Question

A bottle contains 3 liters of a chemical solution with a pH of 8 . (a) Does the bottle contain an acid or a base? (b) Approximately how many ${\mathrm{H}}^{+}$ ions are in the bottle? (c) Would a 3 liter bottle with a pH of 9 contain more or less ions of ${\mathrm{H}}^{+}$ than the bottle with a $\mathrm{pH}$ of 8 ? (d) How many times as many/few ${\mathrm{H}}^{+}$ ions are in the bottle with solution of $\mathrm{pH}8$ than in the bottle with solution of $\mathrm{pH}9$ ?

Short answer

(a) Base, (b) $1.81\times {10}^{16}$ ions, (c) Less, (d) 10 times more.

Step-by-step solution

Determine if it's an Acid or Base

A pH value measures the acidity or basicity of a solution. A pH less than 7 indicates an acid, while a pH greater than 7 indicates a base. The solution, with a pH of 8, is a base because it is greater than 7.

Calculate [H^+] Ion Concentration for pH 8

The pH of a solution is related to the hydrogen ion concentration by the formula: $$\text{pH}=-{\log }_{10}[{\text{H}}^{+}]$$. Given $\text{pH}=8$, rearrange the formula to find: $$[{\text{H}}^{+}]={10}^{-8}\text{ moles per liter}$$.

Calculate Total [H^+] Ions for 3 Liters at pH 8

The total number of ${\text{H}}^{+}$ ions is found by multiplying the hydrogen ion concentration per liter by the volume of the solution. $$\text{Total }[{\text{H}}^{+}]=3\text{liters}\times {10}^{-8}\text{mol/L}=3\times {10}^{-8}\text{mol}$$. To convert this to ions, use Avogadro's number $6.022\times {10}^{23}\text{ ions/mol}$: $$3\times {10}^{-8}\text{ mol}\times 6.022\times {10}^{23}\text{ ions/mol}\approx 1.81\times {10}^{16}\text{ ions}$$.

Calculate [H^+] Ion Concentration for pH 9

Similarly, for a pH of 9, the concentration is: $$[{\text{H}}^{+}]={10}^{-9}\text{ moles per liter}$$.

Calculate Total [H^+] Ions for 3 Liters at pH 9

Using the same method as in Step 3, calculate the total number of ${\text{H}}^{+}$ ions for a pH of 9: $$3\text{liters}\times {10}^{-9}\text{mol/L}=3\times {10}^{-9}\text{mol}$$ Converting to ions gives: $$3\times {10}^{-9}\text{ mol}\times 6.022\times {10}^{23}\text{ ions/mol}\approx 1.81\times {10}^{15}\text{ ions}$$.

Compare Ion Totals

The solution with a pH of 8 contains $1.81\times {10}^{16}$ ions, while the solution with a pH of 9 contains $1.81\times {10}^{15}$ ions. A pH of 8 corresponds to more ${\text{H}}^{+}$ ions than a pH of 9.

Determine the Ion Ratio

To find how many times more ${\text{H}}^{+}$ ions are in the pH 8 solution compared to the pH 9 solution, divide the number of ions at pH 8 by the number at pH 9: $$\frac{1.81\times {10}^{16}}{1.81\times {10}^{15}}=10$$. This means the pH 8 solution has 10 times as many hydrogen ions.

Key concepts

Hydrogen Ion Concentration

The concentration of hydrogen ions ([H^+]) is a key component in determining the pH of a solution. The pH scale is logarithmic, meaning each whole number step represents a tenfold change in [H^+] concentration. The formula connecting pH and hydrogen ion concentration is $$\text{pH}=-{\log }_{10}[{\text{H}}^{+}]$$. If the pH is known, the concentration of hydrogen ions can be found by rearranging this formula to $$[{\text{H}}^{+}]={10}^{-\text{pH}}$$. For example, a solution with a pH of 8 has a hydrogen ion concentration of $${10}^{-8}\text{ moles per liter}$$.This is important because the number of [H^+] ions in a solution directly influences its acidity or basicity. A higher [H^+] indicates a more acidic solution, while a lower [H^+] signifies a more basic one. Understanding [H^+] is crucial in chemistry as it affects reactions, solubility, and biological processes.

Acid-Base Chemistry

Acid-base chemistry is centered on the behavior of protons (H+ ions) in solution. A pH less than 7 indicates an acidic solution, where there is a high concentration of hydrogen ions. Conversely, a pH greater than 7 indicates a basic or alkaline solution, with a lower concentration of hydrogen ions. This classification is vital in understanding chemical reactions and environmental processes. - **Properties of Acids**: Generally taste sour, can conduct electricity, and react with metals to produce hydrogen gas. - **Properties of Bases**: Feel slippery, taste bitter, and can also conduct electricity. Acids and bases interact through neutralization reactions, producing water and a salt. These reactions are important in many biological and industrial processes. pH is an essential measure in acid-base chemistry, providing insights into the strength and concentration of acidic or basic solutions. In daily life, the concept applies to everything from food flavor to the effectiveness of cleaning agents.

Avogadro's Number

Avogadro's number, approximately $6.022\times {10}^{23}$is a fundamental constant that describes the number of particles in a mole. It provides a bridge between the molecular scale and the mass of substances we can measure. Whether you are counting atoms, ions, or molecules, Avogadro's number allows chemists to count out large quantities efficiently.Using Avogadro's number, we can convert moles of a substance into individual particles or vice versa. For instance, if you have $3\times {10}^{-8}\text{ mol}$of hydrogen ions in a solution, multiplying by Avogadro's number gives us the total number of ions: $3\times {10}^{-8}\text{ mol}\times 6.022\times {10}^{23}\text{ ions/mol}\approx 1.81\times {10}^{16}\text{ ions}$.Understanding Avogadro's number is crucial in stoichiometry calculations, chemical formula interpretations, and understanding the scale of chemical reactions in both laboratory and industrial settings.