Question

Calculate the hydrogen ion concentration, in moles per liter, for solutions with each of the following pOH values. a. $\mathrm{pOH}=4.95$ b. $\mathrm{pOH}=7.00$ c. $\mathrm{pOH}=12.94$ d. $\mathrm{pOH}=1.02$

Short answer

a. For pOH = 4.95, the hydrogen ion concentration is $8.91\times {10}^{-10}$ moles/liter. b. For pOH = 7.00, the hydrogen ion concentration is $1.0\times {10}^{-7}$ moles/liter. c. For pOH = 12.94, the hydrogen ion concentration is $8.63\times {10}^{-2}$ moles/liter. d. For pOH = 1.02, the hydrogen ion concentration is $1.05\times {10}^{-13}$ moles/liter.

Step-by-step solution

a. Calculate pH for pOH = 4.95

To calculate the pH for a pOH of 4.95, use the formula $\mathrm{pH}+\mathrm{pOH}=14$: $$\mathrm{pH}=14-\mathrm{pOH}$$ $$\mathrm{pH}=14-4.95=9.05$$

a. Calculate hydrogen ion concentration for pH = 9.05

Now, use the formula $\mathrm{pH}=-\log ({\text{H}}^{+})$ to find the hydrogen ion concentration: $${\text{H}}^{+}={10}^{-\mathrm{pH}}$$ $${\text{H}}^{+}={10}^{-9.05}=8.91\times {10}^{-10}\text{moles/liter}$$

b. Calculate pH for pOH = 7.00

To calculate the pH for a pOH of 7.00, use the formula $\mathrm{pH}+\mathrm{pOH}=14$: $$\mathrm{pH}=14-\mathrm{pOH}$$ $$\mathrm{pH}=14-7.00=7.00$$

b. Calculate hydrogen ion concentration for pH = 7.00

Now, use the formula $\mathrm{pH}=-\log ({\text{H}}^{+})$ to find the hydrogen ion concentration: $${\text{H}}^{+}={10}^{-\mathrm{pH}}$$ $${\text{H}}^{+}={10}^{-7.00}=1.0\times {10}^{-7}\text{moles/liter}$$

c. Calculate pH for pOH = 12.94

To calculate the pH for a pOH of 12.94, use the formula $\mathrm{pH}+\mathrm{pOH}=14$: $$\mathrm{pH}=14-\mathrm{pOH}$$ $$\mathrm{pH}=14-12.94=1.06$$

c. Calculate hydrogen ion concentration for pH = 1.06

Now, use the formula $\mathrm{pH}=-\log ({\text{H}}^{+})$ to find the hydrogen ion concentration: $${\text{H}}^{+}={10}^{-\mathrm{pH}}$$ $${\text{H}}^{+}={10}^{-1.06}=8.63\times {10}^{-2}\text{moles/liter}$$

d. Calculate pH for pOH = 1.02

To calculate the pH for a pOH of 1.02, use the formula $\mathrm{pH}+\mathrm{pOH}=14$: $$\mathrm{pH}=14-\mathrm{pOH}$$ $$\mathrm{pH}=14-1.02=12.98$$

d. Calculate hydrogen ion concentration for pH = 12.98

Now, use the formula $\mathrm{pH}=-\log ({\text{H}}^{+})$ to find the hydrogen ion concentration: $${\text{H}}^{+}={10}^{-\mathrm{pH}}$$ $${\text{H}}^{+}={10}^{-12.98}=1.05\times {10}^{-13}\text{moles/liter}$$ In summary: a. For pOH = 4.95, the hydrogen ion concentration is $8.91\times {10}^{-10}$ moles/liter. b. For pOH = 7.00, the hydrogen ion concentration is $1.0\times {10}^{-7}$ moles/liter. c. For pOH = 12.94, the hydrogen ion concentration is $8.63\times {10}^{-2}$ moles/liter. d. For pOH = 1.02, the hydrogen ion concentration is $1.05\times {10}^{-13}$ moles/liter.

Key concepts

Understanding Hydrogen Ion Concentration

The concentration of hydrogen ions in a solution is crucial in determining the solution's acidity. This is measured in moles per liter. When you hear about the hydrogen ion concentration, it's about counting how many hydrogen ions are present in a unit volume of the solution.
In chemistry, especially in acid-base chemistry, determining the concentration of hydrogen ions helps us understand how acidic or basic a solution is.
The hydrogen ion concentration is directly related to the pH value. The formula used to calculate the hydrogen ion concentration is: - $${\text{H}}^{+}={10}^{-\text{pH}}$$ Here, ${\text{H}}^{+}$ stands for the concentration of hydrogen ions. By using this formula, you can determine how many hydrogen ions are in the solution, hence understanding its properties better.
If you know your pH, you can easily find your hydrogen ion concentration, which paints a clearer picture of the solution's acidity level.

The Basics of Acid-Base Chemistry

Acid-base chemistry is a branch of science that explores the characteristics and behaviors of acids and bases. An acid is usually a substance that can donate a hydrogen ion (${\text{H}}^{+}$), while a base is something that can accept a hydrogen ion.
A solution's pH determines its acidic or basic nature. Low pH values mean more acidic, and high pH values mean more basic. The boundary between acidic and basic is at pH 7, considered neutral, like pure water.
Here’s what happens in acid-base reactions: - Acids release hydrogen ions into the solution, lowering the pH. - Bases absorb hydrogen ions, raising the pH. Understanding these interactions is essential in fields from biology to engineering, because the acidity or basicity of a solution can significantly influence its behavior and reactions.

Mastering Logarithmic Calculations

Logarithmic calculations might seem intimidating, but they are quite fundamental, especially in chemistry. When you calculate the pH or pOH of a solution, you often use logarithmic functions. - The pH is calculated as follows: $$\text{pH}=-\log ({\text{H}}^{+})$$ This formula means you take the negative logarithm of the hydrogen ion concentration. Logarithms help compress the large range of hydrogen ion concentrations into manageable pH values.
Exponential and logarithmic functions are reciprocals. So, knowing one can help you find the other. For example, if you know the pH, you can easily find the hydrogen ion concentration by reversing the log function: - $${\text{H}}^{+}={10}^{-\text{pH}}$$ Remembering these basic logarithm principles can help you solve a variety of problems in science and mathematics. Breaking down complex problems into simple logarithmic calculations makes them much easier to handle.