Math Session: - Measurement - Dimensional Analysis SC155: Introduction to Chemistry Freddie Arocho-Perez

Numbers in Science Integer Numbers: 2 6 Signed Numbers: -2+4 Irrational/Decimal Numbers:

English vs. Metric System Physical QuantityMetric UnitEnglish Unit MassGram (g)Pound (lb) VolumeLiter (L)Gallon (gal) LengthMeter (m)Inch (in) TimeSecond (s)Minute (min) TemperatureCelsius (°C) Kelvin (K) Fahrenheit (°F)

Metric System Length –Measurement of distance or dimension. –The base unit: meter. –It is a little over 1 yard long, more precisely 39.4 inches long. Here are some other conversions: 1 meter (m) = 39.4 inches = yards (about one big step) 1 meter (m) = 100 centimeters (cm) 1 kilometer (km) = 1000 meters = 0.62 miles Mass –Amount of matter or material in an object. –The base unit: gram. –Here are some other conversions: 1 gram (g) = ounce1 pound (lb) = g 1 ounce (oz) = grams 1 kilogram (kg) = 1000 grams

Metric System Volume –Amount of space occupied by an object. –The base unit: liter (L) milliliter (mL) –1 L = 1,000 mL –A milliliter is a cube 1 cm long on each side (1 cm 3 ). –1 mL = 1 cm 3 = 1 cc

Temperature

In scientific measurements, the Celsius (C) and Kelvin (K) scales are most often used. The Celsius scale is based on the properties of water. –0 C is the freezing point of water –100 C is the boiling point of water

Temperature Kelvin is one of the standard units of temperature: K = C Celsius is the other standard unit. Fahrenheit is not used in scientific measurements. Other Formulas: F = (1.8 x C) + 32 C = (F - 32) x 0.555

Temperature If a weather forecaster predicts that the temperature for the day will reach 31 C, what is the predicted temperature: (a) in K ? (b) in F ? Solution: –(a) Using Kelvin Equation, we have K = C = = K ~ 304 K

Temperature Temperature: 31 C Solution: –(b) Using Fahrenheit Equation, we have F = (1.8 x C) + 32 = (1.8 x 31) + 32 = = 87.8 F ~ 88 F

Temperature 85.0 F is approximately the same as? Solution: Use the Celsius Equation C = (F - 32) x = ( ) x = 53 x = 29.4 C

Density Physical property of a substance Relation between mass and volume

Density Calculate the density of mercury if 100 g occupies a volume of 7.36 mL. Solution: d = m / v d = 100 g / 7.36 mL d = 13.6 g/mL

Dimensional Analysis – Also called Factor-Label Method or the Unit Factor Method This a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value.

Dimensional Analysis Unit factors may be made from any two terms that describe the same or equivalent “amounts” of what we are interested in. For example, we know that: 1 inch = 2.54 centimeters 1 dozen = 12 items

Dimensional Analysis We can make two unit factors from this information: 1 dozen = 12 items OR 12 items = 1 dozen Arrangement:

Dimensional Analysis How many items are in 2 dozens? Conversion Factor: 1 dozen = 12 items Solution:

Dimensional Analysis How many dozens are in 6 items? Conversion Factor: 1 dozen = 12 items Solution:

Dimensional Analysis How many centimeters are in 6.0 inches? Conversion Factor: 1 in = 2.54 cm Solution:

Dimensional Analysis How many inches are 24.0 centimeters? Conversion Factor: 1 in = 2.54 cm Solution:

Dimensional Analysis Convert 5.0 L to milliliters (mL). Conversion Factor: 1 L = 1,000 mL Solution:

Dimensional Analysis Convert 50.0 mL to liters (L). Conversion Factor: 1 L = 1,000 mL Solution:

Dimensional Analysis If a lady has a mass of 115 lb, what is her mass in grams? Answer: 52,164 g Solution: Because we want to change from lb to g, we look for a relationship between these units of mass. We have that 1 lb = g. In order to cancel pounds and leave grams, we write the conversion factor with grams in the numerator and pounds in the denominator:

Dimensional Analysis You can also string many unit factors together. How many minutes are in 2.0 years? = 1,051,200 minutes

Dimensional Analysis Units are a critical part of describing every measurement. Before you can work with units mathematically, you frequently must convert from one unit to another. Dimensional analysis does not do your math for you, but it makes sure you get your multiplications and divisions straight. After that, all you have to do is find the conversion factors and plug into a calculator.

Significant Figures The term significant figures refers to digits that were measured. When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers.

Significant Figures 1.All nonzero digits are significant. 2.Zeroes between two significant figures are themselves significant. 3.Zeroes at the beginning of a number are never significant. 4.Zeroes at the end of a number are significant if a decimal point is written in the number.

Significant Figures Examples: How many significant figures are present in the following numbers? Number # Significant Figures Rule(s) 48, , , , 4

Significant Figures When math operations are performed, answers are rounded to the number of digits that corresponds to the least number of significant figures in any of the numbers used in the calculation. Example: How many significant figures should be shown for the following calculation? Answer: = 0.62 (2 significant figures)

Powers of Ten Scientific Notation Way to deal with large and small numbers: abbreviate them. Examples: = 1 x = 5 x ,000 = 3 x ,000 = 1.0 x ,000,000 = 6.0 x 10 6

Powers of Ten For numbers larger than 10, the power of 10 is a positive value and negative for numbers less than 1. For numbers between 0 and 10, the power is a positive fraction. In the examples that follow, notice what happens to the decimal point: 10 0 = 1. = 1. with the decimal point moved 0 places 10 1 = 10. = 1. with the decimal point moved 1 place to the right 10 2 = 100. = 1. with the decimal point moved 2 places to the right 10 6 = = 1. with the decimal point moved 6 places to the right And = 0.1 = 1. with the decimal point moved 1 place to the left = 0.01 = 1. with the decimal point moved 2 places to the left = = 1. with the decimal point moved 6 places to the left