Question

(a) What is the mass, in grams, of one mole of \(^{12} \mathrm{C} ?\) (b) How many carbon atoms are present in one mole of \(^{12} \mathrm{C} ?\)

Short answer

(a) The mass of one mole of \(^{12}C\) is 12 grams. (b) There are 6.022 × \(10^{23}\) carbon atoms in one mole of \(^{12}C\).

Step-by-step solution

a) Mass of one mole of \(^{12}C\)

To find the mass of one mole of \(^{12}C\), we need to know the atomic mass of carbon. The atomic mass of carbon is approximately 12 atomic mass units (amu). Since 1 amu is equal to 1 gram per mole, the mass of one mole of \(^{12}C\) is: Mass = Atomic Mass × (1 g/mol) = 12 amu × (1 g/mol) = 12 g Thus, the mass of one mole of \(^{12}C\) is 12 grams.

b) Number of carbon atoms in one mole of \(^{12}C\)

To find the number of carbon atoms in one mole of \(^{12}C\), we can use Avogadro's number, which states that there are 6.022 × \(10^{23}\) particles (atoms, molecules, etc.) in one mole of any substance. Therefore, the number of carbon atoms in one mole of \(^{12}C\) can be found as: Number of carbon atoms = 1 mole × Avogadro's number = 1 mole × 6.022 × \(10^{23}\) atoms/mole = 6.022 × \(10^{23}\) atoms Thus, there are 6.022 × \(10^{23}\) carbon atoms in one mole of \(^{12}C\).

Key concepts

Atomic Mass Units

The atomic mass unit (amu) is a standard unit of mass that quantifies mass on an atomic or molecular scale. It is defined as one twelfth of the mass of a carbon-12 atom, which is approximately 1.66 × 10^-24 grams. This tiny mass unit is crucial in chemistry because it allows scientists to express the masses of atoms and molecules in a manageable numerical form without involving unwieldy figures.

For example, when we say that the atomic mass of carbon is about 12 atomic mass units, we're simplifying the conversation around how heavy a carbon atom is compared to the standardized carbon-12 isotope. Rather than dealing with grams, which are too large to represent the mass of one atom, atomic mass units provide a convenient and scaled-down value that is more appropriate for atoms and molecules.

Avogadro's Number

Avogadro's number, 6.022 × 10²³, is the number of particles found in one mole of a substance. This constant is named after Amedeo Avogadro, an Italian scientist, and is fundamental in the mole concept of chemistry. The value represents an enormous number of units, reflecting the tiny size of atoms and molecules.

When we measure substances in the laboratory, we often use moles, which directly relate to Avogadro's number. For instance, if you have one mole of carbon atoms, you have 6.022 × 10²³ carbon atoms. This consistency across all substances allows chemists to calculate the amounts of substances needed or produced in a chemical reaction with precision.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It's essentially the math behind chemistry. Stoichiometry allows chemists to calculate how much of a reactant is needed to produce a desired amount of product or how much product can be generated from a known quantity of reactant.

Understanding the mole concept is key to stoichiometry, as it provides the link between mass and number of particles through Avogadro's number and the molar mass of a substance (the mass of one mole). For instance, if a chemical equation indicates that two moles of hydrogen react with one mole of oxygen to produce two moles of water, stoichiometry helps us calculate the exact mass of each substance required or produced, ensuring a controlled and efficient reaction.

Atomic Mass

Atomic mass refers to the mass of an individual atom, usually expressed in atomic mass units (amu). It's theoretically the sum of the masses of the protons, neutrons, and electrons in an atom; however, due to binding energy holding the nucleus together and other factors, the atomic mass is not just a count of these particles. Rather, it's a weight-average mass of all the isotopes of an element as they occur naturally, considering their relative abundance.

The atomic mass of an element is found on the periodic table, usually beneath the chemical symbol. For carbon, with the symbol 'C', the atomic mass is approximately 12.01. This value means that a neutral carbon atom has an average mass slightly over 12 amu, taking into consideration the natural abundance of its isotopes like carbon-12 and carbon-13. When working with the mole concept, we often use a simplified average atomic mass to ease calculations, like using 12 amu for carbon in stoichiometric problems.