Problem 78 - Chemistry An Atoms First Approach

Question

A 30.0 -mL. sample of an unknown strong base is neutralized after the addition of \(12.0 \mathrm{mL}\) of a \(0.150 \mathrm{M} \mathrm{HNO}_{3}\) solution. If the unknown base concentration is 0.0300 \(M,\) give some possible identities for the unknown base.

Step-by-Step Solution

Answer

Possible identities of the unknown base with a concentration of 0.0300 M are Calcium hydroxide (Ca(OH)2), Barium hydroxide (Ba(OH)2), and Strontium hydroxide (Sr(OH)2), as two moles of these bases are needed to neutralize one mole of HNO3 due to their two reactive hydroxide ions (OH-).

Step 1: Calculate the moles of HNO3 used in the reaction

First, we need to find the number of moles of the strong acid (HNO3) used to neutralize the unknown base. The concentration (M) is given, as well as the volume of the HNO3 solution. Using the formula moles = Molarity × Volume (in Liters), we can find the moles of HNO3: moles of HNO3 = (0.150 M) × (12.0 mL × 0.001 L/mL) = 0.00180 moles

Step 2: Calculate the moles of the unknown base

Next, we need to find the number of moles of the unknown strong base, knowing its concentration and volume. We use the same formula as in Step 1: moles of the base = (0.0300 M) × (30.0 mL × 0.001 L/mL) = 0.000900 moles

Step 3: Determine the mole ratio between HNO3 and the unknown base

Now, we can find the mole ratio between the strong acid and the base by dividing the moles of the base by the moles of HNO3: mole ratio = (moles of the base) / (moles of HNO3) mole ratio = 0.000900 / 0.00180 = 0.500 The mole ratio tells us how many moles of the base required to neutralize one mole of HNO3.

Step 4: Determine possible identities of the unknown base

Since the mole ratio between the acid and base is 0.500, this means that two moles of the base are needed to neutralize one mole of HNO3, and as a result, the unknown base has two reactive hydroxide ions (OH-) in its formula. Some examples of strong bases with this property are: 1. Calcium hydroxide (Ca(OH)2) 2. Barium hydroxide (Ba(OH)2) 3. Strontium hydroxide (Sr(OH)2) These are the possible identities of the unknown strong base since they all have two hydroxide ions that would neutralize one mole of the HNO3.

Key Concepts

Neutralization Reactions

Neutralization reactions are fundamental concepts in chemistry, where an acid and base react to form water and a salt. These reactions are pivotal in understanding stoichiometry, as they rely on the 1:1 ratio of reaction between hydrogen ions \( (H^+) \) from the acid and hydroxide ions \( (OH^-) \) from the base. This reaction results in the formation of water (\(H_2O\)). In the given exercise, we use nitric acid \((HNO_3)\), a strong acid, to neutralize an unknown strong base.
Neutralization reactions carry real-world significance in processes such as titration. This process determines the concentration of an unknown solution by observing the point at which it is neutralized by a solution of known concentration.

Molarity Calculations

Molarity is a crucial concept in chemistry that describes the concentration of a solution. It is expressed as the number of moles of a solute per liter of solution. The formula used is:

• \( \text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \)

In the exercise, knowing the molarity and volume of \(HNO_3\) helped us calculate the moles by multiplying the two values. Similarly, to find the moles of the unknown base, we used its concentration and volume. This step is key in stoichiometric calculations, allowing us to establish a mole ratio between reactants.
Understanding molarity calculations helps in solving not only this exercise but also in many experiments involving solutions which require precise concentrations for desired chemical reactions.

Strong Bases Identification

Identifying strong bases is important when predicting the outcome of neutralization reactions. Strong bases are substances that completely dissociate into their ions in water, effectively releasing hydroxide ions \(OH^-\) to react with hydrogen ions \(H^+\). In this exercise, we find that the unknown base is identified based on a 2:1 mole ratio with \(HNO_3\), indicating two \(OH^-\) ions per molecule of base.
Some common strong bases with two reactive \(OH^-\) ions per molecule include:

• Calcium hydroxide (\(Ca(OH)_2\))
• Barium hydroxide (\(Ba(OH)_2\))
• Strontium hydroxide (\(Sr(OH)_2\))

Understanding the properties of strong bases aids in predicting products of reactions and understanding their reactivity. This knowledge is crucial in both academic studies and practical applications where strong bases are utilized.