2.7
Molar Mass
The identity of a substance is defined not only by the types of atoms or ions it contains but by the quantity of each type of atom or ion. For example…
The periodic table gives the average atomic mass of each atom. However, macroscopic samples contain extremely large numbers of atoms. Therefore, it is essential to use a counting unit called Avogadro's number.
Avogadro’s number, expressed as the symbol NA, is usually rounded to 6.022 × 1023. Its value is equal to the number of atoms in exactly 12 grams of pure carbon-12 isotope.
The term mole, abbreviated mol, is used to describe Avogadro's number, just as the familiar term, dozen, is used to describe an amount of 12.
Nonetheless, a dozen of different items can weigh differently despite having the same number of items. Similarly, moles of different elements have different masses but always contain the same number of atoms.
The mass in grams of one mole of an element is called the molar mass, expressed in grams per mole. Its value is numerically equivalent to the element’s atomic mass. Hence, the definition of the mole lets us count particles by weighing them. The molar mass and Avogadro's number can be used as conversion factors.
This can be used to calculate the number of atoms in a 5 gram bar of gold. The average molar mass of gold is 196.96 g/mol. So, to convert the mass into moles, divide the mass of the bar by the average molar mass. Then, multiply the number of moles by Avogadro's number to get the number of total atoms in the sample. So, this bar of gold contains 1.529 × 1022 atoms.
View the full transcript and gain access to JoVE Core videos
Q1: What is Avogadro's number and why is it important in chemistry?
Avogadro's number (NA) is 6.022 × 1023, representing the number of atoms or molecules in one mole of any substance. It is essential because macroscopic samples contain extremely large numbers of atoms, making direct counting impossible. This constant allows chemists to count particles by weighing them, linking measurable mass to the number of discrete entities in a sample.
Q2: How does molar mass relate to atomic mass?
Molar mass, expressed in grams per mole, is numerically equivalent to an element's atomic mass. For example, carbon has an atomic mass of 12 amu and a molar mass of 12 g/mol. This relationship holds for all elements because their atomic masses are measured relative to carbon-12, the amu reference standard. Though numerically equivalent, they differ vastly in scale.
Q3: Why do different elements have different molar masses if one mole always contains the same number of atoms?
Although one mole of any element contains 6.022 × 1023 atoms, the masses of individual atoms differ drastically between elements. Since molar mass is the mass of one mole of an element, and individual atoms have different masses, moles of different elements have different masses despite containing identical numbers of atoms.
Q4: How can you calculate the number of atoms in a sample using molar mass and Avogadro's number?
To find the number of atoms in a sample, first convert mass to moles by dividing the sample mass by molar mass. Then multiply the number of moles by Avogadro's number (6.022 × 1023). For example, a 5-gram gold bar with molar mass 196.96 g/mol contains approximately 1.529 × 1022 atoms using this conversion method.
Q5: What is the mole and how does it function as a counting unit?
The mole is an amount unit similar to familiar terms like dozen or gross. One mole equals 6.022 × 1023 discrete entities—atoms or molecules. The mole provides a bridge between easily measured macroscopic properties like bulk mass and fundamental microscopic properties like the number of atoms or molecules in a substance.
Q6: Why is the relationship between mass and the number of atoms significant in chemistry?
The mole defines the relationship between mass and the number of atoms, allowing chemists to calculate particle quantities from measurable mass. This connection is fundamental because atoms are extremely small and cannot be counted directly. By using molar mass as a conversion factor, scientists can determine how many atoms or molecules are present in any macroscopic sample.
Q7: How does the molar mass of a compound relate to its formula mass?
The molar mass of a compound in grams is numerically equivalent to its formula mass in amu. For instance, helium has an atomic mass of 4.002 amu and a molar mass of 4.002 g/mol. This relationship applies to all compounds because their formula masses are calculated from atomic masses measured relative to the carbon-12 standard.