Question

Calculate the nominal mass of each ion. Unless otherwise indicated, use the mass of the most abundant isotope of each element. (a) \(\left[\mathrm{CH}_{3} \mathrm{Br}\right]^{+}\) (b) \(\left[\mathrm{CH}_{3}{ }^{81} \mathrm{Br}\right]^{+}\) (c) \(\left[{ }^{13} \mathrm{CH}_{3} \mathrm{Br}\right]^{+}\)

Short answer

Answer: The nominal masses of the ions are (a) 94, (b) 96, and (c) 95.

Step-by-step solution

Identify the most abundant isotopes of each element

The most abundant isotopes for Carbon (C), Hydrogen (H), and Bromine (Br) are: - Carbon: \(^{12}C\) - Hydrogen: \(^{1}H\) - Bromine: \(^{79}Br\) (50.69%) and \(^{81}Br\) (49.31%)

Calculate the nominal mass of ion (a)

To calculate the mass of the ion \(\left[\mathrm{CH}_{3} \mathrm{Br}\right]^{+}\), use the most abundant isotopes for each element. Nominal Mass: Mass of Carbon + (3 x Mass of Hydrogen) + Mass of Bromine Nominal Mass = 12 + (3 x 1) + 79 = 94

Calculate the nominal mass of ion (b)

For ion (b), \(\left[\mathrm{CH}_{3}{ }^{81} \mathrm{Br}\right]^{+}\), we are indicated to use the isotope \(^{81}Br\). Nominal Mass = Mass of Carbon + (3 x Mass of Hydrogen) + Mass of \(^{81}Br\) Nominal Mass = 12 + (3 x 1) + 81 = 96

Calculate the nominal mass of ion (c)

For ion (c), \(\left[{ }^{13} \mathrm{CH}_{3} \mathrm{Br}\right]^{+}\), we are indicated to use the isotope \(^{13}C\). Nominal Mass = Mass of \(^{13}C\) + (3 x Mass of Hydrogen) + Mass of Bromine Nominal Mass = 13 + (3 x 1) + 79 = 95 So the nominal masses of the ions are: (a) 94 (b) 96 (c) 95

Key concepts

Isotope Abundance

Isotopes are variations of the same element that differ in the number of neutrons they contain. This means that while they have the same number of protons, they possess different mass numbers. Understanding isotope abundance is crucial for various scientific calculations, including mass spectrometry and nominal mass calculations.

Most elements have multiple isotopes, but typically only one is the most abundant. For example, Carbon has isotopes like \(^{12}C\) and \(^{13}C\), but \(^{12}C\) is significantly more common. Similarly, Bromine has two prevalent isotopes: \(^{79}Br\) and \(^{81}Br\). Their abundances are nearly equal, paving the way for different isotopic calculations.

When calculating the nominal mass of a compound or ion, the most abundant isotope of each element is generally used unless otherwise specified. This approach simplifies the calculation and aligns with typical analytical techniques. Frequently, this process helps in identifying compounds in mass spectrometry, allowing chemists and researchers to deduce molecular structures.

Mass Spectrometry

Mass spectrometry is a powerful analytical tool used to measure the mass-to-charge ratio of ions. It provides detailed insights into the molecular structure of chemical substances and is highly valuable for identifying unknown compounds.

The process starts by ionizing chemical compounds to generate charged particles. These ions are then passed through a magnetic or electric field, which separates them based on their mass-to-charge ratio. Lighter ions deflect more, while heavier ones deflect less, allowing the spectrometer to determine the mass of these ions precisely.

One of the key applications of mass spectrometry is determining the nominal mass of ions, which assists in deducing the molecular formula of the compounds present. It involves calculating the sum of the masses of the most abundant isotopes of the constituent elements. By using the nominal mass, researchers can compare and match the mass spectrum with known data to confirm the identity of a compound.

Organic Chemistry Calculations

Calculating nominal mass is a vital part of organic chemistry calculations. It involves the sum of the integer masses of the most abundant isotopes of all atoms in a molecule or ion.

For organic compounds like hydrocarbons, calculations usually involve elements such as carbon, hydrogen, and sometimes halogens like bromine. Here’s how such a computation proceeds: first, identify the most abundant isotopes for each element involved in the compound, such as \(^{12}C\), \(^{1}H\), and \(^{79}Br\) or \(^{81}Br\) depending on the context. Next, sum their integer masses according to the molecular structure.

For instance, in \(\left[{ }^{13} \mathrm{CH}_{3} \mathrm{Br}\right]^{+}\), we consider \(^{13}C\), \(^{1}H\), and \(^{79}Br\). Each calculation is a stepwise method that includes summing these isotope masses to achieve the total nominal mass. Such calculations provide foundational assistance in organic synthesis and analytical methods, facilitating the identification and study of organic molecules.