Question

The concentration of concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is about \(18 \mathrm{M}\). Assuming only one \(\mathrm{H}^{+}\) comes off the \(\mathrm{H}_{2} \mathrm{SO}_{4}\) molecule, what is its \(\mathrm{pH}\) and \(\mathrm{pOH}\) ? What would the \(\mathrm{pH}\) and \(\mathrm{pOH}\) be if the second \(\mathrm{H}^{+}\) were also ionized?

Short answer

Assuming one ionization, pH = -1.26, pOH = 15.26. With both ionizations, pH = -1.56, pOH = 15.56.

Step-by-step solution

Understanding the Ionization

The chemical formula for sulfuric acid is \( \mathrm{H}_{2} \mathrm{SO}_{4} \). It indicates that each molecule of sulfuric acid can potentially release two hydrogen ions (\( \mathrm{H}^{+} \)). In this problem, we start by assuming only one \( \mathrm{H}^{+} \) ionizes.

Calculating pH with One Ionization

Assuming only one \( \mathrm{H}^+ \) ion is released, the concentration of \( \mathrm{H}^+ \) ions is equal to the concentration of the sulfuric acid, which is \( 18 \mathrm{M} \). The pH value is calculated using the formula \( \mathrm{pH} = -\log[\mathrm{H}^+] \). Plugging in the concentration:\[ \mathrm{pH} = -\log(18) \approx -1.26 \]

Calculating pOH with One Ionization

The relationship between pH and pOH is given by the equation \( \mathrm{pH} + \mathrm{pOH} = 14 \). With \( \mathrm{pH} \approx -1.26 \):\[ \mathrm{pOH} = 14 - (-1.26) = 15.26 \]

Ionization of Second Hydrogen Ion

If the second \( \mathrm{H}^+ \) ion is also released, the total concentration of \( \mathrm{H}^+ \) ions would be doubled, assuming complete ionization. Thus, the concentration becomes \( 36 \mathrm{M} \).

Calculating pH with Both Ionizations

Using the increased \( \mathrm{H}^+ \) concentration of \( 36 \mathrm{M} \), recalculate the pH:\[ \mathrm{pH} = -\log(36) \approx -1.56 \]

Calculating pOH with Both Ionizations

Again, use the relationship \( \mathrm{pH} + \mathrm{pOH} = 14 \). With \( \mathrm{pH} \approx -1.56 \):\[ \mathrm{pOH} = 14 - (-1.56) = 15.56 \]

Key concepts

Ionization of Sulfuric Acid

Sulfuric acid (\( \mathrm{H}_{2} \mathrm{SO}_{4} \)) is a strong acid that can release two hydrogen ions (\( \mathrm{H}^+ \)) when dissolved in water. This process is called ionization. The first ionization, where only one \( \mathrm{H}^+ \) is released, is complete and very strong. This means it happens almost entirely, making sulfuric acid an excellent source of protons.

When we talk about the ionization of strong acids like sulfuric acid, the first hydrogen ion is fully ionized, contributing significantly to the acidity of the solution. However, the second \( \mathrm{H}^+ \) does not ionize as completely as the first. For practical calculations, assuming full ionization means the concentration of \( \mathrm{H}^+ \) ions doubles if both hydrogen ions are considered ionized, significantly affecting the pH of the solution.

By understanding this dual release of \( \mathrm{H}^+ \) ions, we better understand how strong sulfuric acid is and why it's so effective in acid-base reactions.

pOH Calculation

The calculation of pOH is closely linked to the understanding of pH. Since \( \mathrm{pH} + \mathrm{pOH} = 14 \), knowing the pH allows you to easily find the pOH. For sulfuric acid, if you start by ionizing one \( \mathrm{H}^+ \), you calculate the pH first, and then use that to find the pOH using the simple subtraction formula.

Let's consider why the calculation of pOH is important.

• The pOH helps gauge the basic nature of the solution, even when the focus is initially on acidity.
• It is particularly useful in cases where the relation between hydroxide ions (\( \mathrm{OH}^- \)) and hydrogen ions needs to be compared.

In the example scenario, with the pH calculated for one ionization at \( \approx -1.26 \), the pOH would be \( 15.26 \). If both \( \mathrm{H}^+ \) ions are ionized, the resulting stronger pH of \( \approx -1.56 \) raises the pOH to \( 15.56 \), indicating a very acidic solution.

Strong Acids

Strong acids are substances that completely dissociate in water. Typically, these acids release \( \mathrm{H}^+ \) ions readily, making them entirely ionized in their solution. Sulfuric acid is known as one of the strong acids primarily for its ability to lose not one, but potentially two hydrogen ions.

One feature of strong acids is that they result in very low pH values because they significantly increase the concentration of hydrogen ions in the solution.

• These low pH values (< 0 in concentrated forms) show the strong and complete ionization of the acid.
• Such acids lead to solutions that are highly reactive and capable of conducting electricity well.

By knowing these characteristics, you will notice how strong acids significantly alter the chemical behavior of solutions. This understanding helps in predicting reactions, particularly in neutralization processes where strong acids interact with bases.