How to Calculate [OH-] from [H3O ] in Water

In aqueous solutions, the relationship between hydroxide ions ([OH^-]) and hydronium ions ([H_3O^ ]) can be determined using the ion product of water, denoted as K_w. At 25°C, the value of K_w is (1 times 10^{-14}). This relationship is crucial for understanding the basic or acidic nature of a solution. The formula to find the concentration of hydroxide ions from the concentration of hydronium ions is:

[OH^-] frac{K_w}{[H_3O^ ]}

Step-by-Step Calculation

Here is a detailed step-by-step guide on how to calculate the concentration of hydroxide ions from the concentration of hydronium ions:

Identify the concentration of hydronium ions, denoted as [H_3O^ ]. Use the ion product of water, K_w, which is (1 times 10^{-14}) at 25°C. Plug the values into the formula to solve for [OH^-].

Let's work through an example to illustrate this process.

Example Calculation

Suppose you have a concentration of hydronium ions, [H_3O^ ], equal to (1.0 times 10^{-3} , text{M}). Here’s how you can find the concentration of hydroxide ions [OH^-]:

[OH^-] frac{1.0 times 10^{-14}}{1.0 times 10^{-3}} 1.0 times 10^{-11} , text{M}

Therefore, the concentration of hydroxide ions [OH^-] is (1.0 times 10^{-11} , text{M}) when the concentration of hydronium ions is (1.0 times 10^{-3} , text{M}).

User-Specific Values

Feel free to provide specific values for [H_3O^ ] if you need help with a particular calculation.

Additional Considerations

The sum of pH and pOH is always 14. When water is neutral, pH is 7, and pOH is 7. Adding HCl (hydrochloric acid) to water introduces H (hydrogen) ions, which create an acidic solution. These H ions react with hydroxide ions (OH-) to form water (H2O), thereby decreasing the concentration of OH-.

Water Ionization

At 25°C, the ion product of water is:

K_w [H_3O^ ][OH^-] 1 times 10^{-14}

When an acid such as HCl dissociates, it releases H ions to the solution, increasing the concentration of [H_3O^ ]. This means that the concentration of [OH^-] will decrease, as per the equation above.

Base Addition

Similarly, adding a base like NaOH (sodium hydroxide) will increase the concentration of [OH^-], thereby decreasing the concentration of [H_3O^ ]. This is because the NaOH dissociates to provide hydroxide ions, which will react with the existing H_3O^ ions to form water.

For example, if you have a solution with a high concentration of OH^- ions due to the addition of NaOH, the pH will increase, and the pOH will decrease, reflecting the increased basicity of the solution.

Conclusion

Understanding the relationship between [OH^-] and [H_3O^ ] is fundamental in chemistry. By using the ion product of water, you can easily calculate the concentration of hydroxide ions from the concentration of hydronium ions, and vice versa. This knowledge is crucial for determining the acidity or basicity of a solution and is widely applicable in various scientific fields, including environmental science and pharmaceutical analysis.