Question

\((\mathrm{X})=\) Double bond equivalent of \((\mathrm{Q})\) (Y) = Total number of \(\mathrm{CH}_{3}\)-I used Then find \((X+Y)\)

Short answer

Since the molecular formula and structure of compound Q are not provided, we cannot calculate the exact values for X and Y. However, once you have the molecular formula and structure, follow these steps: 1. Plug the number of carbon atoms, hydrogen atoms, and other heteroatoms into the Double Bond Equivalent formula to find X. 2. Count the number of \(\mathrm{CH}_{3}\)-I groups in compound Q to determine Y. 3. Add X and Y together to find the total: \(X + Y\).

Step-by-step solution

Determine the Double Bond Equivalent (X) of compound Q

To determine the Double bond equivalent (X) of the compound, we need to know the molecular formula of compound Q. The Double bond equivalent is calculated using the following formula: \(X = \frac{N_C + 1 - \frac{1}{2}(N_H + N_X)}{2}\) where \(N_C\) is the number of carbon atoms, \(N_H\) is the number of hydrogen atoms, and \(N_X\) is the number of other heteroatoms (like halogens). For the given molecular formula of compound Q, substitute the values in the formula to find X.

Determine the total number of \(\mathrm{CH}_{3}\)-I groups (Y) in compound Q

To find the number of \(\mathrm{CH}_{3}\)-I groups (Y), look at the given molecular structure and count the number of times where \(\mathrm{CH}_{3}\)-I group appears in the structure.

Calculate the sum of X and Y

Now that we have X (Double bond equivalent) and Y (number of \(\mathrm{CH}_{3}\)-I groups), add them together to find the result: \(X + Y =\) total

Key concepts

Molecular Formula

When working with organic chemistry problems, understanding the molecular formula is crucial. A molecular formula indicates the types and numbers of atoms present in a molecule. For example, the molecular formula for water is \(\text{H}_2\text{O}\), which means there are two hydrogen atoms and one oxygen atom in the molecule. In organic chemistry, these formulas help us determine structure and properties, which are key to solving problems such as calculating the double bond equivalent.

To derive a molecular formula, you'll need to know the count of each type of atom—carbon, hydrogen, and sometimes other elements. This formula serves as the foundation for more complex analyses, like calculating the double bond equivalent, where you'll need the precise number of each atom to apply the formula correctly. Remember to reorganize structural formulas into molecular formulas to simplify such calculations efficiently.

Heteroatoms

Heteroatoms are atoms in an organic molecule that are not carbon or hydrogen. Common heteroatoms include oxygen, nitrogen, sulfur, and the halogens (like chlorine or fluorine). These heteroatoms significantly affect the chemical behavior of organic compounds. They can influence the reactivity, polarity, and overall stability of a molecule.

In the context of double bond equivalence (DBE), heteroatoms are crucial because they alter how we calculate structural unsaturation. When using the DBE formula \( X = \frac{N_C + 1 - \frac{1}{2}(N_H + N_X)}{2} \), where \(N_X\) refers to the number of heteroatoms, each heteroatom impacts the overall calculation. Heteroatoms like halogens reduce the hydrogen count affecting the DBE and changing the expected saturation of the molecule. Therefore, accurately identifying and accounting for heteroatoms in a molecular structure is vital for precise DBE calculations.

Organic Chemistry Problem Solving

Organic chemistry problem solving often involves applying systematic approaches to deduce molecular structures or calculate specific properties like the double bond equivalent. Here are some tips to tackle these kinds of problems effectively:

• Start by identifying what you know from the problem, like the molecular formula or structural features such as functional groups or heteroatoms.
• Clearly define what you need to find. In our example, it's values \(X\) and \(Y\), which represent the double bond equivalent and the number of \(\text{CH}_3\text{-I}\) groups, respectively.
• Break the problem into smaller, manageable parts, using formulas such as the DBE formula to calculate structural unsaturation, followed by counting specific group occurrences for each part.
• Check your calculations at each step to minimize errors. Small mistakes can compound into significant discrepancies in organic chemistry.

By methodically working through each part of the problem, you’ll be better equipped to arrive at the correct solution, enhancing your understanding and mastery of organic chemistry.