0.6.2 Multiplying and dividing numbers
When multiplying numbers written in scientific notation, the coefficients (i.e. the numbers in front of the 10n) are multiplied and the exponents are added. So, for example:
When dividing numbers written in scientific notation, the coefficients are divided and the exponents subtracted. So, for example:
Worked Example 0.8
Calculate the answers to the following expressions, and present your result in scientific notation:
1 7.5 × 5.7 =
2 (6.4 × 102) × (1.30 × 104) =
3 (1.751 × 10−3) × (59.0 × 10−2) =
4 1.435 × 10−2 ÷ 2.9 × 10−4 =
Solution
1 7.5 × 5.7 = 42.75 = 43 = 4.3 × 101The smallest number of significant figures is two, so this becomes 43 after reducing the number of significant figures and rounding.
2 (6.4 × 102) × (1.30 × 104) = 8.32 × 106 = 8.3 × 106The smallest number of significant figures is two, so 8.32 becomes 8.3 after reducing the number of significant figures.
3 (1.751 × 10−3) × (59.0 × 10−2) = 103.309 × 10−5 = 1.033 09 × 10−3 = 1.03 × 10−3The smallest number of significant figures is three, so 1.03309 becomes 1.03 after reducing the number of significant figures.
4 = 4.9 × 101The smallest number of significant figures is two, so 4.948 × 101 becomes 4.9 × 101 after reducing the number of significant figures and rounding down. This would normally be written as 49.
0.7 Writing chemical formulae and equations
0.7.1 Writing chemical formulae
Most people are familiar with H2O and CO2 as the formulae that represent water and carbon dioxide, respectively.
A chemical compound has a formula that represents the type and number of atoms in that compound. The plural of ‘formula’ is ‘formulae’ as the word derives from Latin.
The letters in the formulae represent the elements in the periodic table, and the numbers given as subscripts after the letters indicate how many atoms of each element are in one unit of the compound. The formula H2O tells us there are two atoms of hydrogen (H) and one atom of oxygen (O) in one molecule of the compound. In CO2, there is one atom of carbon and two atoms of oxygen.
The terms ‘atom’ and ‘molecule’ will be explained fully in Chapter 1.
In the formulae of some compounds, there may be atoms enclosed in brackets (or parentheses): for example, Ca(NO3)2, the formula for calcium nitrate. The formula indicates that in one formula unit of calcium nitrate, there is one atom of calcium (Ca), two atoms of nitrogen (N), and six atoms of oxygen (O). The brackets act as a multiplier, multiplying all the atoms inside the bracket by the number in subscript outside the bracket.
Substances such as calcium nitrate, Ca(NO3)2, are known as salts. These are composed of ions. Ions are atoms, or groups of atoms, that have an overall charge. The charge can be positive or negative. A positively charged ion is known as a cation. A negatively charged ion is known as an anion. Table 0.4 lists some common cations and anions. You will see that most cations are actually metal ions.
Table 0.4 Symbols and charges for some common cations and anions.
| Common cations | Common anions | ||||
|---|---|---|---|---|---|
| Symbol | Name | Charge | Symbol | Name | Charge |
| Na+ | Sodium | +1 | F− | Fluoride | −1 |
| K+ | Potassium | +1 | Cl− | Chloride | −1 |
| Mg2+ | Magnesium | +2 | Br− | Bromide | −1 |
| Ca2+ | Calcium | +2 | O2− | Oxide | −2 |
| Al3+ | Aluminium | +3 | S2− | Sulfide | −2 |
| Cu2+ | Copper | +2 | CO32− | Carbonate | −2 |
| Fe2+ | Iron | +2 | SO42− | Sulfate | −2 |
| Ag+ | Silver | +1 | NO3− | Nitrate | −1 |
| Zn2+ | Zinc | +2 | PO43− | Phosphate | −3 |
| NH4+ | Ammonium | +1 | OH− | Hydroxide | −1 |
Salts are neutral substances made up of positive cations and negative anions in a ratio that ensures the overall charge on the salt is zero. For example, aluminium sulfate is composed of aluminium (Al3+) ions and sulfate (SO42−) ions. Because the salt is neutral overall, the formula must be Al2(SO4)3.
0.7.2 Writing and balancing chemical