Question

The silver salt of a mono acidic alkyne contains \(67 \%\) Ag. The structure of the alkyne is (a) \(\mathrm{HC} \equiv \mathrm{CH}\) (b) \(\mathrm{HC} \equiv \mathrm{C}-\mathrm{CH}_{2} \mathrm{CH}_{3}\) (c) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_{3}\) (d) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{C} \equiv \mathrm{CH}\)

Short answer

Answer: The correct structure of the alkyne is HC≡C-CH2CH3.

Step-by-step solution

Identify the formula of silver salt of an alkyne

We know that the general formula of alkynes is CnH(2n-2), and it has a triple bond between two carbon atoms. The silver salt of a mono acidic alkyne would have one silver atom replacing the acidic H atom in the alkyne. So, the general formula for the silver salt of alkyne is CnH(2n-3)Ag.

Calculate molecular weights of each option

We'll determine the molecular weight of the silver salts in each of the given structures of alkynes. (a) AgC≡CH: Molecular weight = 12 + 1 + 1 + 107.87 = 121.87 g/mol (b) AgC≡CCH2CH3: Molecular weight = 12*3 + 1*5 + 107.87 = 149.87 g/mol (c) CH3C≡CCH3 + Ag: Molecular weight = 12*4 + 1*7 + 107.87 = 175.87 g/mol (d) CH3C≡CH + Ag: Molecular weight = 12*3 + 1*4 + 107.87 = 151.87 g/mol

Calculate mole fractions of silver

Next, we'll find the mole fraction of silver (Ag) in each option's silver salt. (a) Mole fraction of Ag in AgC≡CH = weight(Ag) / weight(AgC≡CH) = 107.87 / 121.87 ≈ 0.885 (b) Mole fraction of Ag in AgC≡CCH2CH3 = 107.87 / 149.87 ≈ 0.720 (c) Mole fraction of Ag in CH3C≡CCH3 + Ag = 107.87 / 175.87 ≈ 0.613 (d) Mole fraction of Ag in CH3C≡CH + Ag = 107.87 / 151.87 ≈ 0.710

Compare mole fractions to the given percentage

Now we'll compare the calculated mole fractions to the given percentage (67%) and find the closest match. (a) 0.885 * 100 ≈ 88.5 % (Ag) (b) 0.720 * 100 ≈ 72.0 % (Ag) (c) 0.613 * 100 ≈ 61.3 % (Ag) (d) 0.710 * 100 ≈ 71.0 % (Ag) The mole fraction in option (b) is the closest to the 67% given in the exercise. Therefore, the correct structure of the alkyne is: (b) HC≡C-CH2CH3

Key concepts

Molecular Weight Calculation

Molecular weight calculation is a foundational concept in chemistry that involves adding up the atomic masses of all the atoms in a molecule. This is crucial because it helps scientists and students to understand the mass of a substance at the molecular level.

For instance, to calculate the molecular weight of an alkyne silver salt, one must know the atomic weights of carbon (approximately 12 amu), hydrogen (approximately 1 amu), and silver (approximately 107.87 amu). By adding up these atomic masses according to the number of each atom present in the molecule, the molecular weight is determined.

As seen in the step-by-step solution for the original exercise, each alkyne structure option is analyzed to calculate the molecular weight of its respective silver salt. This meticulous procedure helps identify which alkyne corresponds to the given percentage of silver in the salt—critical for problems involving stoichiometry and reactivity of chemical species.

Mole Fraction Concept

The mole fraction is another vital concept in chemistry which helps in the quantitative analysis of mixtures. It refers to the ratio of the number of moles of a component to the total number of moles of all components in the mixture. It is a dimensionless quantity, providing a way to express the composition of a mixture.

For the purposes of our exercise, the mole fraction of silver in the alkyne silver salt is key to finding the correct alkyne structure. By dividing the molecular weight of silver by the total molecular weight of the silver salt, we get the mole fraction of silver. This result is then multiplied by 100 to convert it from a fraction to a percentage.

As demonstrated in the solution, by comparing these percentages to the given data (67% Ag), students can deduce which alkyne structure most likely corresponds to the silver salt's composition. Understanding the mole fraction concept is not only fundamental in solving this exercise but also immensely beneficial in various chemical calculations including concentration measures and partial pressures in gas mixtures.

Acidic Alkyne Identification

Identifying an acidic alkyne is a crucial aspect in organic chemistry. Acidic alkynes are typically terminal alkynes, which means they have at least one hydrogen atom bonded to a carbon atom with a triple bond. Why is this important? Because that hydrogen is relatively acidic and can be replaced with other atoms or groups, such as a silver (Ag) atom, in the formation of silver salts.

In the context of the exercise, the silver salts are formed when the acidic hydrogen in the alkyne reacts with silver ions. The most acidic alkyne would easily form its corresponding silver salt. By comparing structures, we can infer that the alkyne with the hydrogen atom more available for substitution (more acidic) is likely to be the correct answer.

The significance of identifying an acidic alkyne extends beyond this exercise. It is pivotal in reactions like alkylation and addition reactions, where the acidic hydrogen is replaced through chemical reactions, emphasizing the importance of understanding the structure and reactivity of alkynes in organic chemistry.