Molar Mass

• Molar Mass ($M$): This is defined as the mass in grams of exactly one mole of a substance, which contains $6.022 \times 10^{23}$ particles. It is a characteristic property of a substance that does not change regardless of the sample size.

• Units of Measurement: The standard unit for molar mass is grams per mole ($g/mol$ or $g \cdot mol^{-1}$). This unit explicitly shows the relationship between mass and the amount of substance.

• Numerical Equivalence: The numerical value of a substance's molar mass is identical to its average atomic mass or formula mass expressed in atomic mass units ($amu$). For example, if a single atom of an element weighs $12.011$ $amu$, then one mole of those atoms weighs $12.011$ grams.

Calculating Molar Mass from a Formula

• Step 1: Identify Elements: List every unique element present in the chemical formula of the substance.
• Step 2: Determine Subscripts: Note the subscript for each element, which indicates the number of atoms of that element in one formula unit. If no subscript is present, it is assumed to be 1.
• Step 3: Retrieve Atomic Masses: Look up the average atomic mass for each element on the periodic table.
• Step 4: Sum the Totals: Multiply each element's atomic mass by its subscript and add these values together to find the total molar mass.

Converting Between Mass and Moles

• To find Moles ($n$): Divide the given mass ($m$) by the molar mass ($M$).

$n = \frac{m}{M}$

• To find Mass ($m$): Multiply the number of moles ($n$) by the molar mass ($M$).

$m = n \times M$

• Molar Mass vs. Molecular Weight: While often used interchangeably, 'molecular weight' technically refers only to covalent molecules, whereas 'molar mass' is a more universal term that applies to atoms, ions, and ionic formula units as well.

• Significant Figures: Always use the atomic masses provided on the specific periodic table given during the exam. Rounding your intermediate molar mass calculations too early can lead to significant errors in your final answer.

• Diatomic Elements: When an exam question mentions 'oxygen gas' or 'nitrogen gas', remember these are diatomic ($O_2$, $N_2$). You must double the atomic mass of the single element to get the correct molar mass for the gas.

• Sanity Check: Always verify that your final units cancel out correctly using dimensional analysis. If you are looking for moles and your calculation results in $g^2/mol$, you have likely multiplied where you should have divided.

• Parentheses in Formulas: A common error is failing to distribute subscripts outside of parentheses to all elements inside. For example, in $Mg(OH)_2$, the subscript 2 applies to both the Oxygen and the Hydrogen atoms.

• Confusing m and M: Students often mix up the variables in the formula $n = m/M$. Remember that lowercase '$m$' represents the specific mass of your sample (e.g., 5.0 grams), while uppercase '$M$' represents the constant molar mass from the periodic table.

• Hydrates: When calculating the molar mass of a hydrate (e.g., $CuSO_4 \cdot 5H_2O$), the mass of the water molecules must be added to the mass of the salt, not ignored.