Structure 1.4.3—Molar mass M has the units g mol^{–1}

**What You’ll Learn:**

- Solve problems involving the relationships between the number of particles, the amount of substance in moles and the mass in grams.

**Keywords**

IBDP chemistry, mole, mol, amount of substance, elementary entities, atoms, molecules, ions, electrons, carbon-12, Avogadro’s constant, N_{A}, 6.022 x 10^23 mol^{-1}, amount of substance, n, number of entities, formula, oxygen atoms, water molecules, data booklet, units

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**Syllabus Links**

Reactivity 2.1—How can molar masses be used with chemical equations to determine the masses of the products of a reaction?

In chemistry, the relationships between the number of particles, the amount of substance in moles, and the mass in grams are essential for performing calculations and solving problems. These relationships are based on the concept of the mole, which is a fundamental unit used to measure the quantity of a substance.

- Relationship between the number of particles and the amount of substance in moles:

A mole is defined as the amount of a substance that contains the same number of particles (atoms, molecules, ions, or other entities) as there are atoms in 12 grams of carbon-12 (¹²C). This number is known as Avogadro’s number (N_{A}) and is approximately 6.022 x 10²³ particles per mole.

The relationship between the number of particles (n_particles) and the amount of substance in moles (n) can be expressed as:

n_particles = n × N_{A}

where n is the number of moles and N_{A} is Avogadro’s number.

- Relationship between the amount of substance in moles and the mass in grams:

The relative atomic mass (A_{r}) or relative formula mass (M_{r}) of a substance can be used to convert between the amount of substance in moles (n) and the mass in grams (m). This relationship is given by:

m = n × A_{r} (for elements) or m = n × M_{r} (for compounds)

where m is the mass in grams, n is the number of moles, A_{r} is the relative atomic mass of the element, and M_{r} is the relative formula mass of the compound.

- Solving problems involving these relationships:

To solve problems involving the relationships between the number of particles, the amount of substance in moles, and the mass in grams, follow these steps:

a. Identify the given values and the values you need to find. b. Use the appropriate relationship (as mentioned above) to convert between the given values and the values you need to find. c. Perform the calculations using the relationships and the given values.

Example:

Calculate the number of oxygen molecules in 32 grams of oxygen gas (O₂).

Solution:

a. Given values:

- Mass of oxygen gas (m) = 32 g
- Relative formula mass of oxygen gas (M
_{r}) = 32.00 g/mol (as the relative atomic mass of O = 16.00 g/mol)

b. Convert mass to moles:

- n = m / M
_{r} - n = 32 g / 32.00 g/mol
- n = 1 mol

c. Convert moles to the number of particles:

- n_particles = n × N
_{A} - n_particles = 1 mol × 6.022 x 10²³ particles/mol
- n_particles = 6.022 x 10²³ particles

Thus, there are approximately 6.022 x 10²³ oxygen molecules in 32 grams of oxygen gas.

Questions 1.4.3a

- What is the formula for calculating the number of moles in a substance?
- How can you determine the mass of a substance using the number of moles?
- What is the molar mass of a substance and how is it calculated?
- If you know the molar mass of a substance and its mass, how can you find the number of moles?
- How many moles are present in 50 grams of water?
- What is the number of moles of oxygen in 100 grams of carbon dioxide?
- How many grams of iron are present in 2 moles of FeCl3?
- If the molar mass of a substance is 32 grams/mol, how many moles are present in 128 grams of the substance?
- How many moles of methane are present in 4 grams of the substance?
- What is the mass of 0.5 moles of sodium chloride?
- If 10 moles of hydrogen gas react with 5 moles of oxygen gas, what is the limiting reactant?
- What is the number of moles of water produced when 1 mole of propane is combusted?
- What is the number of moles of calcium chloride present in 100 grams of the substance?
- How many moles of oxygen are present in 5 grams of potassium permanganate?
- What is the number of moles of hydrogen gas produced when 2 moles of aluminum react with excess hydrochloric acid?

## SI Unit, or International System of Units

Are a globally accepted system of units used for consistent measurement of physical quantities. SI Units were established in 1960 by the General Conference on Weights and Measures (CGPM) to provide a standardized and coherent system of units for scientific, technical, and everyday use. The SI Units are based on seven fundamental units, from which all other derived units are obtained.

Here is a table of the seven base SI Units:

Property | Unit Name | Symbol |
---|---|---|

Length | meter | m |

Mass | kilogram | kg |

Time | second | s |

Electric Current | ampere | A |

Thermodynamic Temperature | kelvin | K |

Amount of Substance | mole | mol |

Luminous Intensity | candela | cd |

In addition to the base SI Units, there are derived SI Units that are formed by combining the base units. Here is a table of some common derived SI Units:

Property | Unit Name | Symbol | Derived From |
---|---|---|---|

Area | square meter | m² | m × m |

Volume | cubic meter | m³ | m × m × m |

Speed | meter per second | m/s | m / s |

Acceleration | meter per second squared | m/s² | m / s² |

Force | newton | N | kg × m / s² |

Pressure | pascal | Pa | kg / (m × s²) |

Energy | joule | J | kg × m² / s² |

Power | watt | W | kg × m² / s³ |

Electric Charge | coulomb | C | A × s |

Electric Potential | volt | V | kg × m² / (A × s³) |

Electric Resistance | ohm | Ω | kg × m² / (A² × s³) |

Electric Conductance | siemens | S | A² × s³ / (kg × m²) |

Magnetic Flux | weber | Wb | kg × m² / (A × s²) |

Magnetic Field Strength | tesla | T | kg / (A × s²) |

Capacitance | farad | F | A² × s⁴ / (kg × m²) |

Frequency | hertz | Hz | 1/s |

Temperature Difference | degree Celsius | °C | K |

These SI Units provide a uniform and consistent way of measuring physical properties, ensuring accurate communication and understanding of measurements in various fields of science, engineering, and daily life.

Here is a table of some common SI Unit prefixes, their abbreviations, and their corresponding scales:

Prefix | Abbreviation | Scale |
---|---|---|

yocto | y | 10^{-24} |

zepto | z | 10^{-21} |

atto | a | 10^{-18} |

femto | f | 10^{-15} |

pico | p | 10^{-12} |

nano | n | 10^{-9} |

micro | μ | 10^{-6} |

milli | m | 10^{-3} |

centi | c | 10^{-2} |

deci | d | 10^{-1} |

deca | da | 10^{1} |

hecto | h | 10^{2} |

kilo | k | 10^{3} |

mega | M | 10^{6} |

giga | G | 10^{9} |

tera | T | 10^{12} |

peta | P | 10^{15} |

exa | E | 10^{18} |

zetta | Z | 10^{21} |

yotta | Y | 10^{24} |

These prefixes are used to indicate multiples or fractions of SI Units, and are commonly used in scientific and engineering notation to express large or small quantities in a more convenient way.

Questions 1.4.3b

- What is the SI Unit system and why is it important in science?
- What are the seven base SI Units and what properties do they represent?
- How are derived SI Units formed, and what are some examples?
- What is the difference between a base SI Unit and a derived SI Unit?
- Why is the kilogram considered the base unit of mass in the SI system, and how is it defined?
- What is the relationship between the meter and other SI Units, such as the kilogram and the second?
- How is the kelvin used to measure temperature, and what is the significance of the absolute zero point?
- How are SI Units used in everyday life, and what are some examples?
- What are some common SI Unit prefixes and their corresponding values?
- Why is the use of SI Units important in international communication and collaboration among scientists and researchers?

Answers