# Chem I honors Unit 2 Notes: Numbers in Chemistry Measurement

 Date 17.10.2016 Size 44.91 Kb. #280  2014-2015 Chem I Honors Unit 2 Notes: Numbers in Chemistry

Measurement

Measurements and calculations applied to those measurements allow us to determine some of the quantitative properties of a substance. For example, we measure mass and volume, and can calculate density.

Scientific Notation

Measurements and calculations often require the use of very large or very small numbers. To make the numbers easier to handle, we use scientific notation. All numbers are represented by a number between 1 and 10, which is multiplied by a power of 10. If the decimal point moved to the left then the power is positive, if it moved to the right then it is negative.

Example 1: convert 42000 to scientific notation.

• Multiply 4.2 times 10 to the power that makes it equal to 42000. Since the decimal moved 4 places to the left to make it 4.2, the power of 10 used is +4.

42000 = 4.2 x 104

Practice 1: Convert 528,000 to scientific notation.

Example 2: Convert 0.00012 to scientific notation.

• Multiple 1.2 times 10 to the power that makes it equal to 0.00012. Since the decimal moved 4 places to the right, the power of 10 used is -4.

0.00012 = 1.2 x 10-4

Practice 2: Convert 0.000006450 to scientific notation.

1. Convert the following numbers to scientific notation.

1. 24500

2. 356

3. 0.000985

4. 0.222

5. 12200

2. Convert the following scientific notation numbers to non-scientific notation numbers.

1. 4.2 x 103

2. 2.15 x 10-4

3. 3.14 x 10-6

4. 9.22 x 105

5. 9.57 x 102

Uncertainty, Significant Figures, and Rounding

When taking a reading on a piece of laboratory equipment such as a graduated cylinder, there is always a degree of uncertainty in the recorded measurement. The reading falls between divisions on the scale, so you need to estimate between the divisions. The estimated digit is said to be uncertain, and is reflected in the reading with a +/-. All of the digits that can be recorded with certainty are said to be certain. The certain and the uncertain together are called significant figures. The reading below is certain to the 1s place and uncertain to the tenth place (estimated between the 1s) so the reading is 43.1 +/- 0.1. There are 3 significant figures in the measurement. What are the following readings? How many significant figures are there?  In the case of a digital reading, all digits in the readout are considered to be significant. The reading above is 12.68 g +/- .01. There are 4 sig figs in the reading.

Significant Figures in Calculations

When doing calculations with measurements, there are rules about how many numbers the calculated value should carry, based on the significant figures in each measurement.

To determine the number of significant figures in a number use the following rules.

• Any nonzero integers are always significant.

• Leading zeros (the ones that precede the non-zero digits) are never significant.

• Sandwiched zeros are always significant.

• Trailing zeros (at the end of a number) are only significant if there is a decimal point in the number.

• Exact numbers (counts) have an infinite number of significant figures.

• In scientific notation the 10x part is never significant.

Or Use the “Atlantic Pacific Rule” Pacific Side Atlantic Side

• When counting sig figs in a number, check to see if a decimal is Present, or Absent.

• If Present – start counting from the Pacific side of the number. Start with the first NON-ZERO and count everything, left to right.

• If Absent - start counting from the Atlantic side of the number. Start with the first NON-ZERO and count everything, right to left.

• 24,000

• 2.40

• 0.00024

• 0.002400

• 0.02040

• 240,002

• 24.2000

• 24.002

• 2.40 x102

Significant Figures in Calculations

1. When multiplying or dividing: Limit the answer to the same number of significant figures as the number with the fewest number of significant figures.

2. When adding or subtracting: Limit the answer to the same number of decimal places that appear in the number with the fewest number of decimal places.

i.e., don’t record a greater degree of significant figures or decimal places in the calculated answer than the weakest data will allow.

Rounding

Calculators often give many more figures in the answer to a calculation than the significant ones. As a result many of the numbers in the answer are meaningless, and the answer needs to be rounded.

In a multi-step calculation there are 3 options:

• Leave all numbers on the calculator in the intermediate steps, and leave the rounding until the end.

• Round to the correct number of figures in each step.

• Round to an extra figure in each intermediate step and then round to the correct number of significant figures at the end of the calculation.

In most cases it is preferable to leave numbers on the calculator and round at the end.

Whichever method you use, if the digit directly to the right of the final significant figure is less than 5 then the preceding digit stays the same, if it is equal to or greater than 5 round it up.

Task 3 : Use a calculator to carry out the following calculations and record the answer with the correct number of significant figures.

(a) (34.5) (23.46)

(b) 123 / 3

(c) (2.61 x 10-1) (356)

(d) 21.78 + 45.86

(e) 23.888897 - 11.2

(f) 6 - 3.0

SI units

Units tell us the scale that is being used for measurement. Prefixes are used to make writing very large or very small numbers easier.

SI Units Used in Chemistry – MEMORIZE!
 Base Unit Name of Unit Symbol Mass Kilogram Kg Length Meter m Time Second s Amount of substance Mole mol Temperature Kelvin K

Prefixes we will use in Chemistry-MEMORIZE!
 Prefix Symbol Meaning Example using meters Kilo k 103 1km = 103 m Deci d 10-1 1dm = 10-1m Centi c 10-2 1 cm = 10-2m Milli m 10-3 1mm = 10-3m Micro µ 10-6 1 µm = 10-6m Nano n 10-9 1nm = 10-9m

Task 4: Fill in the following

1m = _______ km

1m = _______ dm

1m = _______ cm

1m = _______ mm

1m = _______ µm

1m = _______ nm

Converting units using dimensional analysis. (Factor label method)

One unit can be converted to another by multiplying by an equality called a conversion factor.

DO NOT memorize the conversion factors below. They will be provided for you on a test or quiz. 4 cups = 1 qt

4 qt = 1 gal

2 pt = 1 qt
Using Conversion Factors
There are 2.54 cm in exactly 1 inch, therefore the equality is 2.54 cm = 1.00 in.

We can use the equality in one of two ways in a conversion problem: or The one used is the one that allows you to cancel the unit you don’t want, remembering that dividing a unit by the same unit equals 1.

Example 3: To convert 5.00 cm to inches, use the form of the equality on the right, above. x = _________ in

Example 4: To convert 5.00 inches to cm, use the form of the equality on the left:

Task 5: Convert the following quantities from one unit to the other using the conversion chart above.

1. 30 m to miles

2. 1500 yd to miles

3. 206 miles to m

4. 34 kg to lbs

5. 34 lbs to kg

Temperature

Temperature is considered the “hotness” of matter. It is a reflection of the kinetic energy of the particles of matter in the sample. The faster the particles of matter are moving, the higher the temperature. Temperature determines the direction of heat flow. Heat flows spontaneously from hotter matter to cooler matter.

• In scientific measurements, the Celsius and Kelvin scales are most often used.

• The Celsius scale is based on the properties
of water.

• Freezing Point of water=

• Boiling Point of water=

• The kelvin is the SI unit of temperature.

• It is based on the properties of gases.

• There are no negative Kelvin temperatures.

• The lowest possible temperature is called absolute zero (0 K).

• K = C + 273.15

• The Fahrenheit scale is not used in scientific measurements, but you hear about it in weather reports!

• The equations below allow for conversion between the Fahrenheit and Celsius scales: F = 9/5(C) + 32

C = 5/9(F − 32)

1. Convert the following temperatures from one unit to the other.

1. 263 K to °F

2. 38 K to °F

3. 13 °F to °C

4. 1390 °C to K

5. 3000 °C to °F

1. When evaluating a change in temperature, does it matter if the change is recorded in Celsius or Kelvin?

Derived Units

Volume

All other units can be derived from base units. The most important derived unit in Chemistry is volume. Volume has units of length3. (m3, cm3 etc.) Common units for volume are liters, or milliliters.

Commit these relationships to memory!

1 cm3 = 1mL

1L = 1000mL

Example 5: What is the volume in cm3 of a box that is 1.5 cm long, 1.0 cm wide, and 0.5 cm deep? What is this volume in mL? In L?

Task 7: What is the volume of a pool in L if it is 25 m long, 10 m wide, and 6 ft. deep?

Density

• Density is a physical property of a substance.

• It is a measure of the compactness of matter.

• It varies with the temperature.

• Density = • Typical Units of Density are g/mL for liquids or g/L for gases

Example 7: What is the density of a liquid that has a mass of 10.76 grams and a volume of 11.9 mL?

Specific Gravity: Related to density, specific gravity is the ratio of the density of a substance to the density of a standard, which is water. Since the density of water is 1 g/mL, specific gravity is the same number as density, with no units.

Example 8: Mazola corn oil has a density of 0.875 g/mL. What is its specific gravity?

Example 9: A bottle with a yellow liquid in it has a mass of 5.96 grams. The mass of the bottle alone is 1.87 grams. The volume of liquid in the bottle is 5.06 mL. Calculate the specific gravity of the liquid.

Using Density and Specific Gravity as a conversion factor

Density or specific gravity are often used to convert mass to volume and volume to mass.

Example 10: What is the mass of water needed to fill the pool described in example 6?

Accuracy and Precision

Accuracy refers to how close the measured value is to the actual value of the quantity.

Precision refers to how close several measurements of the same quantity are to one another. Consider three sets of data that have been recorded after measuring a piece of wood that is exactly 6.000 m long.

 Set 1 Set 2 Set 3 5.864 6.002 5.872 5.878 6.004 5.868 Average Length 5.871 6.003 5.870

1. Which set is most accurate?

2. Which set is most precise?

Percent Error

The data that comes from experiments often differs from the actual value.

Percent error is a way to express the accuracy of experimental data.

% Error = x 100