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Calculate the \(\mathrm{pH}\) of a solution prepared by mixing \(10 \mathrm{~mL}\) of \(1.0 \mathrm{M} \mathrm{NaOH}\) with \(100 \mathrm{~mL}\) of \(0.10 \mathrm{M}\) ammonia.

Short Answer

Expert verified
The pH of the solution is approximately 12.96.

Step by step solution

01

Determine moles of NaOH

Calculate the moles of NaOH using the formula: \( ext{moles} = ext{concentration} \times ext{volume} \). The volume must be in liters, so convert 10 mL to 0.01 L. Then the calculation is \( 1.0 \times 0.01 = 0.01 \) moles of NaOH.
02

Determine moles of NH3

Similar to the NaOH calculation, use the formula \( ext{moles} = ext{concentration} \times ext{volume} \). Convert 100 mL to 0.1 L. Then calculate \( 0.10 \times 0.1 = 0.01 \) moles of NH3.
03

Calculate the reaction

NaOH will react with NH3 according to the equation \( ext{NaOH} + ext{NH}_3 \rightarrow ext{Na}^{+} + ext{NH}_4^+ + ext{OH}^- \). Both NaOH and NH3 have 0.01 moles, so they completely neutralize each other. After the reaction, there will be 0 moles of NaOH and 0.01 moles of NH3 will remain unreacted, converted into NH4+ and OH-.
04

Calculate the concentration of OH鈭 ions

The excess OH鈦 ions result from the dissociation of ammonia. Since there are still 0.01 moles of NH3 that has reacted with NaOH, it forms 0.01 moles of NH4+, thus creating approximately 0.01 moles of OH鈦 ions in the solution. The total volume of the solution is 110 mL or 0.11 L. Therefore, the concentration of OH鈦 is \( \frac{0.01}{0.11} \approx 0.091 \text{ M} \).
05

Calculate pOH of the solution

Use the formula \( ext{pOH} = -\log[ ext{OH}^-] \). Substitute the OH鈦 concentration; thus \( ext{pOH} = -\log(0.091) \approx 1.04 \).
06

Calculate pH from pOH

Use the relationship \( ext{pH} + ext{pOH} = 14 \) to find pH. Subtract the pOH from 14: \( ext{pH} = 14 - 1.04 = 12.96 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Acid-Base Reaction
An acid-base reaction is a chemical process that involves the transfer of protons between an acid and a base. In such reactions, acids donate protons (H+) while bases accept these protons. This is a fundamental concept in chemistry associated with the Bronsted-Lowry acid-base theory. When an acid and a base combine, they often form water and a neutralized product known as a salt. For example, when hydrochloric acid reacts with sodium hydroxide, water and sodium chloride are formed.
In our specific case with NaOH and NH3, the reaction doesn't form a typical salt because NH3 is an amine base and undergoes a slightly different process. NaOH provides OH鈦 ions, which react with NH3, which acts as a base but not in the conventional sense of creating a salt. Understanding the intricacies of how each participant in the reaction behaves is key to predicting the outcome of any acid-base reaction.
NaOH and NH3 Reaction
Sodium hydroxide (NaOH) is a strong base, whereas ammonia (NH3) is a weak base. When they react, it's not as straightforward as mixing a strong acid with a strong base. NaOH disassociates completely in water, releasing Na鈦 and OH鈦 ions. NH3, however, primarily remains as an ammonia molecule in solution but can react with OH鈦 to form NH4鈦 and more OH鈦.
In this reaction, NaOH provides the OH鈦 ions that convert ammonia into ammonium ions (NH4鈦). The reaction equation for this process is: \[\text{NaOH} + \text{NH}_3 \rightarrow \text{Na}^+ + \text{NH}_4^+ + \text{OH}^- \].
Since both reactants were in equal molar amounts, they fully react with each other, generating a solution that is rich in OH鈦. Hence, the primary outcome of the interaction is to convert a weak base (ammonia) to a stronger state with prevailing OH鈦 ions.
Solution Concentration
Solution concentration is a measure of how much solute is present in a given volume of solution. It's typically expressed in molarity (M), which is moles of solute per liter of solution. Understanding concentration is crucial, as it affects the properties and reactions of the solution.
In the exercise discussed, both NaOH and NH3 solutions were mixed, changing the overall concentration. Concentration for both solutions is calculated using the formula: \[\text{moles} = \text{concentration} \times \text{volume} \].
The concentrations were initially 1.0 M for NaOH and 0.10 M for NH3. However, after mixing, the new concentrations must consider the combined volume, which in this case is 0.11 L. Thus, even the slightest change in volume can significantly alter the concentration, as seen from the emergence of the OH鈦 concentration post-reaction.
pH and pOH Relationship
The pH and pOH are measures of acidity and basicity of a solution, respectively. They are interconnected by the simple relationship: \[\text{pH} + \text{pOH} = 14 \].
This equation holds at 25掳C, the typical laboratory room temperature, and derives from the ion-product constant of water, \[\text{Kw} = [\text{H}^+] \times [\text{OH}^-] = 1.0 \times 10^{-14} \].
A solution with more OH鈦 ions is basic and thus it has a lower pOH and a higher pH.
In the given solution, the excess concentration of OH鈦 ions led to a relatively low pOH value of 1.04, meaning it is quite basic. The calculation further leads us to a pH of 12.96, which confirms its basic nature. Understanding the intricate relationship between pH and pOH allows chemists to predict how acidic or basic a solution is just by determining one of these values.

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