Unit 2 - Mathematical Calculations and The Mole

Introduction:

Chapter 2 centers on the analysis and usage of data. We will also be introduced to the concept of the mole, which really is a counting number just like "a dozen" means 12. One mole = 6.02 times 10 to the 23rd power. We will learn how to calculate moles of a substance using the dimensional analysis (aka "factor-label") techniques we learned in chapter 2. Near the end of the chapter, we will use our newly-acquired knowledge to calculate empirical and molecular formulas and formulas for hydrates.

2.2

a. The result of nearly every measurement is a number and a unit.

b. The SI system of measurement is used in science. It has seven base units: the meter (length), kilogram (mass), second (time), kelvin (temperature), mole (amount of substance), ampere (electric current) and candela (luminous intensity).

c. Weight is a measure of the gravitational pull on matter.

d. Derived SI units include the square meter (area) and the cubic meter (volume).

e. Density is the ratio of mass to volume.

f. Conversion factors are used to convert from one unit to another.

2.3

a. Accuracy refers to the closeness of a measurement to the correct or accepted value. Precision refers to the closeness of values for a set of measurements.

b. Percent error is the difference between the experimental and the accepted value that is divided by the accepted value and then multiplied by 100.

c. The significant figures in a number consist of all digits known with certainty plus one final digit, which is uncertain.

d. After addition or subtraction, the answer should be rounded so that it has no more digits to the right of the decimal point than there are in the measurement that has the smallest number of digits to the right of the decimal point. After multiplication or division, the answer should be rounded so that it has no more significant figures than there are in the measurement that has the fewest number of significant figures.

Ohio Department of Education - Chemistry Standards:

In earlier grades, properties of materials were quantified with measurements that were always associated with some error. In this course, scientific protocols for quantifying the properties of matter accurately and precisely are studied. Using metric measuring systems, significant digits or figures, scientific notation, error analysis and dimensional analysis are vital to scientific communication.

There are three domains of magnitude in size and time: the macroscopic (human) domain, the cosmic domain and the submicroscopic (atomic and subatomic) domain. Measurements in the cosmic domain and submicroscopic domains require complex instruments and/or procedures.

The atomic mass of an element is calculated given the mass and relative abundance of each isotope of the element as it exists in nature. Because the mass of an atom is very small, the mole is used to translate between the atomic and macroscopic levels. A mole is used as a counting number, like a dozen. It is equal to the number of particles in exactly 12 grams of carbon – 12 atoms. The mass of one mole of a substance is equal to its formula mass in grams. The formula mass for a substance can be used in conjunction with Avogadro’s number and the density of a substance to convert between mass, moles, volume and number of particles of a sample.

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