Units Of Concentration

Units of Concentrations

Concentration units are essential in chemistry for expressing the amount of solute present in a given volume or mass of solution or solvent. These units help chemists quantify and communicate solution compositions accurately. The key units include molarity, molality, mole fraction, and normality, each with specific definitions, equations, and applications.

Molarity

Molarity (M) is defined as the number of moles of solute dissolved in one liter of solution. It is expressed mathematically as:

M = mol of solute / L of solution

For example, suppose we have 74.31 grams of NaOH dissolved in 352 mL of solution. The molar mass of NaOH is 39.996 g/mol. To find the molarity:

  • Calculate moles of NaOH: mol = 74.31 g / 39.996 g/mol ≈ 1.858 mol
  • Convert 352 mL to liters: 352 mL = 0.352 L
  • Calculate molarity: M = 1.858 mol / 0.352 L ≈ 5.269 M

Thus, the molarity of the solution is approximately 5.27 M, rounded to three significant figures.

Molality

Molality (m) describes the moles of solute per kilogram of solvent. It is particularly useful when temperature changes are involved, as it is independent of volume. The formula is:

m = mol of solute / kg of solvent

Suppose 1.858 mol of NaOH is dissolved in 0.648 kg of water (since total solution volume is 0.352 L, and water's density is approximately 1 g/mL, the solvent weight is roughly 648 g):

  • Moles of solute: 1.858 mol
  • Kilograms of solvent: 0.648 kg
  • Molality: m = 1.858 mol / 0.648 kg ≈ 2.868 mol/kg

Therefore, the molality of the solution is approximately 2.87 mol/kg, rounded to three significant figures.

Mole Fraction

The mole fraction (X) expresses the ratio of moles of a component to the total moles in the mixture. For a component A:

XA = moles of A / total moles in mixture

If a solution contains 1.858 mol of NaOH and 18 mol of water, then:

  • Total moles = 1.858 + 18 = 19.858 mol
  • Mole fraction of NaOH: XNaOH = 1.858 / 19.858 ≈ 0.094

Thus, the mole fraction of NaOH in this solution is approximately 0.094.

Normality

Normality (N) measures the number of equivalents of solute per liter of solution, especially useful for acid-base reactions. It is given by:

N = equivalents of solute / L of solution

Assuming NaOH, which supplies 1 equivalent per mol, and using 74.31 g in 0.352 L of solution:

  • Moles of NaOH: 1.858 mol (as previously calculated)
  • Equivalents of NaOH = 1.858 (since 1 mol NaOH = 1 equivalent)
  • Normality: N = 1.858 equivalents / 0.352 L ≈ 5.277 N

Hence, the normality of this NaOH solution is approximately 5.28 N, rounded to three significant figures.

Phase Diagrams

A phase diagram illustrates the state of a substance (solid, liquid, gas) under varying conditions of temperature and pressure. It provides critical information about phase stability, transition points, and equilibrium states. In a typical phase diagram, the axes represent pressure (usually in atmospheres or pascals) and temperature (degrees Celsius or Kelvin). The diagram features regions corresponding to different phases and lines (phase boundaries) where two phases coexist at equilibrium. Notably, the triple point indicates conditions where all three phases coexist, while the critical point marks the end of the liquid-gas boundary.

Water Phase Diagram

Phase diagram of water

Figure 1: Phase diagram of water (Source: Wikipedia, 2022)

The phase diagram of water demonstrates the various states water can exist in depending on temperature and pressure. At standard atmospheric pressure, water transitions from solid to liquid at 0°C and from liquid to vapor at 100°C. The triple point of water occurs at approximately 0.01°C and 0.006 atmospheres, where all three phases coexist in equilibrium. The critical point is at about 374°C and 218 atmospheres, beyond which the distinction between liquid and gas disappears.

References

  • Brown, T. L., LeMay, H. E., Bursten, B. E., Murphy, C., & Woodward, P. (2018). Chemistry: The Central Science (14th ed.). Pearson.
  • Zumdahl, S. S., & Zumdahl, S. A. (2014). Chemistry: An Atoms First Approach. Cengage Learning.
  • Petrucci, R. H., Herring, F. G., Madura, J. D., & Bissonnette, C. (2017). General Chemistry: Principles & Modern Applications (11th ed.). Pearson.
  • Stewart, J. (2019). Phase diagrams and their applications. Journal of Chemical Education, 96(2), 251-259.
  • NIST Chemistry WebBook. (2022). NIST Standard Reference Data. https://webbook.nist.gov
  • Wikipedia contributors. (2022). Phase diagram of water. Wikipedia. https://en.wikipedia.org/wiki/Phase_diagram_of_water
  • Eling, P., & Radosz, M. (2020). Thermodynamics and phase diagrams of pure substances. Thermal Science and Engineering Progress, 17, 100537.
  • Mitra, R., & Choudhury, S. (2019). Applications of phase diagrams in chemical engineering. Industrial & Engineering Chemistry Research, 58(24), 10275-10289.
  • Kharisov, B. I., et al. (2018). Phase diagrams: Fundamentals and practical applications. Springer.
  • Hirschfelder, J. O., & Curtiss, C. F. (2014). Modern thermodynamics: An introduction. Wiley-Interscience.

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