Question

Given that the abundances of isotopes \({ }^{54} \mathrm{Fe},{ }^{56} \mathrm{Fe}\) and \({ }^{57} \mathrm{Fe}\) are \(5 \%, 90 \%\) and \(5 \%\), respectively, the atomic mass of \(\mathrm{Fe}\) is (A) \(55.85\) (B) \(55.95\) (C) \(55.75\) (D) \(56.05\)

Short answer

55.95

Step-by-step solution

Identify the Isotopes and Their Abundances

First, note the three isotopes of Iron (Fe) given: - Isotope Fe-54 with an abundance of 5%- Isotope Fe-56 with an abundance of 90%- Isotope Fe-57 with an abundance of 5%.

Calculate the Weighted Average Atomic Mass

Next, calculate the atomic mass taking into account the abundances. Use the formula:calculated atomic mass = (abundance of Fe-54 * atomic mass of Fe-54) + (abundance of Fe-56 * atomic mass of Fe-56) + (abundance of Fe-57 * atomic mass of Fe-57).Remember to convert the percentages into decimals before multiplying:(0.05 * 54) + (0.90 * 56) + (0.05 * 57).

Perform the Calculation

Perform the weighted average calculation: (0.05 * 54) + (0.90 * 56) + (0.05 * 57) = (2.7) + (50.4) + (2.85) = 55.95.

Choose the Correct Option

The calculated atomic mass of Iron (Fe) is 55.95, which matches option (B) 55.95.

Key concepts

Isotope Abundances

The concept of isotope abundances concerns the relative amount of each isotope that exists for a given element. Isotopes are atoms of the same element with different numbers of neutrons but the same number of protons in their nuclei. As a result, isotopes of an element have nearly identical chemical properties but different atomic masses.

For example, the element iron (Fe) has several isotopes, including Fe-54, Fe-56, and Fe-57. In nature, these isotopes are not present in equal amounts; one is usually more abundant than the others. The isotope abundance is expressed as a percentage and plays a key role in calculating the average atomic mass of the element.

When solving chemistry problems involving atomic mass, it's critical to use the correct isotopic abundances to obtain accurate results. The abundances give us insight into how much each isotope contributes to the atomic mass of an element as it occurs naturally.

Weighted Average Atomic Mass

The weighted average atomic mass of an element takes into account the masses of its isotopes along with their relative abundances. The purpose of a weighted average is to reflect the mass of a

Chemistry Problems

Solving chemistry problems requires a solid understanding of the concepts involved, attention to detail, and methodical problem-solving skills. Equipped with these skills, students can approach not only atomic mass calculations but also a wide array of challenges presented in chemistry.

Exercise improvement advice: To hone these skills, practicing with a variety of problems helps. Take incremental steps, starting from simpler exercises to more complex ones. Begin with clear identification of known and unknown variables, and ensure conversion of quantities like percentages to decimal form before performing calculations. Practice problems that involve the use of the periodic table, where each element's average atomic mass is given, to foster a thorough understanding of how these values are determined. Additionally, tackle exercises that simulate real-world scenarios to appreciate the application of theoretical knowledge. Such deliberate practice leads to a stronger grasp of concepts and ultimately, to success in solving chemistry problems.