Problem 57 - General Chemistry: Principles and Modern Applications

Question

A \(25.00 \mathrm{mL}\) sample of \(0.132 \mathrm{M}\) \(\mathrm{HNO}_{3}\) is mixed with \(10.00 \mathrm{mL}\) of \(0.318 \mathrm{M} \mathrm{KOH} .\) Is the resulting solution acidic, basic, or exactly neutralized?

Step-by-Step Solution

Answer

The resulting solution is acidic.

Step 1: Calculate the moles of acid and base

The moles of HNO3 and KOH can be calculated using the given volume and molarity. The formula used for this is: Molarity = Moles/Volume. Rearranging for Moles gives: Moles = Molarity * Volume (note that the volume must be converted to liters). Hence, the moles of HNO3 and KOH are: Moles(HNO3) = 0.132 M * 0.02500 L = 0.0033 moles Moles(KOH) = 0.318 M * 0.01000 L = 0.00318 moles

Step 2: Determine the limiting reactant

In the reaction of HNO3 with KOH, the acid and the base react in a 1:1 ratio to produce water and a salt (in this case KNO3). Therefore, we compare the number of moles of each reactant to see which one is completely consumed (the limiting reactant). From our calculations in Step 1, we know that there are more moles of HNO3 (0.0033 moles) than there are of KOH (0.00318 moles), so KOH is the limiting reactant.

Step 3: Determine the nature of the solution

Since the KOH, which is a base, is used up completely, there will be a surplus of HNO3 in the solution. Hence, the nature of the resulting solution will be acidic as it contains excess HNO3.

Key Concepts

Understanding Molarity

In chemistry, molarity is a way to express the concentration of a solution. It tells us how many moles of a substance, such as an acid or base, are present in one liter of solution. Built from moles and volume, molarity is quite simple yet powerful.
The formula to calculate molarity is given by:
\[ \text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]- **Moles** of a substance are a measure of quantity, much like a dozen eggs.- **Volume** must be in liters for the formula to work correctly.For instance, in this exercise, calculating the moles of an acid like nitric acid (\(HNO_3\)) and a base such as potassium hydroxide (\(KOH\)) helps us determine their presence in a solution. By multiplying the molarity by the volume (converted to liters), we can find the exact moles of each substance in the solution. This is a crucial step in understanding how they will react with each other.

Finding the Limiting Reactant

The concept of a limiting reactant is crucial in any chemical reaction because it determines which reactant will be completely used up first, thus stopping the reaction. In a perfect chemical world, all reactants are used up at the same time but this is rarely the case.
When we mix an acid with a base, they typically react in a 1:1 ratio to form water and a salt. However, if one of them is present in smaller quantity, it will limit the amount of product formed. This reactant, therefore, is labeled the **limiting reactant**.In our exercise:

• We calculate the moles of each reactant (0.0033 moles of \(HNO_3\) and 0.00318 moles of \(KOH\)).
• The reactant with fewer moles is \(KOH\), making it the limiting reactant.
• As a result, \(KOH\) will be completely consumed first, leaving excess \(HNO_3\).

This concept is critical because it helps predict the amounts of products formed and the type of solution obtained after the reaction.

Determining Solution Acidity

When an acid reacts with a base, they can neutralize each other to form water and a salt, ideally leading to a neutral solution. However, the reality rests on the amounts reacting.
After identifying the limiting reactant, we can easily tell whether the solution will be acidic, basic, or neutral by considering any excess reactants left over.In this scenario:

• Due to the presence of more \(HNO_3\) moles than \(KOH\) moles, not all \(HNO_3\) is used.
• The leftover \(HNO_3\) makes the solution acidic because there's more acid than needed to completely react with the base.

Remember, the final acidity of a solution is driven by the excess reactant left after a neutralization reaction, which in this problem, is \(HNO_3\), an acid.