Question

An unidentified atom is found to have an atomic mass \(7.18\) times that of the carbon-12 isotope. (a) What is the mass of the unidentified atom? (b) What are the possible identities of this atom? (c) Why are you unable to positively identify the element based on the atomic mass and the periodic table? (d) If the element formed a compound \(\mathrm{M}_{2} \mathrm{O}\), where \(\mathrm{M}\) is the unidentified atom, identify \(\mathrm{M}\) by writing the isotopic notation for the atom.

Short answer

The mass of the unidentified atom is 86.16 u. It is likely Strontium (Sr). Identification solely based on atomic mass is limited due to isotopic similarities.

Step-by-step solution

Determine the mass of the carbon-12 isotope

The atomic mass of carbon-12 is defined as exactly 12 atomic mass units (u).

Calculate the mass of the unidentified atom

Given that the unidentified atom's mass is 7.18 times that of carbon-12, calculate this mass using the equation: \[ \text{Mass of unidentified atom} = 7.18 \times 12 \text{ u} = 86.16 \text{ u} \text{So, the mass is } 86.16 \text{ u}. \]

Match the mass to possible elements

Use the periodic table to identify elements with an atomic mass close to 86.16 u. The elements with atomic masses around this value include Strontium (Sr) with an approximate atomic mass of 87.62 u. Hence, Sr is a plausible candidate.

Explain limitations in identifying the element

An exact identification cannot be made only based on atomic mass because isotopes of different elements can have similar masses. Isotopic variations and trace impurities might influence measurements, making it necessary to use additional properties for a definitive identification.

Analyze the given compound formula

The compound formula \(\text{M}_{2} \text{O} \) suggests that two atoms of the unidentified element form a molecule with one oxygen atom. Typically, group 2 elements (alkaline earth metals) form such compounds.

Identify the element based on the compound

Given that the atom forms \(\text{M}_{2} \text{O} \), and considering the atomic mass, the element is likely Strontium, identified with the isotopic notation: \( ^{86}_{38}\text{Sr} \).

Key concepts

Atomic Mass Identification

Atomic Mass is a critical concept in chemistry that refers to the mass of a single atom, usually expressed in atomic mass units (u). The atomic mass of an element is typically based on the weighted average of all the isotopes of that element.
In the exercise provided, the atomic mass of an unidentified atom is calculated to be 7.18 times that of a carbon-12 isotope, meaning it’s 86.16 u. Carbon-12 is used as a standard in chemistry, making calculations straightforward by allowing us to use the exact known mass of 12 u to find our unknown. This exercise underscores understanding how to use given atomic masses and comparisons to standard units to identify an element or isotope.

Understanding Isotopic Notation

Isotopic notation provides a systematic way of identifying specific isotopes of elements. An isotope is a variant of an element where the number of neutrons differs from other variants. Thus, isotopic notation showcases this difference.
The format typically used is \text{\(^{A}_{Z}\text{X}}\), where A represents the mass number (total number of protons and neutrons), Z is the atomic number (number of protons), and X is the element's symbol. For example, in our exercise, the potential isotopic notation for the unidentified atom is \text{\(^{86}_{38}\text{Sr}}\). This informs us that Strontium (Sr) isotope has a mass number of 86 and 38 protons.
By using this notation, we bring precision to identifying isotopes, which is crucial given that isotopes of different elements can have similar masses. This precision becomes essential in differentiating between possible elemental candidates based on atomic mass calculations.

Exploring the Periodic Table

The periodic table is a foundational tool in chemistry used to organize elements based on increasing atomic number and recurring chemical properties. Each element on the periodic table has a unique atomic number representing the number of protons in its nucleus.
In the exercise, we utilize the periodic table to help identify the unknown element by matching its atomic mass. The periodic table arranges elements so that elements with similar properties fall into the same groups (columns). Specifically, elements within the group of alkaline earth metals typically form compounds like \text{M}_{2}\text{O}\, where M is the metal.
The calculated atomic mass of 86.16 u is close to Strontium (Sr) with an atomic mass around 87.62 u. Group 2 elements like Strontium are known to form compounds such as \text{\(M_{2}\text{O}}\), affirming Sr as a candidate. Nonetheless, the periodic table alone might not be sufficient for a positive identification due to isotopic similarities and measurement impurities, necessitating the use of other properties or additional analyses.