Question

Excess methylmagnesium iodide and \(0.1776 \mathrm{~g}\) of compound A of formula \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}_{3}\) Sreact to give \(84.1 \mathrm{cc}\) of methane collected over mercury at \(740 \mathrm{~mm}\) and \(25^{\circ} \mathrm{C}\). How many active hydrogens does compound A possess? Suggest a possible structure for the compound given that the infrared spectrum shows no carbonyl absorption and the n.m.r. spectrum shows only three types of hydrogen with areas in the ratio of \(1: 2: 2\).

Short answer

In conclusion, compound A appears to be 1,2,3-propanetriol (glycerol) with the structural formula CH2OH-CHOH-CH2OH and possesses one active hydrogen. The moles of methane produced (0.00332 mol) correspond to the moles of active hydrogen in compound A, with two molecules of compound A reacting for every mole of methane produced. The infrared spectrum shows no carbonyl absorption, and the NMR spectrum displays three types of hydrogen in a ratio of 1:2:2, in coherence with the compound's structure.

Step-by-step solution

Calculate moles of methane formed

Determine the moles of methane formed using the Ideal Gas Law equation, PV = nRT. The volume (84.1 cc) and pressure (740 mm) have been given along with the temperature (25°C). First, let's convert the given volume, pressure, and temperature to standard units. Volume (V): 84.1 cc = 0.0841 L Pressure (P): 740 mmHg = (740 / 760) atm = 0.973684 atm Temperature (T): 25°C = 298.15 K Now, we can use the Ideal Gas Law formula to determine the moles of methane: PV = nRT n = PV / RT = (0.973684 atm * 0.0841 L) / (0.0821 L atm/mol K * 298.15 K) ≈ 0.00332 mol We obtained 0.00332 mol of methane.

Connect moles of methane to active hydrogen atoms

It is important to know that the moles of methane produced are equal to the moles of active hydrogen in compound A (since each active hydrogen atom in compound A reacts with an equivalent of methylmagnesium iodide to produce methane). Therefore, compound A has 0.00332 mol of active hydrogens.

Calculate active hydrogen atoms in one molecule of compound A

Now, we can determine the moles of compound A used in the reaction by using its mass and molar mass: Moles of compound A = mass / molar_mass = 0.1776 g / (4*12.01 + 10*1.008 + 3*16.00) g/mol ≈ 0.0060 mol Now, divide the moles of active hydrogens by the moles of compound A to find active hydrogens per molecule: Active hydrogens per molecule = (0.00332 mol) / (0.0060 mol) ≈ 0.55 Since we cannot have a fractional number of active hydrogens, it should be interpreted that there are 1 active hydrogen and 2 molecules of compound A reacting for every 1 mole of methane produced.

Suggest a possible structure for compound A

Considering that the infrared spectrum shows no carbonyl absorption, we can rule out the presence of a carbonyl group. The NMR spectrum displays only three types of hydrogen and a ratio of 1:2:2. A possible structure that meets these criteria is 1,2,3-propanetriol (glycerol). The structural formula is CH2OH-CHOH-CH2OH. We can observe three types of hydrogens: one from the central carbon in the ratio of 1 and the other two types from both terminal carbons in the ratio of 2:2. The active hydrogen is the one bonded to the first carbon atom in glycerol. In conclusion, compound A appears to be 1,2,3-propanetriol and possesses one active hydrogen.

Key concepts

Ideal Gas Law

The Ideal Gas Law is an essential concept in chemistry that relates the pressure, volume, and temperature of a gas with the amount of substance present. It is expressed in the equation: \[ PV = nRT \]where:

• \(P\) is the pressure of the gas.
• \(V\) is the volume of the gas.
• \(n\) is the moles of gas.
• \(R\) is the universal gas constant, which is 0.0821 L atm/mol K.
• \(T\) is the temperature in Kelvin.

In this exercise, we used the Ideal Gas Law to calculate the moles of methane produced when compound A reacts. We converted the measurements to standard units to ensure accurate results. By determining the moles of methane, we were able to infer the number of active hydrogens in compound A.

NMR Spectrum

Nuclear Magnetic Resonance (NMR) Spectroscopy is a powerful technique used to determine the structure of organic compounds. It provides insight into the number and types of hydrogen atoms in a molecule by analyzing how they absorb and emit radiofrequency radiation in a magnetic field.
The NMR spectrum gives resonances corresponding to different types of hydrogen in the molecule. Each peak represents a different environment of hydrogen. In our case:

• The NMR spectrum of compound A indicates three types of hydrogens with a peak area ratio of 1:2:2.
• This means that there are three distinct hydrogens, one being unique and the other two existing in pairs.

The NMR data helped narrow down the possible structures of compound A, leading to the suggestion of 1,2,3-propanetriol as a possible structure.

Infrared Spectroscopy

Infrared (IR) Spectroscopy is a technique used to identify functional groups in organic compounds by measuring the absorption of infrared light, which causes molecular vibrations.
In this analysis, the critical observation was the absence of a carbonyl group ( characteristic absorption around 1700 cm⁻¹). As a result, compound A does not have a carbonyl-containing functional group like aldehydes or ketones.
This absence of a carbonyl group further assists in eliminating certain structural possibilities for compound A, pointing to a molecule such as 1,2,3-propanetriol, which does not contain this functional group.

Methylmagnesium Iodide Reaction

Methylmagnesium iodide is a Grignard reagent used extensively in organic chemistry to form carbon-carbon bonds and, in this context, to identify active hydrogens in a molecule.
When methylmagnesium iodide reacts with a molecule containing active hydrogens, it replaces the hydrogen with a methyl group, releasing methane gas in the process. The moles of methane produced can be directly correlated to the moles of active hydrogens present.
In our exercise, compound A reacted with methylmagnesium iodide to produce methane, allowing us to determine the number of active hydrogens by measuring the volume of methane produced using the Ideal Gas Law.

1,2,3-Propanetriol Structure

1,2,3-Propanetriol, commonly known as glycerol, is a simple polyol compound. Its structure is notable for containing three hydroxyl (OH) groups attached to a three-carbon chain.
This triol structure is expressed as CH₂OH-CHOH-CH₂OH, which aligns perfectly with the given data:

• The NMR results, with a hydrogen ratio of 1:2:2, correspond to the hydrogens of glycerol: one from the central carbon and two from each terminal carbon.
• Only one of these hydrogens is considered active in the context of the Grignard reaction.

Glycerol's structure fits the criteria of no carbonyl absorption in the IR spectrum and only three types of hydrogens in the NMR spectrum, thereby making it an ideal candidate for compound A.