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.

Short answer

Given a 30.0 mL sample of an unknown 0.0300 M strong base that is neutralized by 12.0 mL of a 0.150 M HNO₃ solution, the possible identities for the unknown base are calcium hydroxide (Ca(OH)₂), strontium hydroxide (Sr(OH)₂), and barium hydroxide (Ba(OH)₂). These bases have the empirical formula M(OH)₂ and are strong bases that can react with HNO₃ to form water and salt.

Step-by-step solution

Calculate the moles of HNO₃

First, we need to calculate the moles of HNO₃ using the given volume and concentration. The formula for this is: Moles of HNO₃ = Volume of HNO₃ × Concentration of HNO₃ Plugging in the given values, we get: Moles of HNO₃ = 12.0 mL × 0.15 M = 1.8 × 10⁻³ mol

Calculate the moles of the unknown base

Now, we need to calculate the moles of the unknown base using its given volume and concentration. The formula for this is: Moles of unknown base = Volume of the base × Concentration of the base Plugging in the given values, we get: Moles of unknown base = 30.0 mL × 0.0300 M = 9.0 × 10⁻⁴ mol

Calculate the mole ratio between HNO₃ and the unknown base

Since the strong acid and base react with each other in a neutralization reaction, the mole ratio between them must be equal. Therefore, Mole ratio = Moles of HNO₃ / Moles of the unknown base Mole ratio = (1.8 × 10⁻³ mol) / (9.0 × 10⁻⁴ mol) = 2 This means that in the neutralization reaction, 1 mole of the unknown base reacts with 2 moles of HNO₃.

Determine the empirical formula of the unknown base

Considering the mole ratio and the fact that the base is strong, the general neutralization reaction can be defined as: Unknown base + 2 HNO₃ → Water + Salt This implies that the unknown base has two replaceable hydroxide (OH⁻) ions. Therefore, the empirical formula of the unknown base is M(OH)₂, where M is the unknown metal cation.

Suggest possible identities for the unknown base

Since the empirical formula of the unknown base is M(OH)₂ and it's a strong base, some possible identities for the unknown base include: 1. Calcium hydroxide (Ca(OH)₂) 2. Strontium hydroxide (Sr(OH)₂) 3. Barium hydroxide (Ba(OH)₂) These are strong bases with the empirical formula M(OH)₂.

Key concepts

Mole ratio

Understanding **mole ratio** is essential for solving reactions involving acids and bases. In a neutralization reaction, the mole ratio tells us how many moles of one substance react with a certain number of moles of another. In this exercise, we calculated that the mole ratio between the strong acid,
often nitric acid ( ext{HNO}_{3} ), and the unknown strong base is 2:1. This means that two moles of ext{HNO}_{3} are needed to neutralize one mole of the unknown base.
The mole ratio is crucial because it helps us understand the stoichiometry of the reaction. Here are some points to remember about mole ratios:

• They are derived from balancing chemical equations.
• They help determine the proportions in which reactants mix and products form.
• Accurate mole ratios are necessary for preparing desired reaction yields in experiments.

Understanding the mole ratio aids in determining possible unknown reactants based on available experimental data.

Empirical formula

An **empirical formula** is the simplest whole-number ratio of atoms in a compound. It provides insight into the composition of a compound. In this exercise, we learned that the empirical formula of the unknown base is \( ext{M(OH)}_{2}\). This means that each formula unit of the base contains one metal cation (M) and two hydroxide ions ( ext{OH}^- ).
Based on the empirical formula, we can conclude:

• The base contains twice the number of hydroxide ions compared to the metal cations.
• The ratio reflects the mole ratio from the neutralization reaction, as discussed earlier.
• Simple integer ratios allow for easier balancing of equations when predicting reactions or products.

Using the empirical formula, we can suggest structures and properties of compounds, which aids in determining the identities of potential candidates for the unknown base.

Strong base identification

Identifying a **strong base** involves understanding both its structure and its reactivity in water. A strong base is one that completely dissociates in an aqueous solution, releasing ( ext{OH}^-) ions. In this example, possible candidates for the unknown base include compounds with the general formula \( ext{M(OH)}_{2} \), such as calcium hydroxide, strontium hydroxide, and barium hydroxide.
Here are key characteristics of strong bases:

• They fully ionize in aqueous solutions, leaving no undissociated molecules.
• They have higher ( ext{OH}^- ) concentrations, making the solution more basic.
• Examples of strong bases include alkali metal hydroxides ( ext{NaOH}, ext{KOH}) and some alkaline earth metal hydroxides ( ext{Ca(OH)}_{2}, ext{Ba(OH)}_{2}).

The identification process in this example heavily relies on knowing the empirical formula and reaction ratios of strong bases. Knowing these base features helps in predicting their behavior and their reaction equations in a neutralization event.