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.
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.
2. Convert the following scientific notation numbers to non-scientific notation numbers.
4.2 x 103
2.15 x 10-4
3.14 x 10-6
9.22 x 105
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?
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.
The Celsius scale is based on the properties
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)
Convert the following temperatures from one unit to the other.
263 K to °F
38 K to °F
13 °F to °C
1390 °C to K
3000 °C to °F
When evaluating a change in temperature, does it matter if the change is recorded in Celsius or Kelvin?
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 is a physical property of a substance.
It is a measure of the compactness of matter.
It varies with the temperature.
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?