Question

Calculate the pH corresponding to each of the hydroxide ion concentrations given below, and indicate whether each solution is acidic, basic, or neutral. a. $\left[{\mathrm{OH}}^{-}\right]=1.4\times {10}^{-6}M$ b. $\left[{\mathrm{OH}}^{-}\right]=9.35\times {10}^{-9}M$ c. $\left[{\mathrm{OH}}^{-}\right]=2.21\times {10}^{-1}M$ d. $\left[{\mathrm{OH}}^{-}\right]=7.98\times {10}^{-12}M$

Short answer

In conclusion: a. The pH for $\left[{\mathrm{OH}}^{-}\right]=1.4\times {10}^{-6}M$ is approximately 8.15 (basic). b. The pH for $\left[{\mathrm{OH}}^{-}\right]=9.35\times {10}^{-9}M$ is approximately 6.03 (acidic). c. The pH for $\left[{\mathrm{OH}}^{-}\right]=2.21\times {10}^{-1}M$ is approximately 13.34 (basic). d. The pH for $\left[{\mathrm{OH}}^{-}\right]=7.98\times {10}^{-12}M$ is approximately 2.90 (acidic).

Step-by-step solution

To find the corresponding $[{\mathrm{H}}^{+}]$, we need to use the $K_w$ equation: $$[{\mathrm{H}}^{+}]=\frac{K_w}{[{\mathrm{OH}}^{-}]}=\frac{1\times {10}^{-14}}{1.4\times {10}^{-6}}=7.14\times {10}^{-9}$$ #b. Calculate the pH for a.#

Now we calculate the pH using the equation $pH=-\log ([{\mathrm{H}}^{+}])$: $$pH=-\log (7.14\times {10}^{-9})\approx 8.15$$ Since the pH is greater than 7, the solution is basic. #c. Calculate the H+ concentration for b.#

Using the $K_w$ equation: $$[{\mathrm{H}}^{+}]=\frac{1\times {10}^{-14}}{9.35\times {10}^{-9}}=1.07\times {10}^{-6}$$ #d. Calculate the pH for b.#

Calculate the pH: $$pH=-\log (1.07\times {10}^{-6})\approx 6.03$$ Since the pH is less than 7, the solution is acidic. #e. Calculate the H+ concentration for c.#

Using the $K_w$ equation: $$[{\mathrm{H}}^{+}]=\frac{1\times {10}^{-14}}{2.21\times {10}^{-1}}=4.53\times {10}^{-14}$$ #f. Calculate the pH for c.#

Calculate the pH: $$pH=-\log (4.53\times {10}^{-14})\approx 13.34$$ Since the pH is greater than 7, the solution is basic. #g. Calculate the H+ concentration for d.#

Using the $K_w$ equation: $$[{\mathrm{H}}^{+}]=\frac{1\times {10}^{-14}}{7.98\times {10}^{-12}}=1.25\times {10}^{-3}$$ #h. Calculate the pH for d.#

Calculate the pH: $$pH=-\log (1.25\times {10}^{-3})\approx 2.90$$ Since the pH is less than 7, the solution is acidic. In conclusion: a. The pH for $\left[{\mathrm{OH}}^{-}\right]=1.4\times {10}^{-6}M$ is approximately 8.15 (basic). b. The pH for $\left[{\mathrm{OH}}^{-}\right]=9.35\times {10}^{-9}M$ is approximately 6.03 (acidic). c. The pH for $\left[{\mathrm{OH}}^{-}\right]=2.21\times {10}^{-1}M$ is approximately 13.34 (basic). d. The pH for $\left[{\mathrm{OH}}^{-}\right]=7.98\times {10}^{-12}M$ is approximately 2.90 (acidic).

Key concepts

Hydroxide Ion Concentration

Understanding the hydroxide ion concentration in a solution is critical to determining the solution's basicity. The concentration is usually provided in molarity, represented by 'M', which is the number of moles of hydroxide per liter of solution. In the realm of chemistry, this ion concentration directly influences the pH of the solution.

When hydroxide ion concentration increases, it results in a higher pH, indicating a more basic or alkaline solution. Conversely, a lower hydroxide ion concentration suggests a more acidic environment.

Let's take a closer look at an example. With a hydroxide ion concentration of $1.4\times {10}^{-6}M$, we can intuit the solution to be basic as this relatively high concentration of ${\mathrm{OH}}^{-}$ ions pushes the solution's environment toward basicity. The process involves calculating the hydronium ion (${\mathrm{H}}^{+}$) concentration through the water dissociation constant ($K_w$) and subsequently using that to find the pH level.

Acidic and Basic Solutions

The nature of a solution, whether acidic or basic, is not just about the presence of certain ions but also their concentrations. Acidic solutions have a higher concentration of hydrogen ions (${\mathrm{H}}^{+}$), while basic solutions have higher concentrations of hydroxide ions (${\mathrm{OH}}^{-}$).

A crucial point to remember is that the product of the concentrations of these ions always equals the constant $K_w$, which is $1\times {10}^{-14}$ at 25°C.

In practice, if a solution presents a hydroxide ion concentration, such as in our exercise $9.35\times {10}^{-9}M$, determining whether it's acidic or basic depends on calculating the corresponding ${\mathrm{H}}^{+}$ concentration and then finding its pH. If the pH is below 7, the environment is acidic. If it is above 7, it is basic. This understanding is fundamental to chemistry and environmental science, where the acid-base balance is critical to various processes.

pH Scale

The pH scale is an invaluable tool in chemistry, providing a measure of how acidic or basic a solution is. It typically ranges from 0 to 14, with 7 being neutral. Anything below 7 is considered acidic, and anything above 7 is basic or alkaline.

The pH is calculated as the negative logarithm of the hydrogen ion concentration: $pH=-\log ([{\mathrm{H}}^{+}])$. In our exercise, for instance, with ${\mathrm{H}}^{+}$ concentration of $7.14\times {10}^{-9}$, we calculated the pH to be approximately 8.15, placing the solution on the basic end of the pH scale.

Remember, the pH scale is logarithmic, which means each whole pH value below 7 is ten times more acidic than the next higher value. This logarithmic nature allows us to compress the wide range of hydrogen ion concentrations into a manageable scale. This is particularly helpful in laboratory and industrial settings, where precise measurements of acidity or alkalinity are imperative for reactions and processes.