Problem 14 - Chemistry: Principles and Reactions

Question

Chlorine has two isotopes, Cl-35 and Cl-37. Their abundances are \(75.53 \%\) and \(24.47 \%\), respectively. Assume that the only hydrogen isotope present is \(\mathrm{H}-1\). (a) How many different HCl molecules are possible? (b) What is the sum of the mass numbers of the two atoms in each molecule? (c) Sketch the mass spectrum for \(\mathrm{HCl}\) if all the positive ions are obtained by removing a single electron from an HCl molecule.

Step-by-Step Solution

Answer

Additionally, describe the sketch of the mass spectrum for HCl. Answer: There are two different HCl molecules that can be formed, HCl-36 and HCl-38. The sum of the mass numbers of the two atoms in each molecule is 36 for HCl-36 and 38 for HCl-38. The mass spectrum sketch for HCl would show two peaks, one at mass number 36 with a higher height (representing HCl-36 with 75.53% abundance), and another at mass number 38 with a lower height (representing HCl-38 with 24.47% abundance).

Step 1: a) Finding the number of different HCl molecules

Since there are two isotopes of chlorine (Cl-35 and Cl-37) and one isotope of hydrogen (H-1), we can form different HCl molecules by combining each isotope of chlorine with the only isotope of hydrogen. 1. H-1 combined with Cl-35, forming HCl-36 2. H-1 combined with Cl-37, forming HCl-38 So, there are two different HCl molecules possible.

Step 2: b) Finding the sum of mass numbers of each of the HCl molecules

We have already determined the different HCl molecules in part (a). We know their mass numbers as 36 and 38. So, the sum of mass numbers for the two different HCl molecules are: 1. HCl-36: 1 (for H-1) + 35 (for Cl-35) = 36 2. HCl-38: 1 (for H-1) + 37 (for Cl-37) = 38

Step 3: c) Sketching the mass spectrum for HCl

The mass spectrum for HCl will display two peaks, corresponding to the two different HCl molecules. These peaks will appear at their respective mass numbers, 36 and 38. The height of the peaks will be proportional to the abundance of each isotope. Since Cl-35 has an abundance of 75.53%, HCl-36 will have a higher peak. On the other hand, Cl-37 has an abundance of 24.47%, so HCl-38 will have a lower peak. The key features of the mass spectrum sketch will be: 1. A peak at mass number 36 with a higher height (75.53% abundance) representing the HCl-36 molecule. 2. A peak at mass number 38 with a lower height (24.47% abundance) representing the HCl-38 molecule. This mass spectrum sketch will provide a visual representation of the HCl molecules formed by different combinations of isotopes of hydrogen and chlorine.

Key Concepts

Isotopes of Chlorine

Chlorine is an element that exists in nature primarily in two stable isotopes, Cl-35 and Cl-37. Isotopes of an element have the same number of protons but different numbers of neutrons. This variation in the neutron count leads to a difference in the atomic mass despite having identical chemical properties. For chlorine, Cl-35 has 18 neutrons, whereas Cl-37 has 20 neutrons. In terms of natural abundance, Cl-35 is more prevalent, making up about 75.53% of chlorine found on Earth, while Cl-37 accounts for about 24.47%.

Understanding isotopes is crucial because they account for the variations observed in the mass spectrometry of compounds that contain elements like chlorine. When chlorine combines with other elements to form compounds, the isotopic composition can lead to multiple forms, or 'isotopologues', of the molecule. These differing forms will display distinct peaks in a mass spectrum, revealing the unique isotopic fingerprints of the element within the compound.

Molecular Mass Calculation

Calculating the molecular mass of a compound involves adding up the atomic masses of its constituent atoms. In essence, this sum gives you the mass of the molecule, which is generally expressed in unified atomic mass units (u).

For hydrogen chloride (HCl), the calculation becomes straightforward since the molecule consists of only one hydrogen atom and one chlorine atom. The molecular mass of an HCl molecule is the sum of the atomic mass of hydrogen (1 u for H-1) and the atomic mass of the particular isotope of chlorine present. Hence for HCl-36, the calculation is 1 u (for H-1) + 35 u (for Cl-35) to give a total molecular mass of 36 u. Similarly, HCl-38 is calculated as 1 u (for H-1) + 37 u (for Cl-37) providing a total molecular mass of 38 u.

Mass Spectrometry Analysis

Mass spectrometry is a powerful analytical tool used to determine the masses of particles and the elemental composition of a sample. The heart of a mass spectrometer is the ion source where molecules are ionized, often by knocking off an electron, to generate ions. The ions are then accelerated and separated based on their mass-to-charge ratio (m/z) by an electric or magnetic field.

The result of this process is a mass spectrum, a graph that displays the detected ions as peaks at their respective m/z ratios. For a simple molecule like HCl, the mass spectrum will illustrate peaks corresponding to the ions of HCl-36 and HCl-38. These peaks reflect the presence of the different isotopes of chlorine when combined with hydrogen. The height of each peak correlates with the relative abundance of the isotopes, so in a sample of HCl, we expect a taller peak at m/z 36 due to the predominance of Cl-35 in nature.