Question

Number of chlorine atoms in per mole of methyl chloride, methylene chloride, chloroform, carbon tetrachloride and DDT is in (A) Airthmetic progression (B) Geometric progression (C) Harmonic progression (D) None

Short answer

The number of chlorine atoms in the given compounds - methyl chloride, methylene chloride, chloroform, carbon tetrachloride, and DDT - are 1, 2, 3, 4, and 5, respectively. Since the consecutive terms differ by a constant amount (1), the sequence forms an arithmetic progression. Therefore, the answer is (A) Arithmetic progression.

Step-by-step solution

1. Determine the number of chlorine atoms for each compound

For each of the mentioned molecules, write down the chemical formula and count the number of Cl atoms in the formula: 1. Methyl chloride (CH3Cl) - 1 chlorine atom 2. Methylene chloride (CH2Cl2) - 2 chlorine atoms 3. Chloroform (CHCl3) - 3 chlorine atoms 4. Carbon tetrachloride (CCl4) - 4 chlorine atoms 5. DDT (C14H9Cl5) - 5 chlorine atoms Now that we have the number of chlorine atoms for each compound, let's analyze if the sequence follows any progression.

2. Check for arithmetic progression

An arithmetic progression (AP) is a sequence where the consecutive terms differ by a constant amount. Let's see if this holds true for our sequence: 1, 2, 3, 4, 5 The difference between consecutive terms is the same (1), so the series forms an arithmetic progression. Therefore, the answer is (A) Arithmetic progression.

Key concepts

Arithmetic Progression

Arithmetic progression, often abbreviated as AP, is a sequence of numbers in which the difference between consecutive terms remains constant. This consistent difference is what makes such a sequence predictable and simple to understand. Consider the sequence of numbers: 1, 2, 3, 4, 5. Each term here is derived by adding 1 to the previous term. This constant difference is known as the "common difference," which makes identifying an arithmetic progression straightforward.
In our example of chlorine atoms per mole in various compounds, each compound increases by one chlorine atom compared to the previous compound. This is why the sequence follows an arithmetic progression. Understanding this concept helps predict future terms in the sequence easily, just by continuing to add the common difference.
If asked to determine another term, say the 6th term, simply add the common difference of 1 to the 5th term, which would result in 6. This pattern is at the heart of what makes arithmetic progressions fascinating and useful in solving various mathematical problems.

Chemical Formula

A chemical formula is an essential representation that shows the types and numbers of atoms present in a compound. It's like a molecular recipe, indicating how many atoms of each element are involved in forming the particular compound. For instance, the chemical formula CH3Cl tells us that one molecule consists of three hydrogen (H) atoms, one carbon (C) atom, and one chlorine (Cl) atom.
Understanding chemical formulas is crucial in chemistry, as it helps in predicting how substances will interact with each other in chemical reactions. By analyzing chemical formulas, we can determine the properties of the compound, such as reactivity, polarity, and even its physical state at a given temperature.
Chemical formulas also allow us to calculate molecular weights by adding up the atomic masses of each element in the compound. For a more complex compound like DDT, with the formula C14H9Cl5, the chemical formula not only tells us the number of atoms but also suggests the complexity of its chemical behavior and applications.

Chlorinated Compounds

Chlorinated compounds are a significant class of chemicals widely used in industry and everyday life. They are organic compounds where one or more chlorine atoms are covalently bonded to carbon atoms. Chlorine's inclusion in organic molecules can alter the physical and chemical properties significantly, enhancing or diminishing some properties, making them versatile.
Common chlorinated compounds include household products such as disinfectants or cleaners. They are also crucial in industrial applications, such as solvents, insecticides, and plastics like PVC. Each chlorinated compound has a specific role, shaped by the number of chlorine atoms and their position in the molecule.
As seen with methyl chloride (CH3Cl) or carbon tetrachloride (CCl4), the number of chlorine atoms can indicate the compound's potential applications or environmental impact. For instance, increased chlorination often results in improved solubility in non-polar solvents and enhanced durability. Understanding these compounds helps in utilizing them correctly, maintaining safety standards, and addressing environmental concerns efficiently.