A 0.164-g sample of phosphorous acid, \(\mathrm{H}_{3} \mathrm{PO}_{3}\), is dissolved in water so that the total volume of the solution is \(50.0 \mathrm{~mL}\). (a) Estimate the \(\mathrm{pH}\) of this solution. (b) Fstimate the \(\mathrm{pH}\) of the solution that results when \(6.50 \mathrm{~mL}\) of \(0.175 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\) is added to the phosphorous acid solution. (c) Fstimate the \(\mathrm{pH}\) of the solution if an additional \(4.93 \mathrm{~mL}\) of \(0.175 \mathrm{M}\) \(\mathrm{NaOH}(\mathrm{aq})\) is added to the solution in part (b).

Molar concentration, also known as molarity, is a measure of the concentration of a solute in a solution. To calculate molar concentration, you first need to know the number of moles of solute in the solution. A mole is a unit that measures the amount of a substance based on the number of particles, similar to how a dozen measures twelve items. The molecular weight of a substance, expressed in grams per mole, is the mass of one mole of that substance.

For example, in our exercise, we determine the molar mass of phosphorous acid by adding the atomic masses of hydrogen, phosphorus, and oxygen. Converting the mass of phosphorous acid to moles and dividing by the total volume of the solution in liters gives us the molarity. This value is crucial for understanding solutions' behavior in chemical reactions, such as acid-base interactions.

Weak acids only partially dissociate in water, creating an equilibrium between the undissociated acid and its ions. Phosphorous acid, H3PO3, is a weak, diprotic acid, meaning it can donate two protons (H+ ions) when it dissociates. We describe this process with an equilibrium constant, known as the acid dissociation constant (Ka).

The dissociation of a weak acid like H3PO3 is given as: H3PO3 ⇌ H+ + H2PO3-. The calculation of pH from the dissociation involves an equilibrium expression that includes the Ka value. By assuming that the concentration of H+ ions produced is small, we simplify the calculations. But it's essential to note that this assumption might not apply when the acid is very dilute or the Ka value is relatively high.

A neutralization reaction is an acid-base reaction where an acid reacts with a base to produce water and a salt. For instance, when sodium hydroxide (NaOH), a strong base, is added to phosphorous acid (H3PO3), they react to neutralize each other, creating water and sodium phosphate.

The balanced equation for this reaction when NaOH is added to H3PO3 is: H3PO3 + NaOH → NaH2PO3 + H2O. During neutralization, H+ ions from the acid and OH- ions from the base combine to form water, typically resulting in pH changes. In a complex solution such as the one in our example, it's imperative to consider how much acid and base are present to calculate the resulting pH accurately.

The relationship between pH and pOH is an essential concept in acid-base chemistry. While pH measures the concentration of hydrogen ions (H+) in a solution, pOH measures the concentration of hydroxide ions (OH–). They are related by the equation: pH + pOH = 14, at 25°C, which allows us to convert between the two scales for any aqueous solution.

To convert pOH to pH, we subtract the pOH from 14. For example, if a reaction results in excess hydroxide ions, we first calculate the pOH by taking the negative logarithm (base 10) of the OH– concentration. Then we use the equation to find the pH value. This conversion plays a critical role in understanding the acidity or basicity of the resulting solution after a neutralization reaction, as illustrated in our exercise with the addition of NaOH to phosphorous acid.