How to Calculate Molarity
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To calculate molarity, divide the amount of solute in moles by the final solution volume in liters. If the problem gives grams instead of moles, divide grams by molar mass first.
c = n / V
From mass:
c = m / (M_r × V)
Step 1: identify the known quantities
A molarity problem usually follows one of three paths:
- moles of solute and final solution volume;
- solute mass, molar mass, and final solution volume;
- target molarity, molar mass, and final volume when required mass is unknown.
Write every value with its unit before substitution. This exposes most setup errors before calculation.
Step 2: convert to compatible units
Use liters for volume and moles for amount:
1 L = 1,000 mL1 mL = 0.001 L1 g = 1,000 mg1 mol = 1,000 mmol
Do not change a numeric value without changing its unit. For example, 250 mL is 0.250 L, not 250 L.
Step 3: calculate moles when mass is given
Use:
n = m / M_r
For 9.00 g of glucose with a molar mass of 180.16 g/mol:
n = 9.00 / 180.16 = 0.04996 mol
Use the exact chemical form stated by the problem or reagent label. A hydrate includes the associated water in its molar mass.
Step 4: divide by final solution volume
If the glucose solution is brought to a final volume of 250.0 mL, convert the volume to 0.2500 L:
c = 0.04996 mol / 0.2500 L = 0.1998 mol/L
The result is approximately 0.200 M when rounded to three significant figures.
Use the Molarity Calculator to perform the same mass-to-moles and volume normalization with your own values.
Rearranging the equation
The same relationship can solve related problems:
- moles:
n = c × V - final volume:
V = n / c - required mass:
m = c × V × M_r
These rearrangements do not replace a dilution calculation. When a solution is made from an existing stock rather than dry solute, use the M1V1 M2V2 Dilution Formula.
Check the result
- If the same moles occupy a smaller final volume, molarity should increase.
- If the same mass and volume use a larger molar mass, calculated moles and molarity should decrease.
- Unit cancellation should leave mol/L.
- Zero or negative molar mass or final volume is invalid.
- Keep unrounded values through intermediate steps and round the final display once.
Frequently asked questions
Can I calculate molarity without molar mass?
Yes, if amount of solute is already known in moles. Molar mass is required when converting measured mass to moles.
Why do I use final solution volume?
Molarity is defined per volume of the mixture. Starting solvent volume is not necessarily final volume after the solute is dissolved.
What if the volume is in milliliters?
Divide milliliters by 1,000 before using a formula expressed in mol/L.
Should I round moles before calculating molarity?
Keep sufficient working precision and round the final result. Premature rounding can change the last reported digit.
Continue the task
- Molarity Calculator — calculate with your own inputs.
- Molarity Units and Conversions — convert M to smaller concentration units.
- How to Prepare a Molar Solution — calculate required mass for a target solution.
Sources
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