2. Chemical Calculations
2.1. Physical Quantity, Magnitude, and Units
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Physical quantity
A physical quantity is something you can measure.
Examples:
- Length, \(l\)
- Weight (mass), \(m\)
- Speed, \(v\)
- Voltage, \(U\)
- Cost
Unit
A unit is a definite magnitude of a certain physical quantity.
Examples:
- Length, \(l\) – meter/metre, \(\text{m}\)
- Weight (mass), \(m\) – gram, \(\text{g}\)
- Speed, \(v\) – meters per second, \(\text{m/s}\)
- Voltage, \(U\) – volt, \(\text{V}\)
- Cost – € (Euro) etc.
SI units
Get used to them!
- Mass: 1 kg = 1000 g
- Volume: 1 L = 1 dm3 = 1000 mL
Also: Learn the prefixes:
Prefix | Base 10 |
|
Name | Symbol | |
mega | M | 106 |
kilo | k | 103 |
deci | d | 10–1 |
milli | m | 10–3 |
micro | μ | 10–6 |
Numerical magnitude
The amount (magnitude) of the unit you’re measuring.
Examples:
Phys. quant. |
Example | Numerical magnitude |
Length | \(l = 1.93\text{m}\) | 1.93 |
Mass | \(m = 250\text{g}\) | 250 |
Speed | \(v = 25\text{m/s}\) | 25 |
Voltage | \(U = 12\text{V}\) | 12 |
The relation between physical quantity, magnitude, and unit
Note: There is a multiplication sign between "\(250\)" and "\(\text{g}\)": \(m = 250 \times \text{g}\)
- This is similar to algebraic notation, e.g. \(y = 250x\).
How to use physical quantity, magnitude, and unit
Example 1
If I dissolve 25g salt in 0.5dm3 water, which is the salt concentration? Give your answer in the unit g/dm3.
Solution
Since the answer is to be given in the unit \(\frac {\text{g}}{\text{dm}^3}\), I have to divide the mass \(m\) by the volume \(V\). We write the concentration \(c\):
\[c = \frac {m}{V} = \frac {250\text{g}}{0.5\text{dm}^3} = 50 \frac {\text{g}}{\text{dm}^3}\]
Answer: \(c = 50\text{g/dm}^3\)
↑ Note: Both physical quantity, magnitude, and unit in the answer!
Example 2
A salt solution has a concentration of 50g/dm3. From this solution I pour 0.100dm3 in a glass. What is the mass of the salt in the glass?
Solution
I want to know the mass \(m\), which is measured in \(\text{g}\).
I know the concentration \(c\), which is measured in \(\frac {\text{g}}{\text{dm}^3}\).
How do we go from the unit \(\frac {\text{g}}{\text{dm}^3}\) to \(\text{g}\)? We must multiply \(\frac {\text{g}}{\text{dm}^3}\) with \(\text{dm}^3\):
\[\frac {\text{g}}{\text{dm}^3} \times \text{dm}^3 = \text{g}\]
Thus, we can write:
\[m = cV = 500\frac {\text{g}}{\text{dm}^3} \times 0.100\text{dm}^3 = 50.0\text{g}\]
Answer: \(m = 50.0\text{g}\)
Contents
- 1. States of Matter. The Atom and the Periodic Table
- 1.1. Matter. States of Matter
- 1.2. Elements and Chemical Compounds. Pure Substances and Mixtures
- 1.3. The Birth of Chemistry
- 1.4. Atomic Theory. The Atomic Model
- 1.5. Atomic Number, Mass Number, and Atomic Mass
- 1.6. Electron Configurations
- 1.7. Beyond Bohr's Atomic Model
- 1.8. Redox Reactions
- 1.9. The Structure of the Periodic Table
- 1.10. The Noble Gases
- 1.11. The Alkali Metals and the Halogens
- 1.12. The Alkaline Earth Metals and the Oxygen Group
- 1.13. A Few of the Elements in Group 13, 14, and 15
- 2. Chemical Calculations
- 2.1. Physical Quantity, Magnitude, and Units
- 2.2. Atomic Mass, Molecular Mass, and Unit Mass
- 2.3. Amount of Substance, Molar Mass, and Mass
- 2.4. Stoichiometry. Conservation of mass
- 2.5. Water of Crystallization
- 2.6. Calculating the Formula of a Chemical Compound
- 2.7. From Empirical to Molecular Formulas
- 2.8. Equivalent Amounts of Substance and Masses
- 2.9. Gases and Pressure
- 2.10. Concentrations
- 2.11. Dilutions
- 2.12. Yield
- 2.13. Limiting Reactants
- 3. Chemical Bonding
- 3.1. How Ionic Compounds are Formed
- 3.2. Precipitations
- 3.3. Names and Formulas of Ionic Compounds
- 3.4. Ionic Bonds
- 3.5. Properties of Ionic Compounds
- 3.6. Metal Bonding
- 3.7. Covalent Bonds
- 3.8. Polar Covalent Bonding
- 3.9. Dipoles. Polar and non-polar Molecules
- 3.10. The VSEPR Theory
- 3.11. Hydrogen Bonding. The Peculiar Water
- 3.12. Equals Solves Equal
- 3.13. Solubility of Gases in Water
- 3.14. Solubility of Salts in Water
- 4. Thermochemistry
- 5. Chemical Equilibrium
- 5.1. Reaction Rates
- 5.2. The Law of Mass Action
- 5.3. Calculations on Chemical Equilibrium
- 5.4. Heterogenous Equilibria. Solubility Product
- 5.5. Is the System at Equilibrium? The Reaction Quotient Q
- 5.6. Changing the Concentrations in a System in Equilibrium.
- 5.7. Diluting or Compressing Systems in Equilibrium, or Changing the Temperature
- 6. Acids and bases
- 7. Oxidation and Reduction
- 8. Electrochemistry
- 9. Organic Chemistry
- 9.1. Alkanes
- 9.2. Chain Isomers. Nomenclature
- 9.3. Haloalkanes
- 9.4. Nucleophilic Substitution
- 9.5. Alkenes
- 9.6. Electrophilic Addition. Markovnikov’s Rule
- 9.7. Elimination
- 9.8. Alkynes
- 9.9. Arenes and Aromatic Compounds
- 9.10. Alcohols
- 9.11. Oxidation of Alcohols
- 9.12. Aldehydes and Ketones
- 9.13. Thiols and Disulfides
- 9.14. Ethers
- 9.15. Amines
- 9.16. Nitro Compounds and Organic Nitrates
- 9.17. Carboxylic Acids
- 9.18. More on Carboxylic Acids
- 9.19. Stereoisomerism
- 9.20. Esters
- 9.21. Lipids
- 9.22. Mono-, Oligo-, and Polysaccharides
- 9.23. Amino Acids
- 9.24. Nucleotides
- 10. Biochemistry
- 10.1. Proteins
- 10.2. Enzymes
- 10.3. Catabolic Processes
- 10.4. Carrier Molecules
- 10.5. Glycolysis
- 10.6. Beta-oxidation
- 10.7. The Citric Acid Cycle
- 10.8. The Metabolism of Amino Acids
- 10.9. The Electron Transport Chain
- 10.10. Anabolic Processes
- 10.11. Gluconeogenesis and Fatty Acid Synthesis
- 10.12. DNA: Structure and Function
- 11. Analytical chemistry