Understanding the Relationship Between Percent by Mass and Molarity in Chemistry

Introduction: Understanding how chemical substances are dissolved in solutions is fundamental in chemistry. Two common measures of concentration are percent by mass and molarity. This article delves into these concepts and explains their relationship, providing a comprehensive guide for anyone dealing with dissolved solutions.

What is Percent by Mass?

Definition: Percent by mass or mass percent is a measure of how much solute is present in a solution relative to its total mass. It is calculated using the formula:

[ text{Percent by Mass} left(frac{text{Mass of Solute}}{text{Mass of Solution}}right) times 100 ]

What is Molarity?

Definition: Molarity is a measure of concentration expressed as the number of moles of solute per liter of solution. It is denoted by the symbol 'M' and calculated with the formula:

[ text{Molarity M} frac{text{Moles of Solute}}{text{Volume of Solution in Liters}} ]

The Relationship Between Percent by Mass and Molarity

To relate percent by mass to molarity, you need to know the density of the solution in g/mL or g/cm3, and the molar mass of the solute in g/mol. This relationship can be explored through the following steps:

Steps to Convert Percent by Mass to Molarity

tCalculate the Mass of the Solute: tt

If you have a solution with a percent by mass of x in 100 g of solution, the mass of the solute is x g.

t tCalculate the Volume of the Solution: tt

Using the density d of the solution, you can find the volume:

tt

[ text{Volume of Solution L} frac{text{Mass of Solution g}}{text{Density g/mL}} times frac{1 text{ mL}}{1000 text{ L}} ]

tt

For 100 g of solution, this becomes:

tt

[ text{Volume L} frac{100 text{ g}}{d text{ g/mL}} times frac{1 text{ mL}}{1000 text{ L}} ]

t tCalculate the Moles of Solute: tt

Using the molar mass Mu of the solute:

tt

[ text{Moles of Solute} frac{text{Mass of Solute g}}{M_{text{molar}} text{ g/mol}} ]

t tCalculate Molarity: tt

Substitute the values into the molarity formula:

tt

[ M frac{text{Moles of Solute}}{text{Volume of Solution L}} ]

t

Example

Suppose you have a solution that is 10% NaCl by mass with a density of 1.07 g/mL. The molar mass of NaCl is approximately 58.44 g/mol.

tMass of NaCl in 100 g of solution: 10 g tVolume of solution: tt

[ text{Volume} frac{100 text{ g}}{1.07 text{ g/mL}} approx 93.46 text{ mL} approx 0.09346 text{ L} ]

t tMoles of NaCl: tt

[ text{Moles} frac{10 text{ g}}{58.44 text{ g/mol}} approx 0.171 text{ mol} ]

t tMolarity: tt

[ M frac{0.171 text{ mol}}{0.09346 text{ L}} approx 1.83 text{ M} ]

t

Conclusion

In summary, while percent by mass and molarity are both measures of concentration, they express that concentration in different ways. To convert between them, you need to know the density of the solution and the molar mass of the solute.

Additional Resources

For further reading and a deeper understanding of concentration measures in chemistry, consider checking out the following resources:

tGuide to Analyzing Solution Concentrations tInteractive Molarity Calculations: Theory and Practice tUnderstanding Percent by Mass: Practical Chemical Applications