Question

Which of these has the lowest concentration of hydrogen ions: \(0.1 \mathrm{M} \mathrm{HCl}, 0.1 \mathrm{M} \mathrm{NaOH}, 0.1 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\), or pure water? Explain your answer.

Short answer

0.1 M NaOH has the lowest hydrogen ion concentration.

Step-by-step solution

Define Hydrogen Ion Concentration

The concentration of hydrogen ions ({H^{+}}) in a solution indicates its acidity. Strong acids completely dissociate in water, producing {H^{+}} ions, while strong bases provide {OH^{-}} ions which decrease the concentration of {H^{+}} through neutralization.

Calculate {H^{+}} Concentration for Each Solution

- For {0.1 {M} {HCl}}: This strong acid dissociates fully, resulting in a {[H^{+}] = 0.1 {M}}. - {0.1 {M} {H_{2}SO_{4}}: As a diprotic acid, it provides twice the amount of {H^{+}}, {[H^{+}] = 0.2 {M}} after full dissociation. - {0.1 {M} {NaOH}}: This strong base dissociates completely to produce {OH^{-}} ions. The {[H^{+}]} can be found using the ion-product constant for water ({K_{w} = 1 imes 10^{-14}}), yielding {[H^{+}] = 1 imes 10^{-13} {M}}. - Pure Water has a neutral concentration, thus {[H^{+}] = 1 imes 10^{-7} {M}}.

Compare the Concentrations

The lowest hydrogen ion concentration is found in the solution of {0.1 {M} {NaOH}}, which has a {[H^{+}] = 1 imes 10^{-13} {M}}, significantly lower than the other solutions.

Key concepts

Strong Acids and Bases

Strong acids and bases are critical concepts in chemistry, especially when understanding chemical reactions in solutions.

• Strong Acids: Acids like Hydrochloric acid (HCl) and Sulfuric acid (H₂SO₄) are termed "strong" because they completely dissociate into their ions when dissolved in water. This means that all of the acid's molecules break apart to release hydrogen ions (\(H^{+}\)). For example, HCl breaks down in water to give hydrogen ions and chloride ions (\(Cl^{-}\)). In the case of sulfuric acid being a diprotic acid, it can donate two hydrogen ions per molecule, making it even more potent in releasing \(H^{+}\) ions.
• Strong Bases: In contrast, strong bases like Sodium Hydroxide (NaOH) dissociate completely in water to produce hydroxide ions (\(OH^{-}\)). These hydroxide ions act to neutralize \(H^{+}\) ions from acids, effectively reducing the solution's hydrogen ion concentration.

Understanding how strong acids and bases work helps us predict how they will behave in solutions, and estimate their ion concentrations.

pH and Acidity

The concept of pH is a simple yet powerful tool in chemistry that describes the acidity or basicity of a solution.

The pH scale ranges from 0 to 14. A pH less than 7 suggests an acidic solution, a pH of 7 indicates a neutral solution, and a pH greater than 7 indicates a basic solution.

• Acidity: Determined by the concentration of hydrogen ions (\(H^{+}\)) in a solution. More hydrogen ions mean a lower pH and higher acidity. For example, 0.1 M HCl shows a pH value close to 1, revealing strong acidity due to complete dissociation.
• Basicity: In contrast, solutions with higher hydroxide ions (\(OH^{-}\)) show higher pH values. A 0.1 M NaOH solution will have a very high pH, indicating strong basicity since hydroxide ions neutralize hydrogen ions.

The interplay of hydrogen and hydroxide ions determines pH value, guiding us to understand the solution's nature.

Ion-Product Constant for Water

The ion-product constant for water (\(K_{w}\)) is a fundamental concept in understanding the balance of hydrogen and hydroxide ions in water.

This constant is an equilibrium constant for the self-ionization of water, where two water molecules produce a hydrogen ion and a hydroxide ion:

\[ H_2O + H_2O \rightleftharpoons H_3O^+ + OH^-\]

At 25°C, \(K_{w}\ = 1 \times 10^{-14}\). This means in pure water, the concentration of \(H^{+}\) ions is equal to \(OH^{-}\) ions, both being \(1 \times 10^{-7} \, ext{M}\). In solutions, understanding \(K_{w}\) helps to calculate the concentration of \(H^{+}\) if \(OH^{-}\) is known, and vice versa, maintaining a balance crucial for accurately determining acidity or basicity.

This constant becomes specifically useful when dealing with strong acids and bases as it helps in calculating residual ion concentrations after complete dissociation, such as with NaOH where the remaining \(H^{+}\) is remarkably smaller than in acids.