Question

Carbon has two naturally occurring isotopes: carbon-12 \((\mathrm{mass}=12.00 \mathrm{amu})\) and carbon-13 (mass = \(13.00 \mathrm{amu}\) ). Chlorine also has two naturally occurring isotopes: chlorine-35 (mass \(=34.97\) amu) and chlorine-37 (mass \(=36.97\) amu). How many \(\mathrm{CCl}_{4}\) molecules of different masses can exist? Determine the mass (in amu) of each of them.

Short answer

There can be 10 distinct masses of CCl4 molecules, as there are 2 options for carbon isotopes and 5 different combinations for the chlorine isotopes.

Step-by-step solution

Identify the Combinations of Carbon Isotopes

Carbon has 2 isotopes, C-12 and C-13. Since there is only one carbon atom in a CCl4 molecule, these are the only two possibilities for the carbon part of the molecule.

Identify the Combinations of Chlorine Isotopes

Chlorine has 2 isotopes, Cl-35 and Cl-37. Since there are four chlorine atoms in a CCl4 molecule, each of these positions could be occupied by either isotope, resulting in different combinations.

Calculate the Number of Different Mass Combinations

For each carbon isotope, there are multiple combinations of chlorine isotopes. The chlorine combinations can be calculated using binomial distribution. There are 5 different combinations assuming the chlorine isotopes can be distinguished from each other (all clorines being either Cl-35 or Cl-37, 1 chlorine being Cl-37 and the rest Cl-35, etc.).

Determine the Mass of CCl4 Molecules

Calculate the mass of each distinct CCl4 molecule by adding the mass of the carbon isotope to the masses of the chlorine isotopes in each combination.

Calculate Total Number of Distinct Mass CCl4 Molecules

Multiply the number of carbon isotope options (which is 2) by the number of different chlorine isotope combinations (which is 5), resulting in a total number of distinct mass CCl4 molecules.

Key concepts

Isotopic Composition

Understanding the isotopic composition of an element is crucial in chemistry, especially when analyzing molecules with multiple isotopes. Each element can exist in forms known as isotopes, distinguished by the number of neutrons in their nuclei. This variation in neutron number results in different atomic masses for the isotopes of a single element. For instance, carbon typically exists as carbon-12 and carbon-13, having masses of 12.00 amu and 13.00 amu respectively. Similarly, chlorine has isotopes chlorine-35 with a mass of 34.97 amu and chlorine-37 with a mass of 36.97 amu. The isotopic composition affects the physical and chemical properties of molecules they constitute and thus, chemists and students must be keenly aware of these distinctions.

Teachers and resources often suggest that simplifying the concept to visual elements, like using colored balls to represent different isotopes, can be an excellent way for students to grasp the variations in isotopic composition easily.

Mass Spectrometry

Mass spectrometry is a powerful analytical technique used to determine the masses of particles and the elemental composition of a sample. In this method, a sample is ionized, and the resulting ions are separated based on their mass-to-charge ratio. The output is a mass spectrum that displays the different isotopes present in the sample and their relative abundances.

For educational purposes, illustrating the mass spectrometry process with diagrams or animations can greatly enhance student understanding. The key takeaway is that mass spectrometry is an essential tool for identifying the isotopic composition of elements within compounds and for determining molecular masses accurately.

Molecular Mass Calculation

Calculating molecular mass is a fundamental skill in chemistry that involves adding the atomic masses of all atoms in a molecule. With isotopic variations, the calculation becomes slightly more complex, as one has to consider the different masses of isotopes. In the given exercise, the molecular mass of carbon tetrachloride (\( \text{CCl}_4 \)) can vary because of the different isotopic combinations of carbon and chlorine.

By calculating the mass of each distinct combination, students can determine the molecular mass for each variant of the molecule. An effective teaching tip is to encourage students to use periodic tables with isotopic masses and practice with diverse molecules to solidify their understanding of this concept.

Binomial Distribution in Chemistry

In the context of chemistry, binomial distribution helps to predict the probability of combinations when there are two possible outcomes for each event. When applied to isotopic composition in molecules, it calculates the number of possible combinations for isotopes in different positions within the molecule. For example, with chlorine having two isotopes and four positions in the \( \text{CCl}_4 \) molecule, binomial distribution reveals there are five distinguishable combinations.

Breaking down binomial distribution with step-by-step examples, showing the combinations as they increase from one possibility to the next, allows students to grasp this concept incrementally. This incremental approach aids in understanding complex chemical calculations where binomial distribution is applied.

Chemistry Problem-Solving

Problem-solving in chemistry often involves a series of logical steps to arrive at a solution. The exercise provided showcases this approach in determining the number of molecules with distinct masses for \( \text{CCl}_4 \) with different isotopes. The process outlines identifying the isotopes, calculating combination possibilities using binomial distribution, and computing the mass for each variant. Each step is vital and builds upon the previous one.

By teaching students to break down complex problems into smaller, manageable steps and encouraging practice with a variety of problems, educators can enhance students' problem-solving skills. Additionally, using real-life examples and interactive problem-solving sessions can make learning engaging and more effective.