Measurements & Calculations Chapter 2

Nature of Measurement Measurement - quantitative observation consisting of two parts: Part 1 - number Part 2 - scale (unit) Examples: 20 grams 6.63    Joule seconds

Scientific Notation Also called exponential notation and powers of ten notation. Scientific notation has two advantages: the number of significant digits can easily be indicated fewer zeros are needed to write a very large or very small number.

Scientific Notation LIP -- Left is positive. 238,000 = 1,500,000 = RIN -- Right is negative = = 2.38 x x x x 10 -2

International System (le Système International) Based on metric system and units derived from metric system.

The Fundamental SI Units

Table 2.2: The Commonly used Prefixes in the Metric System

Table 2.3: The Metric System for Measuring Length

Figure 2.1: Comparison of English and metric units for length on a ruler

One liter is defined as a cubic decimeter and 1 mL is one cubic centimeter.

Figure 2.3: A 100-ml Graduated Cylinder

Common types of laboratory equipment used to measure liquid volume.

Mass & Weight Mass is a measure of the resistance of an object to a change in its state of motion -- a constant--measured in kilograms. Weight is the measure of the pull of gravity on an object and varies with the object’s location--measured in newtons.

Figure 2.4: An electronic analytical balance used in chemistry labs

Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Measurement of volume using a buret. The volume is read at the bottom of the meniscus.

Figure 2.5: Measuring a Pin

Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several elements of the same quantity.

Types of Error Random Error (Indeterminate Error) - measurement has an equal probability of being high or low. Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique.

a) is neither precise nor accurate, b) is precise but not accurate (small random, large systematic errors) c) both precise and accurate (small random, no systematic errors.

Accuracy TrialGraduated CylinderBuret 125 mL26.54 mL 225 mL26.51 mL 325 mL26.60 mL 425 mL26.49 mL 525 mL26.57 mL Average25 mL26.54 mL Which is more accurate? Graduated cylinder produces systematic error --value is too low. Buret

Rules for Counting Significant Figures - Overview 1.Nonzero integers 2.Zeros - leading zeros - captive zeros - trailing zeros 3.Exact numbers

Rules for Counting Significant Figures - Details Nonzero integers always count as significant figures has 4 sig figs.

Rules for Counting Significant Figures - Details Zeros - Leading zeros do not count as significant figures has 3 sig figs.

Rules for Counting Significant Figures - Details Zeros - Captive zeros always count as significant figures has 4 sig figs.

Rules for Counting Significant Figures - Details Zeros -  Trailing zeros are significant only if the number contains a decimal point has 4 sig figs.

Rules for Counting Significant Figures - Details Exact numbers have an infinite number of significant figures. Can come from counting or definition. 15 atoms 1 inch = 2.54 cm, exactly

Rules for Rounding 1. In a series of calculations, carry the extra digits through to the final result, then round. 2. If the digit to be removed a. is less than five, the preceding digit stays the same. b. is equal to or greater than five, the preceding digit is increased by 1.

Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation  2.0 =  13 (2 sig figs)

Rules for Significant Figures in Mathematical Operations Addition and Subtraction: # sig figs in the result equals the number of decimal places in the least precise measurement =  22.5 (3 sig figs)

Dimensional Analysis Also called unit cancellation is a method of solving problems by using unit factors to change from one unit to another. Unit factor(conversion or equivalence factor) - - the unit that you have goes on bottom, and the unit that you want goes on top.

Dimensional Analysis Proper use of “unit factors” leads to proper units in your answer.

Dimensional Analysis What is the dimension of a 25.5 in bicycle frame in centimeters? (25.5 in)(2.54 cm/1 in) = 64.8 cm Units must be cancelled and the answer must have correct sig figs, be underlined, and include proper units!!

Dimensional Analysis The length of the marathon race is approximately 26.2 miles. What is this distance in kilometers? (26.2 mi)(1760 yd/1 mi)(1 m/1.094 yd) (1 km/1000m) = 42.1 km Look to see if your answer is reasonable!! Had your answer been km, would it have been reasonable?

Temperature Celsius scale =   C Kelvin scale = K Fahrenheit scale =   F

Three major temperature scales.

Figure 2.6: Thermometers based on the three temperature scales in (a) ice water and (b) boiling water

Figure 2.8: Converting 70°C to units measured on the Kelvin scale

Figure 2.9: Comparison of the Celsius and Fahrenheit scales

Temperature

Temperature Calculations Convert o C to Kelvin. K = C K = K = K

Temperature Calculations Convert 375 K to Celsius. K = C C = K C = C = 102 o C

Temperature Calculations Convert o C to Fahrenheit. 100 F = F = F = o F

Temperature Calculations Convert 76.0 o F to Celsius. 180 C = 4400 C = 24.4 o C

Density Density is the mass of substance per unit volume of the substance:

Volume of an Irregular Object How can the volume of an irregular object such as a rock be determined using common laboratory equipment? Water displacement

Density Calculations A medallion has a mass of g. When placed in a graduated cylinder containing 75.2 mL of water, the water level rises to 77.8 mL. Is the medallion platinum? D = 21 g/mL Yes, same density as Pt.

Density Calculations If an object has a density of g/cm 3 and a mass of g, what is its volume? V = cm 3

Density When mass is graphed against volume, what does the slope of the line represent? Slope =  y/  x = m/V  density = slope

Figure 2.11: A hydrometer being used to determine the density of the antifreeze solution in a car’s radiator