What do you call a mass in grams of an atom or molecule numerically equal to its atomic mass or formula mass?

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Avogadro’s number is critical to understanding the structure of molecules as well as their interactions and combinations. e.g. because one atom of oxygen will combine with two atoms of hydrogen to form one molecule of water (H2O), one mole of oxygen (6.022 × 1023 of O atoms) will mix with two moles of hydrogen (2 × 6.022 × 1023 of H atoms) to form one mole of H2O. Another feature of Avogadro’s number is that the mass of one mole of material equals the molecular weight of that substance. Water, for example, has a mean molecular weight of 18.015 a.m.u. implying that one mole of water weighs 18.015 grams. Many chemical computations are made easier by this feature. 

Now let’s discuss some important concepts before understanding the gram atomic mass and gram molecular mass.

• Atomic Mass: Atomic mass is the mass of an atom of the given element. The unit of atomic mass is a.m.u. often denoted as u. One atomic mass unit (a.m.u.) is said to be exactly equal to the 1/12 the ratio of the mass of 1 mole of C-12 atoms to Avogadro’s Constant (NA).
• Molecular Mass: Molecular Mass is the sum of the mass of the atoms present in a molecule of the given substance. Its unit is also a.m.u. e.g. the molecular mass of NH3 = 14 + 1 × 3 = 17 a.m.u.
• Molar Mass: The mass of the 1 mole of a given substance is known as molar mass. The SI unit of molar mass is kg/mol however g/mol is the usually used unit. Molar mass can also be defined as the molecular mass of the given substance expressed in grams. e.g. 2 a.m.u. is the molecular mass of hydrogen gas therefore as per the definition the molar mass of hydrogen gas will be 2 g.
• Mole Concept: It is a concept revolving around 12 g of C-12 isotope containing atoms equal to Avogadro’s Constant. Mole is actually an amount. The amount can be of atoms, molecules, ions, electrons, fruits, or books but our scope would be limited to chemical entities. What we actually do is calculate the mass of chemical entities in terms of mole. The value of Avogadro’s Constant i.e. the value of 1 mole of a substance is 6.0221367 × 1023.
• Mole: One mole is defined as the amount of the substance which contains as many entities as there are atoms in 12 g of C-12 isotope. As measured by mass spectrometer the mass of one atom of C-12 atom is found to be 1.992648 × 10-23 g. Since 1 mole of C-12 atoms is 12g. Therefore, the number of atoms present in 1 mole = 12g / 1.992648*10-23 g atom-1 or 6.0221367 × 1023 atoms. The value of 1 mole is known as Avogadro’s Constant. The term ‘Avogadro’s Constant’ is termed after the great pioneer Amedeo Avogadro. It is denoted by the symbol NA.

Gram atomic mass is the periodic table element’s atomic weight in grams. The molar mass of an element is the mass of one mole in grams. The mass of one mole of an element is defined as its gram atomic mass. 

It is calculated by taking an element’s atomic weight from the periodic table and converting it to grams. Thus, when the mass of an element is expressed in grams then it is known as gram atomic mass. For example, the gram atomic mass of helium is 4 g. Similarly, sodium (Na) has an atomic weight of 22.99 u and a gram atomic mass of 22.99 grams. So one mole of sodium atoms weighs 22.99 g. This implies that the quantity of the element of the given substance when weighs equal to its gram atomic mass is called one gram atom. 

The gram atomic mass of a material is the amount of that substance in grams that is numerically equivalent to its atomic mass. If we wish to write a substance’s gram atomic mass, we first write its atomic mass, then subtract the atomic mass unit u and add grams to the numerical value of the atomic mass. That is,

Mass of the element (in g) = Number of gram atoms / Atomic mass of the element (in g)

Gram Molecular Mass

The mass in grams of one mole of a molecular material is known as the gram molecular mass. The molar mass and gram molecular mass are the same things. The main distinction is that gram molecular mass defines the mass unit. The gram molecular mass (g/mol) can be expressed in grams or grams per mole (g/mol). 

How to find the Gram Molecular Mass?

1. To determine the mass, use the molecular formula.
2. Look up each element’s relative atomic mass in the formula.
3. Multiply the subscript following each element symbol (the number of atoms) by the atomic mass of that element. If there is no subscript, it implies that the molecule contains only one atom of that element.
4. To get the gram molecular mass, add all of the numbers together.

The gram molecular mass of a substance is the amount of that substance in grams that is numerically equivalent to its molecular mass. To write a substance’s gram molecular mass, first, write its molecular mass, then subtract the molecular mass unit u and add grams to the numerical value of the molecular mass. For example, the gram molecular mass of oxygen gas (O2) is 32 g.

Number of gram molecules = Mass of the substance (in g) / Molecular mass of the substance (in g)

The mass of one molecule of material in grams should not be confused with the mass of one molecule of the substance in grams. The real mass or molecular mass of a material is the mass of one molecule.

Sample Problems

Problem 1: What is Avogadro’s Constant?

Solution:

Avogadro’s number is critical to understanding the structure of molecules as well as their interactions and combinations. e.g. because one atom of oxygen will combine with two atoms of hydrogen to form one molecule of water (H2O), one mole of oxygen (6.022 × 1023 of O atoms) will mix with two moles of hydrogen (2 × 6.022 × 1023 of H atoms) to form one mole of H2O. 

Problem 2: Why are the gram atomic mass and gram molecular mass of all elemental substances are same?

Solution:

The mass of a grams of a molecule. a mass in grams equal to a substance’s molecular weight or the sum of all the atomic weights in its molecular formula

The mass in grams of one mole of atoms in a monatomic chemical element is known as gram atomic mass. It is the same as the relative atomic mass (or atomic weight) in grams. Only Nobel gases exist in a monotonic state. Hence, the gram atomic mass and gram molecular mass of all elemental substances are same.

Problem 3: Calculate the number of atoms present in 4 moles of hydrogen gas.

Solution:

1 molecule of hydrogen gas has 2 atoms

1 mole of hydrogen gas has NA molecules ⇒ 1 mole of hydrogen gas has 2 × NA atoms

Therefore, 4 moles hydrogen gas has 4 × 2 × NA atoms i.e. 8 × NA atoms

Problem 4: What is a mole?

Solution:

A mole is the unit of amount of substance. The number of entities present in a mole is equal to Avogadro’s Constant. Mole is the former term used for the term ‘ one gram atom’.

Problem 5: How many moles of oxygen gas are required to produce 3 moles of CO2?

Solution:

Chemical reaction for the formation of carbon dioxide is

C +O2 ⇢ CO2

The above equation is balanced. Hence we can say that

1 mole of carbon and 1 mole of oxygen gas combine to form 1 mole of carbon dioxide.

Therefore, for the formation of 3 moles of carbon dioxide there will be requirement of 3 moles of oxygen gas.

By the end of this section, you will be able to:

• Define the amount unit mole and the related quantity Avogadro’s number
• Explain the relation between mass, moles, and numbers of atoms or molecules, and perform calculations deriving these quantities from one another

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, water, H2O, and hydrogen peroxide, H2O2, are alike in that their respective molecules are composed of hydrogen and oxygen atoms. However, because a hydrogen peroxide molecule contains two oxygen atoms, as opposed to the water molecule, which has only one, the two substances exhibit very different properties. Today, we possess sophisticated instruments that allow the direct measurement of these defining microscopic traits; however, the same traits were originally derived from the measurement of macroscopic properties (the masses and volumes of bulk quantities of matter) using relatively simple tools (balances and volumetric glassware). This experimental approach required the introduction of a new unit for amount of substances, the mole, which remains indispensable in modern chemical science.

The mole is an amount unit similar to familiar units like pair, dozen, gross, etc. It provides a specific measure of the number of atoms or molecules in a bulk sample of matter. A mole is defined as the amount of substance containing the same number of discrete entities (atoms, molecules, ions, etc.) as the number of atoms in a sample of pure 12C weighing exactly 12 g. One Latin connotation for the word “mole” is “large mass” or “bulk,” which is consistent with its use as the name for this unit. The mole provides a link between an easily measured macroscopic property, bulk mass, and an extremely important fundamental property, number of atoms, molecules, and so forth.

The number of entities composing a mole has been experimentally determined to be [latex]6.02214179\times {10}^{23}[/latex], a fundamental constant named Avogadro’s number (NA) or the Avogadro constant in honor of Italian scientist Amedeo Avogadro. This constant is properly reported with an explicit unit of “per mole,” a conveniently rounded version being [latex]6.022\times {10}^{23}\text{/mol}[/latex].

Consistent with its definition as an amount unit, 1 mole of any element contains the same number of atoms as 1 mole of any other element. The masses of 1 mole of different elements, however, are different, since the masses of the individual atoms are drastically different. The molar mass of an element (or compound) is the mass in grams of 1 mole of that substance, a property expressed in units of grams per mole (g/mol) (see Figure 1).

Figure 1. Each sample contains 6.022 × 1023 atoms—1.00 mol of atoms. From left to right (top row): 65.4g zinc, 12.0g carbon, 24.3g magnesium, and 63.5g copper. From left to right (bottom row): 32.1g sulfur, 28.1g silicon, 207g lead, and 118.7g tin. (credit: modification of work by Mark Ott)

Because the definitions of both the mole and the atomic mass unit are based on the same reference substance, 12C, the molar mass of any substance is numerically equivalent to its atomic or formula weight in amu. Per the amu definition, a single 12C atom weighs 12 amu (its atomic mass is 12 amu). According to the definition of the mole, 12 g of 12C contains 1 mole of 12C atoms (its molar mass is 12 g/mol). This relationship holds for all elements, since their atomic masses are measured relative to that of the amu-reference substance, 12C. Extending this principle, the molar mass of a compound in grams is likewise numerically equivalent to its formula mass in amu (Figure 2).

Figure 2. Each sample contains 6.02 × 1023 molecules or formula units—1.00 mol of the compound or element. Clock-wise from the upper left: 130.2g of C8H17OH (1-octanol, formula mass 130.2 amu), 454.9g of HgI2 (mercury(II) iodide, formula mass 459.9 amu), 32.0g of CH3OH (methanol, formula mass 32.0 amu) and 256.5g of S8 (sulfur, formula mass 256.6 amu). (credit: Sahar Atwa)

Figure 3. A single drop of water.

While atomic mass and molar mass are numerically equivalent, keep in mind that they are vastly different in terms of scale, as represented by the vast difference in the magnitudes of their respective units (amu versus g). To appreciate the enormity of the mole, consider a small drop of water weighing about 0.03 g (see Figure 3). The number of molecules in a single droplet of water is roughly 100 billion times greater than the number of people on earth.

Although this represents just a tiny fraction of 1 mole of water (~18 g), it contains more water molecules than can be clearly imagined. If the molecules were distributed equally among the roughly seven billion people on earth, each person would receive more than 100 billion molecules.

The mole is used in chemistry to represent [latex]6.022\times {10}^{23}[/latex] of something, but it can be difficult to conceptualize such a large number. Watch this video to learn more.

The relationships between formula mass, the mole, and Avogadro’s number can be applied to compute various quantities that describe the composition of substances and compounds. For example, if we know the mass and chemical composition of a substance, we can determine the number of moles and calculate number of atoms or molecules in the sample. Likewise, if we know the number of moles of a substance, we can derive the number of atoms or molecules and calculate the substance’s mass.

According to nutritional guidelines from the US Department of Agriculture, the estimated average requirement for dietary potassium is 4.7 g. What is the estimated average requirement of potassium in moles?

Check Your Learning

Beryllium is a light metal used to fabricate transparent X-ray windows for medical imaging instruments. How many moles of Be are in a thin-foil window weighing 3.24 g?

A liter of air contains [latex]9.2\times {10}^{-4}[/latex] mol argon. What is the mass of Ar in a liter of air?

Check Your Learning

What is the mass of 2.561 mol of gold?

Copper is commonly used to fabricate electrical wire (Figure 7). How many copper atoms are in 5.00 g of copper wire?

Figure 7. Copper wire is composed of many, many atoms of Cu. (credit: Emilian Robert Vicol)

Check Your Learning

A prospector panning for gold in a river collects 15.00 g of pure gold. How many Au atoms are in this quantity of gold?

Our bodies synthesize protein from amino acids. One of these amino acids is glycine, which has the molecular formula C2H5O2N. How many moles of glycine molecules are contained in 28.35 g of glycine?

Check Your Learning

How many moles of sucrose, C12H22O11, are in a 25-g sample of sucrose?

Vitamin C is a covalent compound with the molecular formula C6H8O6. The recommended daily dietary allowance of vitamin C for children aged 4–8 years is [latex]1.42\times {10}^{-4}\text{mol.}[/latex] What is the mass of this allowance in grams?

Check Your Learning

What is the mass of 0.443 mol of hydrazine, N2H4?

A packet of an artificial sweetener contains 40.0 mg of saccharin (C7H5NO3S), which has the structural formula:

Given that saccharin has a molar mass of 183.18 g/mol, how many saccharin molecules are in a 40.0-mg (0.0400-g) sample of saccharin? How many carbon atoms are in the same sample?

Check Your Learning

How many C4H10 molecules are contained in 9.213 g of this compound? How many hydrogen atoms?

A convenient amount unit for expressing very large numbers of atoms or molecules is the mole. Experimental measurements have determined the number of entities composing 1 mole of substance to be [latex]6.022\times {10}^{23}[/latex], a quantity called Avogadro’s number. The mass in grams of 1 mole of substance is its molar mass. Due to the use of the same reference substance in defining the atomic mass unit and the mole, the formula mass (amu) and molar mass (g/mol) for any substance are numerically equivalent (for example, one H2O molecule weighs approximately18 amu and 1 mole of H2O molecules weighs approximately 18 g).

1. Write a sentence that describes how to determine the number of moles of a compound in a known mass of the compound if we know its molecular formula.
2. Compare 1 mole of H2, 1 mole of O2, and 1 mole of F2.
   1. Which has the largest number of molecules? Explain why.
   2. Which has the greatest mass? Explain why.
3. Which contains the greatest mass of oxygen: 0.75 mol of ethanol (C2H5OH), 0.60 mol of formic acid (HCO2H), or 1.0 mol of water (H2O)? Explain why.
4. Which contains the greatest number of moles of oxygen atoms: 1 mol of ethanol (C2H5OH), 1 mol of formic acid (HCO2H), or 1 mol of water (H2O)? Explain why.
5. How are the molecular mass and the molar mass of a compound similar and how are they different?
6. Calculate the molar mass of each of the following compounds:
   1. hydrogen fluoride, HF
   2. ammonia, NH3
   3. nitric acid, HNO3
   4. silver sulfate, Ag2SO4
   5. boric acid, B(OH)3
7. Calculate the molar mass of each of the following:
   1. S8
   2. C5H12
   3. Sc2(SO4)3
   4. CH3COCH3 (acetone)
   5. C6H12O6 (glucose)
8. Calculate the molar mass of each of the following minerals:
   1. limestone, CaCO3
   2. halite, NaCl
   3. beryl, Be3Al2Si6O18
   4. malachite, Cu2(OH)2CO3
   5. turquoise, CuAl6(PO4)4(OH)8(H2O)4
9. Calculate the molar mass of each of the following:
   1. the anesthetic halothane, C2HBrClF3
   2. the herbicide paraquat, C12H14N2Cl2
   3. caffeine, C8H10N4O2
   4. urea, CO(NH2)2
   5. a typical soap, C17H35CO2Na
10. Determine the number of moles of compound and the number of moles of each type of atom in each of the following:
    1. 25.0 g of propylene, C3H6
    2. [latex]3.06\times {10}^{-3}\text{g}[/latex] of the amino acid glycine, C2H5NO2
    3. 25 lb of the herbicide Treflan, C13H16N2O4F (1 lb = 454 g)
    4. 0.125 kg of the insecticide Paris Green, Cu4(AsO3)2(CH3CO2)2
    5. 325 mg of aspirin, C6H4(CO2H)(CO2CH3)
11. Determine the mass of each of the following:
    1. 0.0146 mol KOH
    2. 10.2 mol ethane, C2H6
    3. [latex]1.6\times {10}^{-3}\text{ mol }{\text{Na}}_{2}{\text{SO}}_{4}[/latex]
    4. [latex]6.854\times {10}^{3}\text{ mol glucose},{\text{C}}_{6}{\text{H}}_{12}{\text{O}}_{6}[/latex]
    5. 2.86 mol Co(NH3)6Cl3
12. Determine the number of moles of the compound and determine the number of moles of each type of atom in each of the following:
    1. 2.12 g of potassium bromide, KBr
    2. 0.1488 g of phosphoric acid, H3PO4
    3. 23 kg of calcium carbonate, CaCO3
    4. 78.452 g of aluminum sulfate, Al2(SO4)3
    5. 0.1250 mg of caffeine, C8H10N4O2
13. Determine the mass of each of the following:
    1. 2.345 mol LiCl
    2. 0.0872 mol acetylene, C2H2
    3. [latex]3.3\times {10}^{-2}\text{ mol }{\text{Na}}_{2}{\text{CO}}_{3}[/latex]
    4. [latex]1.23\times {10}^{3}\text{ mol fructose, }{\text{C}}_{6}{\text{H}}_{12}{\text{O}}_{6}[/latex]
    5. 0.5758 mol FeSO4(H2O)7
14. The approximate minimum daily dietary requirement of the amino acid leucine, C6H13NO2, is 1.1 g. What is this requirement in moles?
15. Determine the mass in grams of each of the following:
    1. 0.600 mol of oxygen atoms
    2. 0.600 mol of oxygen molecules, O2
    3. 0.600 mol of ozone molecules, O3
16. A 55-kg woman has [latex]7.5\times {10}^{-3}\text{mol}[/latex] of hemoglobin (molar mass = 64,456 g/mol) in her blood. How many hemoglobin molecules is this? What is this quantity in grams?
17. Determine the number of atoms and the mass of zirconium, silicon, and oxygen found in 0.3384 mol of zircon, ZrSiO4, a semiprecious stone.
18. Determine which of the following contains the greatest mass of hydrogen: 1 mol of CH4, 0.6 mol of C6H6, or 0.4 mol of C3H8.
19. Determine which of the following contains the greatest mass of aluminum: 122 g of AlPO4, 266 g of Al2Cl6, or 225 g of Al2S3.
20. Diamond is one form of elemental carbon. An engagement ring contains a diamond weighing 1.25 carats (1 carat = 200 mg). How many atoms are present in the diamond?
21. The Cullinan diamond was the largest natural diamond ever found (January 25, 1905). It weighed 3104 carats (1 carat = 200 mg). How many carbon atoms were present in the stone
22. One 55-gram serving of a particular cereal supplies 270 mg of sodium, 11% of the recommended daily allowance. How many moles and atoms of sodium are in the recommended daily allowance?
23. A certain nut crunch cereal contains 11.0 grams of sugar (sucrose, C12H22O11) per serving size of 60.0 grams. How many servings of this cereal must be eaten to consume 0.0278 moles of sugar?
24. A tube of toothpaste contains 0.76 g of sodium monofluorophosphate (Na2PO3F) in 100 mL
    1. What mass of fluorine atoms in mg was present?
    2. How many fluorine atoms were present?
25. Which of the following represents the least number of molecules?
    1. 20.0 g of H2O (18.02 g/mol)
    2. 77.0 g of CH4 (16.06 g/mol)
    3. 68.0 g of CaH2 (42.09 g/mol)
    4. 100.0 g of N2O (44.02 g/mol)
    5. 84.0 g of HF (20.01 g/mol)

Glossary

Avogadro’s number (NA): experimentally determined value of the number of entities comprising 1 mole of substance, equal to [latex]6.022\times {10}^{23}{\text{mol}}^{-1}[/latex]

molar mass: mass in grams of 1 mole of a substance

mole: amount of substance containing the same number of atoms, molecules, ions, or other entities as the number of atoms in exactly 12 grams of 12C