Q. how to calculate molar mass of a compound

Goal. Learn how to calculate the molar mass (also called molecular weight) of a compound, step by step, and see worked examples. The molar mass has units of grams per mole, g/mol. Follow each step carefully.

Step 1. Identify the chemical formula and parse the counts of each element. If the formula contains parentheses, apply the multiplier outside the parentheses to every element inside. For example, for water write the formula as \( \mathrm{H_2O} \). For calcium phosphate write the formula as \( \mathrm{Ca_3(PO_4)_2} \).

Step 2. Look up the standard atomic mass (relative atomic mass) of each element from the periodic table. Use the atomic mass values in units of grams per mole. Typical values (to three significant figures or more) that we will use here are: hydrogen \( \mathrm{H}: 1.008\ \mathrm{g\ mol^{-1}} \), oxygen \( \mathrm{O}: 16.00\ \mathrm{g\ mol^{-1}} \), calcium \( \mathrm{Ca}: 40.08\ \mathrm{g\ mol^{-1}} \), phosphorus \( \mathrm{P}: 30.97\ \mathrm{g\ mol^{-1}} \).

Step 3. Multiply the atomic mass of each element by the number of atoms of that element in one formula unit. If an element appears inside parentheses with a subscript, multiply by the product of the parenthesis multiplier and the element subscript. Sum the contributions for all elements. The arithmetic gives the molar mass.

Worked example 1: water, \( \mathrm{H_2O} \).

Identify element counts. There are 2 hydrogens and 1 oxygen. Write contributions as products of counts and atomic masses.

Compute hydrogen contribution. Multiply count by atomic mass. \( 2 \times 1.008\ \mathrm{g\ mol^{-1}} = 2.016\ \mathrm{g\ mol^{-1}} \).

Compute oxygen contribution. \( 1 \times 16.00\ \mathrm{g\ mol^{-1}} = 16.00\ \mathrm{g\ mol^{-1}} \).

Sum contributions to get molar mass. \( 2.016\ \mathrm{g\ mol^{-1}} + 16.00\ \mathrm{g\ mol^{-1}} = 18.016\ \mathrm{g\ mol^{-1}} \). Therefore the molar mass of water is \( 18.016\ \mathrm{g\ mol^{-1}} \).

Worked example 2: calcium phosphate, \( \mathrm{Ca_3(PO_4)_2} \).

Parse the formula. There are 3 calcium atoms. The group \( \mathrm{PO_4} \) appears with subscript 2, so every element inside the parentheses is multiplied by 2. Therefore total phosphorus atoms: \( 1 \times 2 = 2 \). Total oxygen atoms from the phosphate groups: \( 4 \times 2 = 8 \).

Compute calcium contribution. \( 3 \times 40.08\ \mathrm{g\ mol^{-1}} = 120.24\ \mathrm{g\ mol^{-1}} \).

Compute phosphorus contribution. \( 2 \times 30.97\ \mathrm{g\ mol^{-1}} = 61.94\ \mathrm{g\ mol^{-1}} \).

Compute oxygen contribution. \( 8 \times 16.00\ \mathrm{g\ mol^{-1}} = 128.00\ \mathrm{g\ mol^{-1}} \).

Sum contributions. \( 120.24\ \mathrm{g\ mol^{-1}} + 61.94\ \mathrm{g\ mol^{-1}} + 128.00\ \mathrm{g\ mol^{-1}} = 310.18\ \mathrm{g\ mol^{-1}} \). Therefore the molar mass of \( \mathrm{Ca_3(PO_4)_2} \) is \( 310.18\ \mathrm{g\ mol^{-1}} \).

Step 4. Report the molar mass with units and sensible significant figures. Use the precision appropriate to the atomic masses you used. If you need higher precision, use more precise atomic masses from a trusted source and repeat the arithmetic.

Summary checklist you can apply to any compound.

1. Write the correct chemical formula. 2. Count atoms of each element, including multipliers from parentheses and hydration terms. 3. Look up atomic masses in g/mol. 4. Multiply each atomic mass by its atom count. 5. Add all contributions to get the total molar mass in g/mol.