it there are 12 eggs / dozen, how many eggs can be bought for $4.32? Given amount: Desired unit: Conversion Factors: Example: The car gas tank of a car holds 39.5 L of gas. If 1 L of gas is equal to gallon in the USA, and gas is $4.56/ gallon in Dallas, how much will it cost to fill the tank? II. SI Units: The International System (SI) has several units The Base Units: WORKSHEET: Multiple Unit Conversion Worksheet online or Hebden p. 15 #3-10 Measurement Written Base Unit Base Unit Symbol Length/Distance Meter m Mass Gram g Time Second s Amount of Substance mole mol Volume Liter L

4 Multiples of Base Units: Prefix nano micro milli centi deci BASE UNIT Deca_ Hecta Kilo Mega Giga Symbol m n μ m c d L g (etc) D h k M G Exp Multi of Base Unit In order to write units in multiples of the base unit, it is usually easiest to express it in. Scientific Notation: writing a number between multiplied by some of ten. Example: Express 1500 in Scientific Notation: 1.5: the, 10 3 : the Example: How many micrometers are there in 5 cm? Example: Express 5 Mg / ml in kg / L. Example: Express 25.3cm 2 /sec 2 in km 2 /hr 2 WORKSHEETS: Unit Conversion Worksheet #3 and Scientific Notation Worksheet online OR Hebden p. 19 #11-14 and p. 21 #15-18

5 III. The Mole - A Very Special Unit: UNIT II: MATHEMATICS in CHEMISTRY Earland The Mole: a unit that describes the amount of in a. Avogadro s Number (6.02 x ): the number of in a substance x = 1 mole = Avogadro s Number IV. Derived Quantity: Derived Quantity: a value obtained by or more other. Derived Units: a unit made by combining two or more other units. Example: Heat Change Equation: ΔH = c x m x ΔT, where ΔH: J m: g ΔT: o C We wish to derive a unit for c : Example: Derive a unit for the Universal Gas Constant (R), using the equation PV = nrt. DENSITY: WORKSHEET: Density Worksheet online OR Hebden p26 #31-40

6 V. Uncertainty in Measurements: A. Accuracy vs. Precision: Accuracy: how close a measurement is to the correct or accepted value. Precision: how reproducible the measurement is. In general, the more precise a measurement is, the more SIG FIGS it will have. High precision does NOT guarantee. Example: B. Experimental Uncertainty: Experimental Uncertainty: the estimated amount by which a measurement may be in error. Example: Temperature reading: 39.6 o C. The uncertainty is ± 0.1 o C 39.6 ± C This tells us the true value lies somewhere between 39.5 to C. There are two types of experimental uncertainties: a) Random Error: an uncertainty that can up or down. Usually attributed to or. b) Systematic Error: an error that is. Usually attributed to calculation errors.

7 Determining Margin of Error in an Instrument: UNIT II: MATHEMATICS in CHEMISTRY Earland The margin of error in an instrument is of the smallest increment. Example: Determine the uncertainty in a 10mL graduated cylinder. WORKSHEET: Uncertainty in Measurements Worksheet Online OR Hebden p #43-52 C. Significant Figures: All measurements have a certain amount of uncertainty associated with them. As a result, when we record values, we must only report those that are within the of certainty. (i) Rules for Figuring out What is Significant: 1. The total of two or more measurements is only as meaningful as the least precise measurement made. A significant figure then is only the meaningful digits of a reading. Example: Two stop watches recorded Ben s sprint time: Stop watch A: 20.25sec. Stop watch B: 20.4sec. Find Ben s average sprint time 2. The number of sig. figs in a number is equal to all the certain digits PLUS the first uncertain digit. Example: 42.6 ml measured. 42 ml is definitely correct. 0.6 ml: This digit is somewhat uncertain but still within expected accuracy, therefore, it is considered the first uncertain digit, but is still counted as significant. 3. Measurements recorded with ZEROS at the end, followed by NO DECIMAL POINTS, these ZEROS are not considered significant.

8 Example: 10 (1 sig. fig) (3 sig figs) (4 sig figs) (4 sig figs) (6 sig figs) 4. Leading zeroes are NOT considered significant. This is because these zeroes are simply placement holders. They do not change the accuracy of the reading. Example: km (3 sig figs) hrs. (7 sig figs) 5. Defined numbers and counting numbers are considered to infinitely accurate. They are exempt from the rules of sig. figs. Example: 4 students weighed their books and the mass of each was g. 4 students is an exact number. You cannot have 4.25 students g is a measured value. It is subject to the rules of sig. fig. (4 sig figs) (ii) Significant Figures in Calculations: 1) After multiplying or dividing numbers, round off the answer to the least number of sig figs contained in the calculation. Example: 15.55cm x 0.012cm = cm 2 Least sig figs in equation is 2 sig figs. Therefore answer is 0.19cm 2 Example: m / 8.000sec = 0.3m/sec (Final Answer = ) Example: x 10 2 g/ x 10 1 cm 3 = g/cm 3 (Final Answer: ) NOTE: If an uncertain digit is 5, round up. 2) After adding or subtracting numbers, round off the answer to the least number of decimal places contained in the equation. Example: = (Final Answer: )

9 Example: x x 10 7 Since the exponents are different, must convert the measurements so that the exponents are identical. This gives us the correct amount of decimal places x x 10 7 = x 10 7 (Final Answer: ) WORKSHEETS: * Math with Significan Figures Worksheet * Math with Sig. Figs Worksheet #2 * Unit Conversion with Sig. Figs Worksheet Hebden p 28#42, p #55-59