Question

To which of the following would the addition of an equal volume of \(0.60 \mathrm{M} \mathrm{NaOH}\) lead to a solution having (b) \(0.30 \mathrm{M} \mathrm{HCl}\) (c) \(0.70 \mathrm{M} \mathrm{KOH}\) a lower \(\mathrm{pH}\) : (a) water, (d) \(0.40 \mathrm{M} \mathrm{NaNO}_{3}\) ?

Short answer

Adding NaOH to HCl results in the lowest pH, around neutral.

Step-by-step solution

Analyze the Effect of Adding NaOH to Water

When you add an equal volume of \(0.60 \mathrm{M} \mathrm{NaOH}\) to water, the resulting solution's molarity for NaOH becomes half, which means it will be \(0.30 \mathrm{M} \mathrm{NaOH}\). This is a basic solution, and it increases the pH past 7.

Analyze the Effect of Adding NaOH to HCl

Adding \(0.60 \mathrm{M} \mathrm{NaOH}\) to an equal volume of \(0.30 \mathrm{M} \mathrm{HCl}\) results in a solution where the NaOH fully neutralizes the HCl (since there are equal numbers of moles). The resulting solution is neutral, so the pH increases from acidic to around 7.

Analyze the Effect of Adding NaOH to KOH

When \(0.60 \mathrm{M} \mathrm{NaOH}\) is added to \(0.70 \mathrm{M} \mathrm{KOH}\) with equal volumes, the resulting solution's molarity will be the averaged value: \(0.35 \mathrm{M} \mathrm{NaOH} + 0.35 \mathrm{M} \mathrm{KOH} = 0.70 \mathrm{M} \text{ base}\). The resultant pH remains high, and the solution stays basic.

Analyze the Effect of Adding NaOH to NaNO3

Adding \(0.60 \mathrm{M} \mathrm{NaOH}\) to \(0.40 \mathrm{M} \mathrm{NaNO}_{3}\) results in a mixture that stays predominantly basic since NaNO3 doesn't contribute to the pH, given that it forms a neutral salt. The pH thus increases, categorizing the solution as basic.

Determine Which Contains the Solution with the Lower pH

Comparing the scenarios, adding NaOH to water creates a basic solution, which is a higher pH than 7. Neutralizing HCl with NaOH results in a pH close to 7, the potential lowest given the conditions since it starts as acidic and moves towards neutral. The other solutions end up being more basic.

Key concepts

pH Calculation

Understanding pH is crucial in chemistry, especially when dealing with solutions' acidity or basicity. The pH scale ranges from 0 to 14, where a pH of 7 indicates a neutral solution. Values below 7 denote acidic solutions, while values above 7 indicate basic solutions.
To calculate pH for strong acids and bases, we rely on the formula:
\[ pH = -\log [H^+] \]
For bases, we calculate pOH and then use the relationship:
\[ pH + pOH = 14 \]

• Adding a strong acid like HCl to water decreases the pH, making the solution acidic.
• Conversely, adding a strong base like NaOH increases the pH, creating a basic solution.

Knowing how to calculate and interpret pH is essential for predicting changes when substances are mixed.

Neutralization Reaction

Neutralization reactions occur when an acid and a base combine to form water and a salt. These reactions are pivotal for maintaining balance in chemical solutions. The general formula for such a reaction is:
\[ ext{Acid} + ext{Base} \rightarrow ext{Salt} + ext{Water} \]
For instance, when NaOH is added to HCl, the strong base neutralizes the strong acid, resulting in water and sodium chloride (NaCl).

• This process is exothermic, releasing heat.
• The resulting solution is usually neutral, with pH approximately equating to 7.

When mixing equal molar concentrations of an acid and a base, the solution's pH will trend towards neutral, which is vital for reactions like titrations.

Solution Molarity

Molarity helps us understand the concentration of a solute within a solution. It is expressed as moles of solute per liter of solution, given as M (mol/L). Calculating molarity is crucial for predicting how the mixture of solutions affects pH.
To determine a solution's molarity after mixing different solutions, we often take an average or sum based on their respective concentrations. For example, mixing equal volumes of equal molar NaOH and KOH results in a solution of higher molarity:
\[ ext{Combined molarity} = rac{ ext{Molarity of NaOH} + ext{Molarity of KOH}}{2} \]
Understanding molarity helps us predict which of the resultant solutions will have higher or lower pH post mixing.

Basic Solutions

Basic solutions are characterized by having a pH greater than 7. They are formed when bases are dissolved in water, releasing hydroxide ions \( (OH^-) \). A common strong base is sodium hydroxide (NaOH), which increases the solution's pH significantly when added.

• Basic solutions turn red litmus paper blue.
• They often feel slippery to the touch due to the saponification reaction.
• They can neutralize acids to form water and salts, resulting in neutral or higher pH solutions.

Adding NaOH to a neutral salt solution, like NaNO3, results in the mixture remaining basic because the salt doesn't contribute to pH changes. Basic solutions are essential in cleaning supplies, various chemical reactions, and industrial processes.