Molar Mass: Calculation and Applications in GOB Chemistry

Molar Mass

Definition and Physical Property

Molar mass is a physical property that represents the mass of a substance divided by the amount of that substance. It is commonly used in chemistry to relate the mass of a sample to the number of moles present.

• The SI unit for mass is kilogram (kg), but molar mass is typically expressed in grams per mole (g/mol).

• Molar mass is also referred to as molecular weight or molecular mass.

Molar Mass Formula

The formula for molar mass is:

$ext{Molar Mass} = rac{ ext{grams}}{ ext{mole}}$

Steps to Calculate Molar Mass

Calculating the molar mass of a compound involves several systematic steps:

1. Count the number of each element within the compound.

   • If elements are within parentheses, distribute the subscript to each element inside.

   • Example: For (NH4)2SO4, the number of atoms is: N: 2 × 1 = 2 H: 2 × 4 = 8 S: 1 O: 4

2. Find the atomic masses of each element from the Periodic Table.

   • Example atomic masses: N: 14.01 g/mol H: 1.008 g/mol S: 32.07 g/mol O: 16.00 g/mol

3. Multiply the number of each element by its atomic mass to get the total mass contribution of each element.

   • Example for (NH4)2SO4: N: 2 × 14.01 = 28.02 g/mol H: 8 × 1.008 = 8.064 g/mol S: 1 × 32.07 = 32.07 g/mol O: 4 × 16.00 = 64.00 g/mol

4. Add up the totals after multiplication to determine the molar mass of the compound.

   • For (NH4)2SO4: $28.02 + 8.064 + 32.07 + 64.00 = 132.154$ g/mol

Practice Problems

Practice problems help reinforce the calculation of molar mass for various compounds:

• Calculate the molecular weight of C4H7N2O2 Step 1: Count atoms: C:4, H:7, N:2, O:2 Step 2: Find atomic masses: C:12.01, H:1.008, N:14.01, O:16.00 Step 3: Multiply and sum: C: 4 × 12.01 = 48.04 H: 7 × 1.008 = 7.056 N: 2 × 14.01 = 28.02 O: 2 × 16.00 = 32.00 Total molar mass: $48.04 + 7.056 + 28.02 + 32.00 = 115.116$ g/mol

• Nickel (II) chloride hexahydrate, NiCl2·6H2O Step 1: Count atoms: Ni:1, Cl:2, H:12, O:6 Step 2: Find atomic masses: Ni:58.69, Cl:35.45, H:1.008, O:16.00 Step 3: Multiply and sum: Ni: 1 × 58.69 = 58.69 Cl: 2 × 35.45 = 70.90 H: 12 × 1.008 = 12.096 O: 6 × 16.00 = 96.00 Total molar mass: $58.69 + 70.90 + 12.096 + 96.00 = 237.686$ g/mol

• Diazepam (Valium) Given: 0.05570 mol weighs 15.86 g Step 1: Use the formula: $ext{Molar Mass} = rac{ ext{grams}}{ ext{moles}}$ $ext{Molar Mass} = rac{15.86}{0.05570} = 284.86$ g/mol

Summary Table: Steps for Molar Mass Calculation

Step	Description	Example
1	Count atoms of each element	N:2, H:8, S:1, O:4
2	Find atomic masses	N:14.01, H:1.008, S:32.07, O:16.00
3	Multiply number by atomic mass	N:28.02, H:8.064, S:32.07, O:64.00
4	Add totals for molar mass	132.154 g/mol

Applications of Molar Mass

• Used to convert between mass and moles in chemical calculations.

• Essential for stoichiometry, solution preparation, and quantitative analysis.

• Helps in determining the amount of reactants and products in chemical reactions.

Key Terms

• Mole: The SI unit for amount of substance, equal to $6.022 imes 10^{23}$ entities.

• Atomic Mass: The mass of an atom, usually expressed in atomic mass units (amu) or g/mol.

• Molecular Formula: Shows the number and type of atoms in a molecule.

Additional info: The notes infer standard atomic masses and calculation steps for compounds not fully detailed in the original file.