Problem 34 - Chemistry The Central Science In Si Units

Question

(a) What is the mass in \(\mathrm{u}\) of a carbon- 12 atom? (b) Why is the atomic weight of carbon reported as 12.011 in the table of elements and the periodic table in the front inside cover of this text?

Step-by-Step Solution

Answer

(a) The mass of a carbon-12 atom is exactly 12 u. (b) The atomic weight 12.011 is an average of naturally occurring carbon isotopes.

Step 1: Understanding Atomic Mass Units (u)

An atomic mass unit (amu), also known as a unified atomic mass unit (u), is defined as one twelfth the mass of a carbon-12 atom. Thus, by definition, the mass of a carbon-12 atom is exactly 12 u.

Step 2: Discussing Carbon-12 Mass

Since the atomic mass unit is defined based on the carbon-12 isotope, the mass of a carbon-12 atom is exactly 12 atomic mass units (u) by definition.

Step 3: Exploring Atomic Weights

The atomic weight of an element like carbon takes into account the natural isotopic distribution of all isotopes of that element. Atomic weights are weighted averages of the masses of the isotopes and their abundances.

Step 4: Explaining Carbon's Atomic Weight

The atomic weight of carbon is reported as 12.011 because it is a weighted average of the masses of carbon's naturally occurring isotopes, primarily carbon-12 and carbon-13, based on their natural abundance. This includes both the exact mass of each isotope and how often each isotope occurs in nature.

Key Concepts

Carbon-12

Carbon-12 is a specific isotope of the element carbon. An isotope is a version of an element's atom that has the same number of protons but a different number of neutrons. Carbon-12 contains 6 protons and 6 neutrons in its nucleus, making it have a total mass number of 12. This isotope is particularly important in science because it serves as the standard for measuring atomic masses. Whenever we talk about atomic mass unit (amu), it refers to one twelfth of the mass of a single carbon-12 atom. This provides a consistent baseline that scientists can use across various areas of chemistry and physics.

Atomic Weight

Atomic weight, sometimes called relative atomic mass, represents the average mass of an element's atoms, considering all of its isotopes and their respective frequencies in nature. It is not a simple mass number like carbon-12's mass of exactly 12 u. Rather, atomic weight takes into account the isotopic composition of an element. For instance:

• It involves contributions from different isotopes that exist naturally.
• It averages their masses based on how common each isotope is.

Atomic weight is often seen in the periodic table and is essential for calculations in chemistry, such as determining the quantities of substances in reactions.

Isotopes

Isotopes of an element are different forms of the element's atoms. They share the same number of protons but vary in the number of neutrons. This leads to different mass numbers. Most elements in nature exist as a mix of multiple isotopes. Key details about isotopes:

• They influence the atomic weight of an element.
• Some isotopes are more stable than others.
• Naturally occurring isotopes are considered when determining atomic weight.

An example is carbon, which has isotopes like carbon-12 and carbon-13. The variations in their neutron count affect their individual masses and their contribution to the average atomic weight of carbon.

Weighted Average

Weighted average is a mathematical concept used to calculate the mean of a set of numbers, where each number has a specific importance or weight. In the context of atomic weight, it is about averaging the masses of isotopes while taking their natural abundance into account. For example:

• If an isotope is more prevalent in nature, it has a greater impact on the weighted average.
• It ensures that all isotopes contribute appropriately according to their natural occurrence.

This method gives a realistic value that can be used practically. That is why the atomic weight of carbon is not simply 12 but a slightly higher 12.011, reflecting the natural mix of carbon isotopes in the earth.