Molarity Calculator
Calculate the molar concentration of a solution from mass, molar mass, and volume. Solve for any unknown variable or use the dilution equation M1V1 = M2V2.
Step-by-Step Solution
Step-by-Step Solution
What Is Molarity?
Molarity (symbol: M), formally called molar concentration, is the number of moles of a solute dissolved in one liter of solution. It is the most widely used unit of concentration in chemistry and is essential for preparing laboratory solutions, performing stoichiometric calculations, and understanding chemical reactions in solution.
The SI unit of molarity is mol/L (moles per liter), often written simply as M. For example, a 1 M NaCl solution contains exactly 1 mole of sodium chloride dissolved in enough water to make a total volume of 1 liter.
Molarity depends on the total volume of the solution, not just the volume of the solvent. This is an important distinction when preparing solutions in the laboratory, because adding a solute to a solvent changes the total volume.
Molarity Formula and How to Calculate It
The molarity formula connects four key variables. Given any combination of known values, you can solve for the unknown.
where n = moles of solute, V = volume of solution in liters
Since the number of moles can be calculated from mass and molar mass:
Combining these gives the expanded formula:
Rearranged for Each Variable
| Solve For | Formula |
|---|---|
| Molarity (M) | M = n / V = mass / (molar mass × V) |
| Moles (n) | n = M × V |
| Volume (V) | V = n / M |
| Mass | mass = n × molar mass = M × V × molar mass |
| Molar mass | molar mass = mass / n = mass / (M × V) |
Step-by-Step Examples
Example 1: NaCl Solution
Problem: What is the molarity of a solution made by dissolving 58.44 g of NaCl (molar mass = 58.44 g/mol) in water to make 1 L of solution?
Step 1: Calculate moles: n = 58.44 g / 58.44 g/mol = 1 mol
Step 2: Calculate molarity: M = 1 mol / 1 L = 1 M
Answer: The solution is 1 M NaCl.
Example 2: Glucose Solution
Problem: You dissolve 36.03 g of glucose (C6H12O6, molar mass = 180.16 g/mol) in water to make 500 mL of solution. What is the molarity?
Step 1: Convert volume: 500 mL = 0.5 L
Step 2: Calculate moles: n = 36.03 g / 180.16 g/mol = 0.2 mol
Step 3: Calculate molarity: M = 0.2 mol / 0.5 L = 0.4 M
Answer: The solution is 0.4 M glucose.
Example 3: HCl Solution
Problem: How many grams of HCl (molar mass = 36.46 g/mol) are needed to make 250 mL of a 2 M solution?
Step 1: Convert volume: 250 mL = 0.25 L
Step 2: Calculate moles needed: n = M × V = 2 mol/L × 0.25 L = 0.5 mol
Step 3: Calculate mass: mass = n × molar mass = 0.5 mol × 36.46 g/mol = 18.23 g
Answer: You need 18.23 g of HCl.
How to Make a Molar Solution (Lab Procedure)
Preparing a solution of a specific molarity in the laboratory requires careful technique. Here is the standard procedure:
- Calculate the mass needed. Use the formula: mass = Molarity × Volume (L) × Molar mass. For example, to prepare 500 mL of 1 M NaCl: mass = 1 × 0.5 × 58.44 = 29.22 g.
- Weigh the solute. Use an analytical balance to accurately weigh the calculated mass of solute.
- Dissolve in less than the final volume of solvent. Transfer the solute to a beaker and add distilled water (about 70-80% of the final volume). Stir until completely dissolved.
- Transfer to a volumetric flask. Pour the solution into a volumetric flask of the desired final volume (e.g., 500 mL).
- Add solvent to the mark. Add distilled water carefully until the bottom of the meniscus aligns exactly with the calibration mark on the flask.
- Mix thoroughly. Stopper the flask and invert several times to ensure a homogeneous solution.
Important: Always add water to the mark on the volumetric flask, not to a pre-measured volume of water. The molarity is based on the total volume of solution, not the volume of solvent added.
Molarity vs. Concentration vs. Molality
These three terms are related but distinct. Understanding the differences is essential for accurate scientific communication.
| Property | Molarity (M) | Molality (m) | Mass Concentration |
|---|---|---|---|
| Definition | Moles of solute per liter of solution | Moles of solute per kilogram of solvent | Mass of solute per volume of solution |
| Units | mol/L (M) | mol/kg (m) | g/L, mg/mL, etc. |
| Depends on temperature? | Yes (volume changes with temperature) | No (mass does not change) | Yes |
| Denominator | Total solution volume | Solvent mass only | Total solution volume |
| Common use | Most lab work, titrations, stoichiometry | Colligative property calculations | Clinical and industrial settings |
Key takeaway: Molarity uses volume of the total solution, while molality uses mass of the solvent only. For dilute aqueous solutions at room temperature, molarity and molality are nearly identical because the density of the solution is close to 1 kg/L.
Dilution Equation: M1V1 = M2V2
When you dilute a concentrated solution by adding more solvent, the number of moles of solute stays constant. This gives us the dilution equation:
Where:
- M1 = initial (concentrated) molarity
- V1 = initial volume (the amount of concentrated solution you use)
- M2 = final (diluted) molarity
- V2 = final total volume after dilution
Dilution Example
Problem: You have a 6 M HCl stock solution. How much of it do you need to make 500 mL of 1 M HCl?
Solution: M1V1 = M2V2
6 M × V1 = 1 M × 0.5 L
V1 = (1 × 0.5) / 6 = 0.0833 L = 83.3 mL
Answer: Measure 83.3 mL of the 6 M HCl stock and dilute with water to a final volume of 500 mL.
Safety note: When diluting strong acids, always add acid to water, never water to acid. This prevents dangerous splashing from the exothermic reaction.
Molarity of Common Substances
The table below lists the approximate molar concentrations of some commonly encountered substances:
| Substance | Formula | Approximate Molarity | Notes |
|---|---|---|---|
| Pure water | H2O | 55.5 M | 1000 g/L / 18.015 g/mol |
| Concentrated hydrochloric acid | HCl | ~12 M | 37% by mass, density 1.19 g/mL |
| Concentrated sulfuric acid | H2SO4 | ~18 M | 98% by mass, density 1.84 g/mL |
| Concentrated nitric acid | HNO3 | ~16 M | 70% by mass, density 1.42 g/mL |
| Concentrated acetic acid (glacial) | CH3COOH | ~17.4 M | 99.7% by mass |
| Concentrated ammonia | NH3 | ~15 M | 28-30% by mass |
| Concentrated sodium hydroxide | NaOH | ~19 M | 50% by mass, density 1.52 g/mL |
| Concentrated phosphoric acid | H3PO4 | ~14.8 M | 85% by mass, density 1.68 g/mL |
| Seawater (NaCl component) | NaCl | ~0.6 M | ~3.5% salinity |
| Blood glucose (normal) | C6H12O6 | ~0.005 M | ~90 mg/dL |
Applications in Chemistry and Biology
Molarity is fundamental across many scientific disciplines:
Analytical Chemistry
- Titrations: Molarity is used to calculate the amount of titrant needed and to determine the concentration of unknown solutions.
- Standard solutions: Solutions of precisely known molarity are prepared as reference standards for quantitative analysis.
Organic and Inorganic Synthesis
- Reaction stoichiometry: Molar concentrations allow chemists to mix reactants in the correct stoichiometric ratios.
- Yield calculations: Knowing the molarity of reagents helps predict theoretical and actual yields.
Biochemistry and Molecular Biology
- Buffer preparation: Biological buffers (PBS, Tris, HEPES) are prepared at specific molarities to maintain pH.
- Enzyme kinetics: Substrate concentrations in Michaelis-Menten experiments are expressed in molarity.
- Cell culture media: Nutrient and ion concentrations in growth media are specified as molar concentrations.
Medicine and Pharmacology
- IV solutions: Molar concentration of electrolytes in intravenous fluids must be precisely controlled.
- Drug dosing: Some medications are dosed based on the molar concentration in plasma.
Environmental Science
- Water quality: Pollutant concentrations in natural water are sometimes reported in molarity.
- Soil chemistry: Ion exchange capacity and nutrient availability involve molar concentrations.
Frequently Asked Questions
What is the difference between molarity and molality?
Molarity (M) is moles of solute per liter of solution, while molality (m) is moles of solute per kilogram of solvent. Molarity changes with temperature because volume expands or contracts, but molality remains constant because it is based on mass. For dilute aqueous solutions at room temperature, they are nearly equal.
Can molarity be greater than 1?
Yes, absolutely. Many concentrated stock solutions have molarities well above 1. For example, concentrated sulfuric acid is approximately 18 M, and pure water itself has a molarity of about 55.5 M. There is no upper limit other than the physical solubility of the solute.
Why does molarity change with temperature?
Molarity is defined using volume, and the volume of a liquid changes with temperature due to thermal expansion or contraction. As temperature increases, the solution expands, the volume increases, and the molarity decreases slightly (and vice versa). If temperature-independence is required, use molality instead.
How do I convert between molarity and mass concentration (g/L)?
Multiply molarity by the molar mass of the solute: mass concentration (g/L) = Molarity (mol/L) × Molar mass (g/mol). For example, 0.5 M NaCl = 0.5 × 58.44 = 29.22 g/L.
What does "molar" mean when describing a solution?
A "molar" solution, or a "1 M" solution, contains exactly 1 mole of solute per liter of total solution. The term "molar" is used as an adjective to describe the concentration. For instance, "0.1 molar NaOH" means a solution with 0.1 mol of NaOH per liter.
How do I prepare a solution from a solid solute?
Calculate the required mass using: mass = Molarity × Volume (L) × Molar mass. Weigh the solute, dissolve it in about 70-80% of the target volume of water, transfer to a volumetric flask, and add water to the final volume mark. Mix thoroughly.
Is molarity the same as concentration?
Molarity is one specific type of concentration. Concentration is a general term that can be expressed in many ways: molarity (mol/L), molality (mol/kg), mass percent (%), parts per million (ppm), mass per volume (g/L), and more. Molarity is simply the most commonly used form in chemistry.