Question

What is the \(\mathrm{OH}^{-}\)concentration in each of the following solutions? (a) gastric juice, \(\mathrm{pH}=1.00\) (b) Milk of Magnesia, \(\mathrm{pH}=10.50\) (c) Seven-Up, \(\mathrm{pH}=3.60\)

Short answer

The \(\mathrm{OH}^{-}\) concentrations for each solution are: (a) gastric juice: \(1.0 \times 10^{-13} \, \mathrm{M}\), (b) Milk of Magnesia: \(3.16 \times 10^{-4} \, \mathrm{M}\), (c) Seven-Up: \(3.98 \times 10^{-11} \, \mathrm{M}\)

Step-by-step solution

Understand \(\mathrm{pH}\), \(\mathrm{pOH}\) and \(\mathrm{OH}^{-}\) concentration relationship

First, note that \(\mathrm{pH} + \mathrm{pOH} = 14\) at 25°C. The \(\mathrm{OH}^{-}\) concentration can be derived from the \(\mathrm{pOH}\) using the relation \(\mathrm{pOH} = -\log[\mathrm{OH}^{-}]\), therefore \([\mathrm{OH}^{-}] = 10^{-\mathrm{pOH}}\).

Calculate \(\mathrm{pOH}\) for each solution

From the \(\mathrm{pH}\) given for each solution, find the \(\mathrm{pOH}\) using the formula \(\mathrm{pOH} = 14 - \mathrm{pH}\).\n\n(a) For gastric juice, \(\mathrm{pOH} = 14 - 1.00 = 13.00\)\n(b) For milk of magnesia, \(\mathrm{pOH} = 14 - 10.50 = 3.50\)\n(c) For seven-up, \(\mathrm{pOH} = 14 - 3.60 = 10.40\)

Calculate \(\mathrm{OH}^{-}\) concentration

Now, calculate the \(\mathrm{OH}^{-}\) concentration using the formula \([\mathrm{OH}^{-}] = 10^{-\mathrm{pOH}}\).\n\n(a) For gastric juice, \([\mathrm{OH}^{-}] = 10^{-13.00} = 1.0 \times 10^{-13} \, \mathrm{M}\)\n(b) For milk of magnesia, \([\mathrm{OH}^{-}] = 10^{-3.50} = 3.16 \times 10^{-4} \, \mathrm{M}\)\n(c) For seven-up, \([\mathrm{OH}^{-}] = 10^{-10.40} = 3.98 \times 10^{-11} \, \mathrm{M}\)

Key concepts

pOH Calculation

Understanding the calculation of pOH is essential in acid-base chemistry. At 25°C, the sum of pH and pOH of an aqueous solution is always 14. This is because pH is defined as the negative logarithm of the hydrogen ion concentration \( [H^+] \), while pOH is the negative logarithm of the hydroxide ion concentration \( [OH^-] \). To find pOH, you simply subtract the given pH from 14. For example, if a solution has a pH of 3, its pOH would be \( 14 - 3 = 11 \).

Once you have the pOH, you can calculate the hydroxide ion concentration using the formula \( [OH^-] = 10^{-pOH} \). If you're dealing with a solution with a pOH of 11, as in our example, the hydroxide ion concentration would be \( 10^{-11} \). This approach is straightforward and is vital for fields such as environmental science, medicine, and any field that deals with the pH of solutions.

Hydroxide Ion Concentration

The hydroxide ion concentration in a solution gives insight into its basicity—higher concentrations indicating stronger bases. Once you have the pOH, as outlined in the first section, determining the hydroxide ion concentration is done directly by using the formula \( [OH^-] = 10^{-pOH} \). This equation reflects the inverse logarithmic relationship between pOH and the hydroxide ion concentration.

For instance, if you have a solution with a pOH of 7, which is neutral with respect to hydroxide ions, the concentration would be \( 10^{-7} \) M (moles per liter). When working with this formula, you might encounter very small or very large numbers, which is why scientists use the logarithmic scale to represent them in a more manageable form.

Acid-Base Chemistry

Acid-base chemistry is a fundamental concept in chemistry that deals with the properties and reactions of acids and bases. Acids are substances that increase the hydrogen ion concentration \( [H^+] \) in a solution, while bases do the opposite by increasing the hydroxide ion concentration \( [OH^-] \). The strength of an acid or base is usually conveyed through its pH or pOH value. Acids have a pH less than 7, while bases have a pH greater than 7.

The pH scale runs from 0 to 14, with 7 being neutral. It's logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value, and each whole pH value above 7 is ten times more basic. Understanding the relationship between pH, pOH, and the ion concentrations they represent is crucial in predicting the behavior of solutions during chemical reactions and in maintaining the proper balance in environmental and biological systems.