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Molarity Calculator

A comprehensive chemistry calculator for solution preparation. Calculate molarity from mass and volume, find required mass for a solution of specific molarity, or determine volume needed based on desired concentration. Essential for laboratory work and chemistry studies.

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g/mol

The molar mass of the solute

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Understanding Molarity in Chemistry

What is Molarity?

Molarity (symbolized by M) is a measure of concentration that describes the number of moles of a solute per liter of solution. It is one of the most common ways of expressing concentration in chemistry and is particularly useful for stoichiometric calculations.

Molarity (M)=Moles of solute (mol)Volume of solution (L)\text{Molarity (M)} = \frac{\text{Moles of solute (mol)}}{\text{Volume of solution (L)}}

Since the number of moles equals the mass divided by the molar mass, we can also express molarity as:

Molarity (M)=Mass of solute (g)Molar mass (g/mol)×Volume of solution (L)\text{Molarity (M)} = \frac{\text{Mass of solute (g)}}{\text{Molar mass (g/mol)} \times \text{Volume of solution (L)}}

Key Concepts

1. Mole Concept

A mole is the amount of substance containing exactly 6.02214076 × 1023 elementary entities (atoms, molecules, ions, etc.). This number is known as Avogadro's constant.

2. Molar Mass

The molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For compounds, it equals the sum of the atomic masses of all atoms in the compound.

3. Solution Preparation

When preparing a solution of specific molarity:

  • Calculate the required mass of solute using Mass=Molarity×Molar mass×Volume\text{Mass} = \text{Molarity} \times \text{Molar mass} \times \text{Volume}
  • Dissolve the solute in less than the final volume of solvent
  • Add additional solvent until the desired volume is reached

Calculation Examples

Example 1: Calculating Molarity

Problem: If 5.85 g of sodium chloride (NaCl, molar mass = 58.44 g/mol) is dissolved in water to make 500 mL of solution, what is the molarity?

Solution:

First, convert volume to liters: 500 mL = 0.5 L

Then calculate moles of NaCl:

Moles of NaCl=MassMolar mass=5.85 g58.44 g/mol=0.1001 mol\text{Moles of NaCl} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{5.85 \text{ g}}{58.44 \text{ g/mol}} = 0.1001 \text{ mol}

Finally, calculate molarity:

Molarity=MolesVolume (L)=0.1001 mol0.5 L=0.2002 M\text{Molarity} = \frac{\text{Moles}}{\text{Volume (L)}} = \frac{0.1001 \text{ mol}}{0.5 \text{ L}} = 0.2002 \text{ M}

Answer: The molarity of the NaCl solution is 0.2002 M (or approximately 0.2 M).

Example 2: Finding Mass from Molarity

Problem: How many grams of potassium hydroxide (KOH, molar mass = 56.11 g/mol) are needed to prepare 250 mL of a 0.5 M solution?

Solution:

Convert volume to liters: 250 mL = 0.25 L

Calculate moles needed:

Moles of KOH=Molarity×Volume=0.5 M×0.25 L=0.125 mol\text{Moles of KOH} = \text{Molarity} \times \text{Volume} = 0.5 \text{ M} \times 0.25 \text{ L} = 0.125 \text{ mol}

Calculate mass:

Mass of KOH=Moles×Molar mass=0.125 mol×56.11 g/mol=7.01 g\text{Mass of KOH} = \text{Moles} \times \text{Molar mass} = 0.125 \text{ mol} \times 56.11 \text{ g/mol} = 7.01 \text{ g}

Answer: 7.01 grams of KOH are needed.

Example 3: Finding Volume from Molarity

Problem: What volume (in mL) of a 1.5 M glucose solution contains 27 g of glucose (C₆H₁₂O₆, molar mass = 180.16 g/mol)?

Solution:

Calculate moles of glucose:

Moles of glucose=MassMolar mass=27 g180.16 g/mol=0.1499 mol\text{Moles of glucose} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{27 \text{ g}}{180.16 \text{ g/mol}} = 0.1499 \text{ mol}

Calculate volume in liters:

Volume=MolesMolarity=0.1499 mol1.5 M=0.0999 L\text{Volume} = \frac{\text{Moles}}{\text{Molarity}} = \frac{0.1499 \text{ mol}}{1.5 \text{ M}} = 0.0999 \text{ L}

Convert to milliliters:

Volume=0.0999 L×1000 mL/L=99.9 mL\text{Volume} = 0.0999 \text{ L} \times 1000 \text{ mL/L} = 99.9 \text{ mL}

Answer: The required volume is 99.9 mL.

Applications of Molarity in Chemistry

Laboratory Use

  • Preparing reagents for chemical analysis
  • Standardizing solutions for titrations
  • Preparing buffer solutions of specific pH
  • Creating calibration standards for instruments

Industrial Applications

  • Pharmaceutical manufacturing
  • Food and beverage production
  • Water treatment processes
  • Quality control procedures

Common Molar Masses of Frequently Used Chemicals

ChemicalFormulaMolar Mass (g/mol)
WaterH2O18.02
Sodium ChlorideNaCl58.44
GlucoseC6H12O6180.16
Sodium HydroxideNaOH40.00
Hydrochloric AcidHCl36.46
Sulfuric AcidH2SO498.08
Acetic AcidCH3COOH60.05
Potassium PermanganateKMnO4158.03

Unit Conversions in Molarity Calculations

When working with molarity calculations, it's common to need to convert between different units:

Mass Conversions

  • 1 kilogram (kg) = 1000 grams (g)
  • 1 gram (g) = 1000 milligrams (mg)
  • 1 milligram (mg) = 0.001 grams (g)

Volume Conversions

  • 1 liter (L) = 1000 milliliters (mL)
  • 1 milliliter (mL) = 0.001 liters (L)
  • 1 deciliter (dL) = 100 milliliters (mL) = 0.1 liters (L)

Conclusion

Understanding molarity is fundamental to chemistry and many scientific disciplines. It provides a precise way to express concentration and is essential for preparing solutions, conducting experiments, and solving chemical problems. The molarity calculator allows you to easily perform these calculations, saving time and reducing errors in laboratory settings.

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