Determination of H? Ions in a pH 13 Solution: A Comprehensive Guide

Understanding the concentration of hydrogen ions (H?) in a solution of a given pH value is a fundamental concept in chemistry and is crucial in various scientific applications. This article will guide you through the step-by-step process of calculating the number of H? ions in 1 milliliter (mL) of a solution with a pH of 13. We will also explore the relationship between pH, hydrogen ions, and other chemical species in a solution.

Understanding pH and Hydrogen Ion Concentration

The pH scale, which is a logarithmic scale ranging from 0 to 14, is used to express the acidity or basicity of a solution. The pH value is defined as the negative logarithm of the molar concentration of hydrogen ions (H?) in a solution:

( text{pH} -log[H^ ] )

A pH value less than 7 indicates an acidic solution, while a pH value greater than 7 indicates a basic solution. In the case of a solution with a pH of 13, this solution is strongly basic.

Calculating the Concentration of Hydrogen Ions (H?)

Given a pH of 13, let us calculate the concentration of H? ions. Using the formula:

( [H^ ] 10^{-text{pH}} )

Substituting the given pH value:

( [H^ ] 10^{-13} , text{mol/L} )

This means that in 1 liter (L) of the solution, there are (10^{-13}) moles of H? ions. To find the number of moles in 1 milliliter (mL) of the solution, we use the following conversion:

( text{moles in 1 mL} [H^ ] times text{volume in L} )

Since 1 mL is 0.001 L:

( text{moles in 1 mL} 10^{-13} , text{mol/L} times 0.001 , text{L} 10^{-16} , text{mol} )

Finding the Number of H? Ions

To find the number of H? ions in the solution, we need to multiply the number of moles by Avogadro's number (approximately (6.022times10^{23}) ions/mol), which is the number of particles in one mole of a substance. Therefore:

( text{Number of } H^ text{ ions} 10^{-16} , text{mol} times 6.022 times 10^{23} , text{ions/mol} )

Calculating this gives:

( text{Number of } H^ text{ ions} approx 6.022 times 10^{7} text{ ions} )

Thus, there are approximately 60.22 million H? ions present in 1 mL of a solution with a pH of 13.

Exploring the Role of Sodium Hydroxide (NaOH)

Sodium hydroxide (NaOH) is a strong base that dissociates completely in aqueous solutions. The dissociation reaction can be written as:

( text{NaOH} rightarrow text{Na}^ text{OH}^- )

The equilibrium in aqueous solutions of bases involves the concentration of H? and OH? ions, which are given by the relationship:

( text{H}^ times text{OH}^- 10^{-14} )

To calculate the number of moles of NaOH, we use the molar mass of NaOH (40 g/mol) and the given mass of the substance. For example, if 2 grams of NaOH are dissolved in 500 mL of water, the calculation is:

( text{moles of NaOH} frac{2 , text{g}}{40 , text{g/mol}} 0.05 , text{moles} )

The molar concentration of NaOH is then calculated as follows:

( text{concentration of NaOH} frac{text{moles of NaOH}}{text{volume in liters}} frac{0.05 , text{moles}}{0.5 , text{L}} 0.1 , text{M} )

Using the relationship ( text{H}^ times text{OH}^- 10^{-14} ), the concentration of H? ions is:

( text{concentration of } H^ frac{10^{-14}}{0.1} 10^{-13} , text{M} )

Finally, taking the log of the concentration of H? and multiplying by -1 gives the pH value:

( text{pH} -log(10^{-13}) 13 )

This confirms that the solution indeed has a pH of 13, as we initially calculated using the H? ions concentration.

Conclusion

Understanding the concentration of hydrogen ions in a solution, especially in the context of pH, is fundamental in chemistry and many other fields. By using the appropriate formulas and constants, we have determined that there are approximately 60.22 million H? ions in 1 mL of a solution with a pH of 13. This process can be extended to other solutions and materials, providing valuable insights into the behavior and interactions of different chemical species in aqueous environments.