Calculations in Chemistry Scientific Math

Over the next few lessons you will learn some basic math essential to studying chemistry: Temperature Scales/Conversions Scientific Notation Significant Figures in Measurement/Calculations

I CAN convert between common and scientific temperature scales.

Temperature vs Heat What is TEMPERATURE and how is it different from HEAT? Temperature and Heat are NOT the same thing. How are they different? Remember KINETIC ENERGY? HEAT is a measure of the TOTAL ENERGY possessed by a substance. TEMPERATURE is a measure of the AVERAGE ENERGY possessed by the particle of a substance.

Example Two beakers of water are placed on a hot plate and heated until both reach the boiling point of water, 100 °C. What is the TEMPERATURE of each beaker? 100 °C Which beaker of water has MORE ENERGY? The larger one on the right.

Temperature Scales Since the invention of the first modern thermometer in 1724, scientists have created a number of temperature scales. A common widely used scale is the FAHRENHEIT scale. Freezing Point (water) 32 oF. Boiling Point (water) 212 oF. 180 degree range between FP and BP. Temperatures can be LESS THAN ZERO.

CELSIUS TEMPERATURE SCALE The Celsius Scale is the preferred scale for most scientific work. Part of the SI (Metric) System Freezing Point is 0 oC. Boiling Point is 100 oC. 100 degree range between FP and BP. Temperatures can be LESS THAN ZERO.

In these instances, a third scale is used. For most science work the Celsius Scale is fine. However, in some calculation, temperatures less than ZERO present a problem. Example Volume/Mass calculations cannot use temperatures less than zero because volume or masses CANNOT BE NEGATIVE. In these instances, a third scale is used.

The KELVIN SCALE is based on the expansion and contraction of matter. For every degree of change (+ or -) Kelvin, matter expands or contracts by 1/273.15 of its original volume. If matter’s temperature could be lowered to -273.15 K, matter would have a ZERO VOLUME, which is THEORETICALLY impossible.

This temperature is known as ABSOLUTE ZERO. At this temperature matter would possess NO KINETIC ENERGY! Scientist have come within a few millionths of a degree of absolute zero!

Temperature Calculations Often in scientific work, it is necessary to convert temperatures from one system to another. This is easily done with the appropriate equation.

oC = 0.56(oF-32) Fahrenheit to Celsius To convert a temperature given in oF to Celsius, use this equation: oC = 0.56(oF-32)

oF = 1.8 (oC) + 32 Celsius to Fahrenheit To convert a temperature in oC to Fahrenheit, use this equation: oF = 1.8 (oC) + 32

Converting Celsius Kelvin K = oC + 273.15 oC = K – 273.15 (Generally just 273 is fine!)

Fahrenheit  Kelvin K = 0.56 (oF-32) + 273.15 To convert Fahrenheit to Kelvin: K = 0.56 (oF-32) + 273.15

Practice Problems Complete the practice problems sheet.

I CAN convert number to and from SCIENTIFIC NOTATION.

What are Measurements A measurement is a QUANTITY with both a NUMBER and a UNIT. In science, you will encounter very, very large numbers as well as very, very small ones. To simply the handling of such numbers, we often write them in a compressed form called SCIENTIFIC NOTATION.

In scientific notation, numbers with many digits are often written as a coefficient and a power of 10. Example 6.022 x 1023 Coefficient Power of 10

Converting Numbers to Scientific Notation Converting numbers to scientific notation is easy. 1. Locate the DECIMAL [may be an understood decimal] 2. MOVE the decimal to the LEFT or to the RIGHT until it is to the RIGHT OF THE FIRSTNON-ZERO DIGIT in the number. Example 24567.88 would be 2.456788 3. COUNT THE NUMBER OF PLACES the decimal was moved…this is the POWER OF 10.

When the decimal is moved to the LEFT the power of 10 is POSITIVE. When the decimal is moved to the RIGHT the power of 10 is NEGATIVE. You may DROP TERMINAL ZEROS to round off or follow the directions in the problem.

SAMPLE PROBLEM Convert this number to scientific notation: 602200000000000000000000 Locate the decimal. Decide if the decimal needs to move left or right. Count the number of places it has to move. Rewrite the number with the decimal in its new location [drop terminal zeros]. Add the power of 10 with the correct sign.

The decimal was moved a total of 23 places to the left. 602200000000000000000000 Since there was no written decimal it is understood to be at the end of the number. Which direction should it be moved? We will need to move it toward the LEFT to get it between the first two non-zero digits. The decimal was moved a total of 23 places to the left.

6 02200000000000000000000 Drop the terminal zeros to get 6 022 Since the decimal moved 23 places to the LEFT, the power of 10 is POSITIVE 23.

So the number in scientific notation is: 6.022 X 1023

MORE PRACTICE Write this number is Scientific Notation: 0.0000475000

Decimal First two non-zero digits 0.0000475000 Decimal First two non-zero digits This time the decimal has to be moved to the RIGHT. This will make the power of 10 NEGATIVE. 000004.75000 DROP these zeros!

The decimal was moved 5 places to the right, so the power of 10 is -5. 4.75 The decimal was moved 5 places to the right, so the power of 10 is -5. 4.75 X 10-5

Write each number in scientific notation. 0.07882 = 0.00000272338 = 118000 = 87200 = 0.00002786 = 0.000000664 = 450 = 74171.7 = 770 = 0.0000085 =

0.07882 = 7.882 × 10-2 0.00000272338 = 2.72338 × 10-6 118000 = 1.18 × 105 87200 = 8.72 × 104 0.00002786 = 2.786 × 10-5 0.000000664 = 6.64 × 10-7 450 = 4.5 × 102 74171.7 = 7.41717 × 104 770 = 7.7 × 102 0.0000085 = 8.5 × 10-6