Some Basic Concepts of Chemistry: Laws of Chemical Combination

Overview of Laws of Chemical Combination

In the study of chemistry, particularly for JEE and NEET preparation, understanding the fundamental laws that govern chemical reactions is essential. There are five primary laws of chemical combination:

• Law of Mass Conservation: Deals with the preservation of mass in a system.

• Law of Constant Proportions (Definite Proportions): Deals with the fixed composition of compounds.

• Law of Multiple Proportion: Concerns elements forming more than one compound.

• Law of Reciprocal Proportion: Relates to the ratios in which different elements combine with a fixed mass of a third element.

• Law of Gaseous Volume: Relates to the volumes of reacting gases.

Law of Mass Conservation

The Law of Mass Conservation is a cornerstone of classical chemistry and provides the basis for balancing chemical equations.

• Historical Context: This law was proposed by Antoine Lavoisier in 1774.

• Core Definition: During any physical or chemical change, the total mass of the products remains equal to the total mass of the reactants. Mass can neither be created nor destroyed in a chemical reaction.

• Synonym: It is also frequently referred to as the "Law of Indestructibility of Matter."

• Mathematical Expression: $\text{Total Mass of the reactants} = \text{Total Mass of the products}$

Practical Application and System Logic

In a chemical reaction, atoms rearrange themselves to form new substances. The conservation of mass depends on the nature of the system:

• Closed System: If the reaction occurs in a closed system, the mass of the reactants will strictly equal the mass of the products because no matter can escape to or enter from the environment.

• Treatment of Unreacted Materials: If reactants are not completely consumed during the reaction, the relationship is refined as: $\text{Total mass of reactants} = \text{Total mass of products} + \text{Mass of unreacted reactants}$

Illustrative Examples

• Synthesis of Hydrogen Chloride: When Hydrogen ($H_2$) reacts with Chlorine ($Cl_2$):   - $H_2 + Cl_2 \rightarrow 2HCl$   - Mass of Reactants: $2\,g\,H_2 + 71\,g\,Cl_2 = 73\,g$   - Mass of Products: $2 \times (1 + 35.5) = 73\,g\,HCl$

• Reaction of Calcium Oxide and Water:   - $CaO + H_2O \rightarrow Ca(OH)_2$   - If $56\,g$ of Calcium Oxide ($CaO$) reacts with $18\,g$ of Water ($H_2O$), the total mass of the product Calcium Hydroxide ($Ca(OH)_2$) is exactly $74\,g$.

Law of Constant Proportions

Also known as the Law of Definite Proportions, this law governs the elemental makeup of chemical substances.

• Historical Context: This law was established by Joseph Proust in 1779.

• Core Definition: A chemical compound, regardless of its source or method of preparation, always contains its constituent elements combined together in the same fixed proportion by mass.

• Example: Water ($H_2O$):   - Water can be sourced from sea water, tap water, river water, or rain water.   - Regardless of the source, water is always composed of Hydrogen and Oxygen combined in a fixed ratio of $1:8$ by mass.   - Calculation: Since Hydrogen has a mass of approximately $1\,u$ and Oxygen $16\,u$, the ratio in $H_2O$ is $(2 \times 1) : 16$, which simplifies to $2:16$ or $1:8$.   - Example Demonstration: $4\,g$ of Hydrogen reacting with $32\,g$ of Oxygen yields a ratio of $4:32$, which is $1:8$.

Questions and Doubt Resolution

Q1: Which of the following best demonstrates the law of conservation of mass?

• A) Burning paper in open air

• B) Dissolving salt in water

• C) Chemical reaction in a closed container

• D) Melting ice

• Answer: C. A closed container prevents the escape of gases or entry of external matter, ensuring the measured mass remains constant.

Q2: When magnesium burns in air, the mass of magnesium oxide formed is:

• A) Less than magnesium

• B) Equal to magnesium

• C) More than magnesium

• D) Zero

• Answer: C. The magnesium combines with oxygen from the air ($2Mg + O_2 \rightarrow 2MgO$). Therefore, the mass of the resulting oxide includes the mass of the oxygen that was added to the solid magnesium.

Q3: Numerical - Law of Mass Conservation:

• Question: What mass of $BaCl_2$ would react with $24.4\,g$ of sodium sulphate ($Na_2SO_4$) to produce $46.6\,g$ of barium sulphate ($BaSO_4$) and $23.4\,g$ of sodium chloride ($NaCl$)?

• Solution:   - Let mass of $BaCl_2 = x$   - $x + 24.4\,g = 46.6\,g + 23.4\,g$   - $x + 24.4 = 70.0$   - $x = 70.0 - 24.4 = 45.6\,g$

• Result: $45.6\,g$

Q4: Ratio in Compounds:

• Question: If a compound contains $4\,g$ of hydrogen and $32\,g$ of oxygen, what is the ratio?

• Answer: A ($1:8$). Derived by simplifying $4:32$.

Q5: Stoichiometry based on Constant Proportions:

• Question: Carbon and Oxygen react in the ratio $3:8$ by mass. What weight of carbon is needed to react completely with $40\,g$ of oxygen?

• Solution:   - Ratio is $\frac{\text{Carbon}}{\text{Oxygen}} = \frac{3}{8}$   - Set up proportion: $\frac{3}{8} = \frac{x}{40}$   - $8x = 120$   - $x = 15\,g$

• Result: $15\,g$ of Carbon.

Homework and Extended Learning

Today's Homework Question

If the law of conservation of mass is true, what mass of silver nitrate ($AgNO_3$) will react with $5.85\,g$ of sodium chloride ($NaCl$) to produce $14.35\,g$ of silver chloride ($AgCl$) and $8.5\,g$ of sodium nitrate ($NaNO_3$)?

• Calculation:   - $x + 5.85 = 14.35 + 8.5$   - $x + 5.85 = 22.85$   - $x = 22.85 - 5.85 = 17\,g$

• Answer: $17\,g$

Significant Figures Discussion

• Problem 1: Determination of mass with significant figures. If density = $3.12\,g\,mL^{-1}$ and volume = $1.5\,mL$, find the mass.   - Calculation: $\text{Mass} = \text{Volume} \times \text{Density} = 1.5\,mL \times 3.12\,g\,mL^{-1} = 4.68\,g$   - Rule: In multiplication, the result must have the same number of significant figures as the measurement with the fewest significant figures.   - Analysis: $1.5$ has two significant figures. Therefore, $4.68\,g$ must be rounded to two significant figures.   - Final Answer: $4.7\,g$

• Problem 2: Significant figures in the value of $\pi$.   - Question: How many significant figures are in $\pi$ ($\pi = 22/7$)?   - Explanation: $\pi$ is an exact mathematical constant. When expressed as a decimal ($3.1428571...$), it continues indefinitely without repeating in a terminating way.   - Final Answer: Infinite.

Teaser for Next Session

The transcript concludes with a teaser regarding the combination of Carbon and Oxygen to form different compounds: Carbon Monoxide ($CO$) and Carbon Dioxide ($CO_2$). This introduces the concept of the Law of Multiple Proportions which will be discussed in the next lecture.