Question

Calculate $\left[{\mathrm{H}}^{+}\right]$ for each of the following solutions, and indicate whether the solution is acidic, basic, or neutral: (a) $\left[{\mathrm{OH}}^{-}\right]=0.00045M;$ (b) $\left[{\mathrm{OH}}^{-}\right]=8.8\times {10}^{-9}\mathrm{M};$ (c) a solution in which $\left[{\mathrm{OH}}^{-}\right]$ is 100 times greater than $\left[{\mathrm{H}}^{+}\right]$ .

Short answer

For the given solutions: (a) $[{\mathrm{H}}^{+}]=2.22\times {10}^{-12}\text{M}$ and the solution is basic; (b) $[{\mathrm{H}}^{+}]=1.14\times {10}^{-6}\text{M}$ and the solution is acidic; (c) $[{\mathrm{H}}^{+}]=1.0\times {10}^{-7}\text{M}$ and the solution is neutral.

Step-by-step solution

Find $[{\mathrm{H}}^{+}]$

Given that $[{\mathrm{OH}}^{-}]=0.00045\text{M}$, we can find $[{\mathrm{H}}^{+}]$ using the K_w expression: $$\left[{\mathrm{H}}^{+}\right]=\frac{K_{\text{w}}}{\left[{\mathrm{OH}}^{-}\right]}=\frac{1.0\times {10}^{-14}}{0.00045}$$

Calculate $[{\mathrm{H}}^{+}]$ and determine the solution type

Calculating the concentration of hydrogen ions: $$\left[{\mathrm{H}}^{+}\right]=2.22\times {10}^{-12}\text{M}$$ Since $[{\mathrm{H}}^{+}]<[{\mathrm{OH}}^{-}]$, the solution is basic. #Case (b):#

Find $[{\mathrm{H}}^{+}]$

Given that $[{\mathrm{OH}}^{-}]=8.8\times {10}^{-9}\text{M}$, we can find $[{\mathrm{H}}^{+}]$ using the K_w expression: $$\left[{\mathrm{H}}^{+}\right]=\frac{K_{\text{w}}}{\left[{\mathrm{OH}}^{-}\right]}=\frac{1.0\times {10}^{-14}}{8.8\times {10}^{-9}}$$

Calculate $[{\mathrm{H}}^{+}]$ and determine the solution type

Calculating the concentration of hydrogen ions: $$\left[{\mathrm{H}}^{+}\right]=1.14\times {10}^{-6}\text{M}$$ Since $[{\mathrm{H}}^{+}]>[{\mathrm{OH}}^{-}]$, the solution is acidic. #Case (c):#

Write the given relation

We are given that $[{\mathrm{OH}}^{-}]$ is 100 times greater than $[{\mathrm{H}}^{+}]$: $$\left[{\mathrm{OH}}^{-}\right]=100\left[{\mathrm{H}}^{+}\right]$$

Find $[{\mathrm{H}}^{+}]$ using the K_w expression

Using the K_w expression and substituting the given relation: $$\left[{\mathrm{H}}^{+}\right]\left(100\left[{\mathrm{H}}^{+}\right]\right)=1.0\times {10}^{-14}$$

Solve for $[{\mathrm{H}}^{+}]$ and determine the solution type

Solving the equation for $[{\mathrm{H}}^{+}]$ we get: $$\left[{\mathrm{H}}^{+}\right]=1.0\times {10}^{-7}\text{M}$$ Since $[{\mathrm{H}}^{+}]=[{\mathrm{OH}}^{-}]$ (given their ratio is 100), the solution is neutral.

Key concepts

Understanding Acidic Solutions

An acidic solution is one in which the concentration of hydrogen ions $[{\mathrm{H}}^{+}]$ is greater than the concentration of hydroxide ions $[{\mathrm{OH}}^{-}]$.
This means that the solution has a pH less than 7. pH is a measure of how acidic or basic a solution is, with lower values indicating higher acidity.
Acidic solutions can be found in various places, like vinegar, orange juice, and even in our stomachs.

• An excess of $[{\mathrm{H}}^{+}]$ ions in a solution means more acidity.
• The formula for calculating $[{\mathrm{H}}^{+}]$ is helpful to determine acidity: $[{\mathrm{H}}^{+}]=\frac{K_{\text{w}}}{[{\mathrm{OH}}^{-}]}$.
• In calculations, if $[{\mathrm{H}}^{+}]>[{\mathrm{OH}}^{-}]$, the solution is acidic.

Simply put, knowing the balance between $[{\mathrm{H}}^{+}]$ and $[{\mathrm{OH}}^{-}]$ helps identify and understand the nature of acidic solutions.

Exploring Basic Solutions

A basic solution, often referred to as alkaline, has a higher concentration of hydroxide ions $[{\mathrm{OH}}^{-}]$ compared to hydrogen ions $[{\mathrm{H}}^{+}]$.
This results in a pH greater than 7. Such solutions are common in cleaning products like soaps and detergents.
Bases can neutralize acids, hence they're used in various applications to balance pH.

• The formula for $[{\mathrm{H}}^{+}]$ helps in identifying basic solutions: $[{\mathrm{H}}^{+}]=\frac{K_{\text{w}}}{[{\mathrm{OH}}^{-}]}$.
• If $[{\mathrm{H}}^{+}]<[{\mathrm{OH}}^{-}]$, the solution is basic.
• Basic solutions feel slippery and can change red litmus paper blue.

Understanding these properties helps us use basic solutions effectively and safely in our everyday life.

Defining Neutral Solutions

Neutral solutions are characterized by an equal concentration of hydrogen ions $[{\mathrm{H}}^{+}]$ and hydroxide ions $[{\mathrm{OH}}^{-}]$, resulting in a pH of exactly 7.
The most common example of a neutral solution is pure water.
These solutions are neither acidic nor basic, making them perfect benchmarks in scientific studies.

• Using the equation $[{\mathrm{H}}^{+}]=[{\mathrm{OH}}^{-}]$, we identify a solution as neutral.
• This balance is crucial in many natural and industrial processes for maintaining stability.
• Neutral solutions do not alter the color of litmus paper, staying unaltered like water.

The balance in neutral solutions provides a foundation for understanding both acidic and basic solutions.