Problem 56 - General Chemistry: Principles and Modern Applications

Question

Both sodium hydrogen carbonate (sodium bicarbonate) and sodium hydroxide can be used to neutralize acid spills. What is the pH of \(1.00 \mathrm{M} \mathrm{NaHCO}_{3}(\mathrm{aq})\) and of \(1.00 \mathrm{M} \mathrm{NaOH}(\mathrm{aq}) ?\) On a per-liter basis, do these two solutions have an equal capacity to neutralize acids? Explain. On a per-gram basis, do the two solids, \(\mathrm{NaHCO}_{3}(\mathrm{s})\) and \(\mathrm{NaOH}(\mathrm{s}),\) have an equal capacity to neutralize acids? Explain. Why do you suppose that \(\mathrm{NaHCO}_{3}\) is often preferred to \(\mathrm{NaOH}\) in neutralizing acid spills?

Step-by-Step Solution

Answer

The pH of a 1.00 M \(\mathrm{NaHCO}_{3}\) solution is around 8.3 and for a 1.00 M \(\mathrm{NaOH}\) solution is 14. On a per-liter basis, \(\mathrm{NaOH}\) has a greater capacity to neutralize acids than \(\mathrm{NaHCO}_{3}\) because it dissociates completely in the solution. On a per-gram basis, \(\mathrm{NaOH}\) also has a greater capacity to neutralize acids because it has a lower molar mass and thus provides more OH- ions per gram. \(\mathrm{NaHCO}_{3}\) is often preferred as it is safer to handle, less likely to result in injury, and provides an indicator (CO2 gas) when reacting with acids.

Step 1: Calculate pH of Sodium Hydroxide (\(\mathrm{NaOH}\)) solution

Using the formula: pH = -log[H+], and knowing that a 1.00 M \(\mathrm{NaOH}\) solution is a strong base and it will completely dissociate into \(\mathrm{Na}^{+}\) and \(\mathrm{OH}^{-}\) ions resulting in [OH-] = 1.00 M. The relationship between [H+] and [OH-] is represented as Kw=[H+][OH-], where Kw is the ion product of water, equal to \(1 * 10^{-14}\). Solving for [H+], we get [H+] = Kw/[OH-] = \(1 * 10^{-14}/1.00\). Using this value to solve for pH, we get pH = -log[H+] = 14.

Step 2: Calculate pH of Sodium Bicarbonate (\(\mathrm{NaHCO}_{3}\)) solution

Considering \(\mathrm{NaHCO}_{3}\) as a weak base, and knowing that it partially dissociates in water to form bicarbonate ions \(HCO_{3}^{-}\) and hydronium ions \(H_{3}O^{+}\). The reaction can be written as: \(\mathrm{NaHCO}_{3}\) + H2O <-> \(H_{3}O^{+}\) + \(\mathrm{HCO}_{3}^{-}\). Now the equation for the bicarbonate ion acting as an acid can be written as: \(\mathrm{HCO}_{3}^{-}\) <-> \(H_{3}O^{+}\) + \(\mathrm{CO}_{3}^{2-}\). By setting up an equilibrium constant expression for this reaction with the known \(Ka\) and \(Kb\) values for the bicarbonate ion, the [H+] concentration can be solved. Using this \(H^{+}\) concentration, the pH of the solution can be calculated, which results to be approximately 8.3.

Step 3: Neutralizing Capacity on a Per-Litre Basis

To neutralize an acid, a base must provide OH- ions. A 1.00 M solution of NaOH will provide a greater number of OH- ions (and hence a greater acid-neutralizing capacity) than a 1.00 M solution of NaHCO3, because the NaOH dissociates completely while NaHCO3 only partially dissociates to provide OH- ions.

Step 4: Neutralizing Capacity on a Per-gram Basis

To neutralize an acid, a base must provide OH- ions. Comparing the molar masses (NaHCO3: 84 g/mol, NaOH: 40 g/mol), we find that per gram, NaOH provides a greater number of OH- ions (and hence a greater acid-neutralizing capacity) than NaHCO3.

Step 5: Preference of \(\mathrm{NaHCO}_{3}\) over \(\mathrm{NaOH}\) for Acid Spills

\(\mathrm{NaHCO}_{3}\) is often preferred over \(\mathrm{NaOH}\) in neutralizing acid spills because it is a weaker base as compared to \(\mathrm{NaOH}\), so it is inherently safer to handle and less likely to cause injury due to excessive neutralization (over-shooting the pH to highly basic). It also releases carbon dioxide gas when it reacts with acids, providing an indicator of reaction progress.

Key Concepts

Understanding pH Calculation

Calculating the pH of a solution is essential to understanding its acidity or basicity. The pH scale ranges from 0 to 14. A pH less than 7 indicates acidity, while a pH greater than 7 indicates basicity.

For strong bases like sodium hydroxide (NaOH), the pH calculation involves complete dissociation into ions in water. NaOH dissociates into sodium (Na⁺) and hydroxide (OH^-) ions. In a 1.00 M NaOH solution, the concentration of OH^- ions is 1.00 M.

The relationship between the concentrations of hydrogen ions \[ \text{[H⁺]} \] and hydroxide ions \[ \text{[OH^-]} \] is given by the water dissociation constant \[ K_w = 10^{-14} \]. Solving for [H⁺], we use \[ \text{[H⁺]} = \frac{K_w}{\text{[OH^-]}} \].

For NaOH: \[ \text{[H⁺]} = \frac{10^{-14}}{1.00} = 10^{-14} \]. The pH is calculated as \[ pH = -\log(\text{[H⁺]}) = 14 \].

• For weak bases like sodium bicarbonate (NaHCO₃), only partial dissociation occurs.
• This results in a basic but less high pH value, around 8.3 for a 1.00 M solution.

The Role of Sodium Hydroxide

Sodium hydroxide (NaOH) is a powerful, strong base widely used in chemical processes. It fully dissociates in water, releasing hydroxide ions \[ \text{OH^-} \].

It is highly effective in neutralizing acids due to this complete dissociation, making it a go-to choice in many industrial applications. However, handling NaOH requires caution. Its strong basic nature can cause chemical burns and should be managed with appropriate safety measures.

• Effective in neutralizing strong acids.
• Provides a high concentration of hydroxide ions.

Despite its efficiency, it is not always preferred for neutralizing acid spills because it can cause the pH to rise too rapidly, leading to a strongly alkaline, rather than neutral, solution.

Understanding Sodium Bicarbonate

Sodium bicarbonate (NaHCO₃), often known as baking soda, is a versatile, weak base. In water, it partially dissociates to produce bicarbonate \[ \text{HCO^-₃} \] and minimal hydroxide ions.

This mild dissociation results in a moderate pH, making NaHCO₃ suitable for gentle pH adjustments. Its benefits include:

• Being safer to handle than stronger bases.
• Less risk of drastically overshooting the target pH.
• Production of carbon dioxide gas when reacting with acids, providing a visual cue of reaction efficacy.

This makes sodium bicarbonate a safer option for neutralizing acid spills, where a more controlled reaction is desired to avoid creating a highly basic environment.