Gram Formula Mass, Solved Examples

What is Gram Formula Mass (GFM)?

Gram Formula Mass , often referred to simply as molecular weight, is the mass of a molecule expressed in grams. It is a quantitative measure of the average mass of atoms or ions in a compound. GFM is usually expressed in atomic mass units (amu) or unified atomic mass units (u).

Calculating Gram Formula Mass:

The formula for calculating Gram Formula Mass is straightforward. It involves adding up the atomic masses of all the atoms present in a molecule. Here's the general formula:

GFM = (Mass of Atom 1) x (Number of Atoms of Atom 1) + (Mass of Atom 2) x (Number of Atoms of Atom 2) + ...

To illustrate this, let's calculate the GFM of a familiar compound: water (H2O).

1. Hydrogen (H) has an atomic mass of approximately 1 amu.
2. Oxygen (O) has an atomic mass of approximately 16 amu.

Using the formula:

GFM of H2O = (1 amu x 2) + (16 amu x 1) = 2 amu + 16 amu = 18 amu

So, the Gram Formula Mass of water (H2O) is 18 amu.

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Significance of Gram Formula Mass:

Gram Formula Mass is a crucial concept in chemistry for several reasons:

1. Stoichiometry: It is essential for calculating reactant and product masses in chemical reactions.
2. Empirical and Molecular Formulas: GFM is used to determine the empirical and molecular formulas of compounds.
3. Mole Concept: It connects the number of moles of a substance to its mass.
4. Percent Composition: GFM helps determine the percentage of each element in a compound.
5. Chemical Analysis: It aids in identifying unknown compounds through mass spectrometry.

Formulas Used in Gram Formula Mass Calculation:

Here are the atomic masses of some common elements used in GFM calculations:

• - Hydrogen (H): ~1 amu
• - Helium (He): ~4 amu
• - Carbon (C): ~12 amu
• - Oxygen (O): ~16 amu
• - Nitrogen (N): ~14 amu

You can use these values to calculate the GFM of various compounds by summing the atomic masses of their constituent atoms.

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Difference Between Molar Mass And Gram Molar Mass

1. Molar Mass:

Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a substance. It is expressed in units such as grams per mole (g/mol) or atomic mass units (amu). The molar mass of a substance is numerically equal to its atomic or molecular weight.

Here are some key points about molar mass:

• - It is a property of a pure substance and is constant for a particular element or compound.
• - The molar mass is calculated by adding up the atomic masses (in amu) of all the atoms in a molecule or the molecular formula of a compound.
• - It is used in various chemical calculations, such as determining the number of moles of a substance, calculating the mass of a given number of moles, and performing stoichiometric calculations.

For example, the molar mass of water (H2O) is approximately 18.015 g/mol, which means that one mole of water molecules has a mass of approximately 18.015 grams.

2. Gram Molar Mass:

Gram molar mass, also known as gram formula mass or gram molecular mass, is essentially the same as molar mass but is specifically expressed in grams per mole (g/mol). In other words, it's the molar mass of a substance, but the unit is explicitly stated as grams per mole.

Here are some key points about gram molar mass:

• - Gram molar mass provides a more explicit indication of the mass of one mole of a substance in grams.
• - It is often used when dealing with chemical calculations where the mass of a substance needs to be directly related to its molar quantity.
• - The term "gram molar mass" is used to emphasize that the value is expressed in grams.

For example, the gram molar mass of oxygen (O2) is approximately 32.00 g/mol, which means that one mole of oxygen molecules has a mass of approximately 32.00 grams.

In summary, the main difference between molar mass and gram molar mass lies in their units of expression. Molar mass is a more general term that can be expressed in various units, including g/mol and amu, whereas gram molar mass specifically expresses the molar mass in grams per mole. The numerical value of molar mass and gram molar mass is the same; it's the units that differ.

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Examples

1. Water (H2O):

- Gram Molar Mass: Approximately 18.015 g/mol

- Explanation: The gram molar mass of water (H2O) is about 18.015 g/mol, which means that one mole of water molecules weighs approximately 18.015 grams. This value is calculated by adding the atomic masses of two hydrogen atoms and one oxygen atom in a water molecule.

2. Carbon Dioxide (CO2):

- Gram Molar Mass: Approximately 44.01 g/mol

- Explanation: The gram molar mass of carbon dioxide (CO2) is about 44.01 g/mol. This indicates that one mole of carbon dioxide molecules weighs approximately 44.01 grams. It's calculated by adding the atomic masses of one carbon atom and two oxygen atoms in a CO2 molecule.

3. Sodium Chloride (NaCl):

- Gram Molar Mass: Approximately 58.44 g/mol

- Explanation: The gram molar mass of sodium chloride (NaCl) is roughly 58.44 g/mol. This implies that one mole of sodium chloride, a common table salt, weighs approximately 58.44 grams. It's calculated by adding the atomic masses of one sodium atom and one chlorine atom.

4. Oxygen Gas (O2):

- Gram Molar Mass: Approximately 32.00 g/mol

- Explanation: The gram molar mass of oxygen gas (O2) is approximately 32.00 g/mol, indicating that one mole of oxygen molecules weighs about 32.00 grams. This value is calculated by adding the atomic masses of two oxygen atoms in an O2 molecule.

5. Methane (CH4):

- Gram Molar Mass: Approximately 16.04 g/mol

- Explanation: The gram molar mass of methane (CH4) is around 16.04 g/mol, which means that one mole of methane molecules weighs approximately 16.04 grams. It's calculated by adding the atomic mass of one carbon atom and four hydrogen atoms in a CH4 molecule.

6. Iron (Fe):

- Gram Molar Mass: Approximately 55.85 g/mol

- Explanation: The gram molar mass of iron (Fe) is about 55.85 g/mol. This indicates that one mole of iron atoms weighs roughly 55.85 grams. It's the atomic mass of a single iron atom.

7. Hydrochloric Acid (HCl):

- Gram Molar Mass: Approximately 36.46 g/mol

- Explanation: The gram molar mass of hydrochloric acid (HCl) is about 36.46 g/mol. This means that one mole of HCl molecules weighs approximately 36.46 grams. It's calculated by adding the atomic mass of one hydrogen atom and one chlorine atom.

8. Carbon (C):

- Gram Molar Mass: Approximately 12.01 g/mol

- Explanation: The gram molar mass of carbon (C) is roughly 12.01 g/mol, indicating that one mole of carbon atoms weighs about 12.01 grams. It's the atomic mass of a single carbon atom.

9. Nitrogen Gas (N2):

- Gram Molar Mass: Approximately 28.02 g/mol

- Explanation: The gram molar mass of nitrogen gas (N2) is about 28.02 g/mol, which means that one mole of nitrogen molecules weighs approximately 28.02 grams. This value is calculated by adding the atomic masses of two nitrogen atoms in an N2 molecule.

10. Ethanol (C2H5OH):

- Gram Molar Mass: Approximately 46.07 g/mol

- Explanation: The gram molar mass of ethanol (C2H5OH) is roughly 46.07 g/mol, indicating that one mole of ethanol molecules weighs about 46.07 grams. It's calculated by adding the atomic masses of two carbon atoms, six hydrogen atoms, and one oxygen atom in an ethanol molecule.

These examples illustrate the gram molar masses of various substances and how they are calculated based on the atomic masses of their constituent elements.