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The Law of Conservation of Mass states that in a chemical reaction, the total mass of the reactants is equal to the total mass of the products. In other words, mass can neither be created nor destroyed in a chemical reaction. This principle was first established by a French chemist named Antoine Lavoisier in 1789. For example, consider the reaction between hydrogen gas (H_2) and oxygen gas (O_2) to form water (H_2O): \(2H_2 + O_2 → 2H_2O\) The total mass of the reactants (4 g of hydrogen + 32 g of oxygen = 36 g) is equal to the total mass of the products (36 g of water). Thus, the Law of Conservation of Mass holds true for this reaction.

The Law of Definite Proportion, also known as the Law of Constant Composition, states that a compound is always composed of the same elements in the same proportion by mass. In other words, the ratio of the masses of the elements in a compound is always constant. This law was proposed by the French chemist Joseph Proust in the early 19th century. For example, consider water (H_2O). Water is always composed of two parts hydrogen and one part oxygen by mass. The proportion of hydrogen and oxygen in water remains the same, regardless of the source or quantity: Mass of hydrogen: \(2 \times 1 g/mol = 2 g/mol\) Mass of oxygen: \(1 \times 16 g/mol = 16 g/mol\) Ratio of hydrogen to oxygen in water: \(2 g : 16 g = 1:8\)

The Law of Multiple Proportions, also known as Dalton's Law, states that when two elements form more than one compound, the ratios of the masses of one element that combines with a fixed mass of the other element are small whole numbers. John Dalton, an English chemist, proposed this law in the early 1800s. For example, consider carbon and oxygen, which can form two different compounds: carbon monoxide (CO) and carbon dioxide (CO_2). Mass of carbon in both compounds: \(12 g/mol\) In carbon monoxide (CO): Mass of oxygen: \(16 g/mol\) In carbon dioxide (CO_2): Mass of oxygen: \(2 \times 16 g/mol = 32 g/mol\) The ratio of oxygen masses in CO and CO_2 is \(16 g/mol : 32 g/mol\), which simplifies to \(1:2\), a small whole number ratio. Thus, the Law of Multiple Proportions holds true for these compounds.