Summer 2018 Part I Key

Transcription

1 Summer 2018 Part I Key 1

2 Section 1: Scientific notation Chemists often deal with numbers that are either extremely large of extremely small. For example, in 1g of the element hydrogen there are roughly 602,200,000,000,000,000,000,000 hydrogen atoms. Each hydrogen atom has a mass of only g These numbers are cumbersome to handle, and it is easy to make mistakes when using them in arithmetic computations. Consider the following multiplication: x = It would be easy for us to miss one zero or add one more zero after the decimal point. Consequently, when working with very large and very small number, we use a system called scientific notation. Regardless of their magnitude, all numbers can be expressed in the form where, N x 10 n N = a number between 1 and 10 and n = the exponent which is a positive or negative integer (whole number). If the decimal has to be moved to the right, the exponent is negative. If the decimal has to be moved to the left, the exponent is positive. Examples: 1) = x ) = 7.72 x ) = 5.8 x ) 0.21 = 2.1 x 10-1 Practice 1) = ) 60 = ) = ) = ) = ) =

3 Section 2: SI units and Prefixes used with SI Units The metric system used for measurements is called the International System of Units which is abbreviated as SI. The table below shows the seven SI base units. All other measurements can be derived from the base units. Prefixes can be used to determine the magnitude of physical quantities. The table below shows these prefixes and their magnitudes. Practice 1) 1 km = 10 3 m 2) 1 cm = 10-2 m 3) 1 ks = 10 3 s 5) 1 g = 10 3 mg 6) 1 g = 10 9 ng 7) 1 µg = 10-6 g 4) 1 s = 10-3 ks 3

4 Section 3: Significant figures Guidelines for using Significant figures: 1. Any digit that is not zero is significant. 845 cm = 3 sig fig kg = 4 sig fig 2. Zeros between NON ZERO digits are significant 606 m = 3 sig figs kg = 5 sig figs 3. Zeros to the left of the first NON ZERO digit are not significant L = 1 sig fig = 3 sig figs 4. If a number is greater than 1, then all the zeros written to the right of the decimal point count as significant. 2.0 mg = 2 sig figs ml = 5 sig figs If a number is less than 1, then only the zeros that are at the end of the number and the zeros that are between nonzero digits are significant kg = 2 sig figs L = 4 sig figs 5. For numbers that do not contain decimal points, the trailing zeros (zeros after the last NON ZERO digit) are not significant. 400 cm = 1 sig fig. 6. For addition/subtraction, the answer will contain the number of least decimal places in the function = =

5 For multiplication/division, the answer will contain the number of least significant figures in the function x 6.01 = = 24.1 Example: ( ) (4.2694) =0.04 x = 0.02 ( ) 9.73 ******add practical application*****copy/paste from chem packet****** Practice Give the number of significant digits in each of the following measurements: 1) 1, = 6 2) 120,000 = 2 3) = 5 4) = 3 5) =4 6) 2.60 = 3 7) = 6 8) = 5 9) = 3 10) 387,465 = 6 Perform the following operations giving the proper number of significant figures in the answer. 11) 23.4 x 14 = ) = ) = ) / 34.0 = ) ( )/0.056 = ) ( ) ( ) = ) (4 972) + ( ) (12 7) = = ) ( ) = ( ) = = ( ) ( )

6 A few things to remember about units: 1. Unlike units must be changed to common units before calculations can be made. For example, you can t work with cm and mm you need to make sure they have the same base prefix. 2. Units are manipulated in the same manner as numbers. That is, they must be squared or canceled during calculations. For example: 3 cm 2 x 2 cm = 6 cm 3 Dimensional Analysis: Overview Section 4: Dimensional analysis Dimensional analysis is the procedure used to convert between units in solving chemistry problems. It is based on the relationship between different units that express the same physical quantity. For example, 1 dollar = 100 pennies can be written as 2 different conversion factors: 1 dollar 100 pennies 100 pennies or 1 dollar Conversion factors can be used to move from what you have to what you want. Units can only cancel out if they have a top-bottom relationship. If the setup is correct, then all units will cancel except the desired one. If this is not the case, then an error must have been made somewhere and it can usually be spotted by reviewing the solution. Let us review a few examples before we practice. 6

7 1) A person's average daily intake of glucose (a form of sugar) is pound (lb). What is this mass in milligrams (mg)? (1lb = g.) The sequence of conversion for the problem is: pounds grams milligrams We can setup the following dimensional analysis equation: lb x g x (1x10 3 ) mg = 3.78 x 10 4 mg 1 lb 1 g 2) An average adult has 5.2 L of blood. What is the volume of blood in m 3? The sequence of conversion for the problem is: L cm 3 m 3 We can setup the following dimensional analysis equation: 5.2 L 10 cm (1m) 1L (10 cm) = m Practice 1. An international group of zookeepers with successful breeding programs made the following animal exchanges last year. Using the same bartering system, how many oryxes can a zoo obtain in exchange for 15 flamingoes? 3 oryxes = 1 tiger 1 camel = 6 anteaters 1 rhino = 4 monkeys 3 monkeys = 1 tiger 2 flamingoes = 1 anteater 5 lemurs = 1 rhino 3 lemurs = 1 camel 1 rhino = 4 oryxes a) two oryxes b) four oryxes c) three oryxes d) one oryx e) five oryxes 15 flamingos 1 anteater 2 flamingos 1 camel 6 anteaters 3 lemurs 1 rhino 1 camel 5 lemurs 4 oryxes = 3 oryxes 1 rhino 7

8 2. Convert mi/hr to m/s miles hour 5280 ft 1 mile 12 in 2.54 cm 1 ft 1 in 1 m 10 cm 1 hr 60 min 1 min = m/s 60 sec 3). You are in Paris and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches are 11.5 francs per kilogram. Given that there are approximately 5 francs to the dollar, calculate what a pound of peaches will cost in dollars. 1 lb peaches.. = 1 dollar 8

9 Density Worksheet Density is defined as the degree of compactness of a substance. Density is found through dividing a substances mass by its volume. It is a physical property of matter that does not depend on the quantity of the substance. Properties, such as density, are thus referred to as intensive properties. For example, water is always 1g/mL. Knowing the densities of your materials can help to identify different parts of a mixture, aid in separating them, and can help you convert between volume and mass in dimensional analysis. 1) A cube of lead has a volume of 6.61 cm 3. Its mass is 75.0 grams. What is its density? D = =. = g/cm3 = 11.3 g/ml 2) At 25 C, 1.00 cm 3 of iron has a mass of 7.62 grams. What volume of iron is occupied by 125 grams of iron? 1.00 cm 125 g = cm g 3) Calculate the mass of a liquid with a density of 3.2 g/ml and a volume of 25 ml. 25 ml 3.2 g 1.0 ml = g 4) An irregular object with a mass of 18 kg displaces 2.5 L of water when placed in a large D = m v overflow container. Calculate the density of the object. 18 kg = = 7. 2 kg/l 2.5 L 5) A graduated cylinder has a mass of 80 g when empty. When 20 ml of water is added, the graduated cylinder has a mass of 100 g. If a stone is added to the graduated cylinder, the water level rises to 45 ml and the total mass is now 156 g. What is the density of the stone? mass: 156 g 100 g = 56 g; volume: 45 ml 20 ml = 25 ml D = m v = 56 g = 2. 2 g/ml 25 ml 9