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

Some possible identities for the unknown strong base with a concentration of \(0.0300 M\) include Sodium hydroxide (NaOH), Potassium hydroxide (KOH), Lithium hydroxide (LiOH), Rubidium hydroxide (RbOH), and Cesium hydroxide (CsOH), as they all have a 1:1 stoichiometry with strong acids in a neutralization reaction.

Step-by-step solution

Find moles of HNO₃

To find the moles of HNO₃, we can use the formula: moles of HNO₃ = volume (L) × molarity (M) First, we need to convert the given volume of HNO₃ solution from mL to L: volume (L) = 12.0 mL × (1 L / 1000 mL) = 0.012 L Now, we can find the moles of HNO₃: moles of HNO₃ = (0.012 L) × (0.150 M) = 0.0018 moles

Find moles of the strong base

Given that the neutralization reaction goes completely (as the reactants are strong acid and base), the moles of the strong base will be the same as the moles of HNO₃. moles of strong base = 0.0018 moles

Calculate the volume of the strong base

We are given the volume of the strong base solution as 30.0 mL, so we convert it to L: volume (L) = 30.0 mL × (1 L / 1000 mL) = 0.030 L

Find the molarity of the strong base

We have the moles of strong base (0.0018 moles) and volume (0.030 L), so we can calculate molarity: molarity = moles / volume molarity of strong base = 0.0018 moles / 0.030 L = 0.0300 M

Determine the possible identities of the strong base

With the molarity of the strong base given as 0.0300 M, we can list some common strong bases with a 1:1 reaction with the strong acid: 1. Sodium hydroxide (NaOH) 2. Potassium hydroxide (KOH) 3. Lithium hydroxide (LiOH) 4. Rubidium hydroxide (RbOH) 5. Cesium hydroxide (CsOH) These are some possible identities for the unknown strong base, as all of them have a 1:1 stoichiometry with strong acids in a neutralization reaction.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. Essentially, it's a way to balance the 'chemical equation' of a reaction to know how much of each substance is needed or produced.

In the context of acid-base neutralization, which is the type of reaction in our exercise, stoichiometry involves looking at the 'mole ratio' between the acid and the base. Since we're dealing with strong acid and strong base reactions, they usually have a simple stoichiometry, often a 1:1 ratio meaning one mole of acid reacts with one mole of base. Calculating the number of moles of one reactant allows us to directly calculate the moles of the other if the stoichiometric ratio is known.

In our textbook problem, finding the moles of the known concentration of nitric acid (\( HNO_3 \)) and assuming a 1:1 ratio lets us figure out the moles of the unknown strong base, an essential step towards identifying its molarity and, consequently, its possible identity.

Molarity Calculation

Molarity calculation is a crucial concept in chemistry that indicates the concentration of a solution. It is defined as the number of moles of solute (the substance being dissolved) per liter of solution.

The calculation is straightforward:
\[\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\].
This formula was applied in the problem to find the concentration of the unknown strong base. After calculating the moles of the strong base (from the known moles of nitric acid, thanks to stoichiometry), you divide those moles by the volume of the base (which needs to be in liters). The outcome tells us how concentrated the base solution is. Understanding molarity is key to many areas of chemistry, including stoichiometry, since it helps predict how substances in a solution will react with one another. In the exercise, we used it to deduce several potential identities for the unknown strong base.

Strong Acid and Base Reactions

Strong acids and bases are characterized by their complete dissociation in water, meaning they readily donate H+ ions and accept H+ ions, respectively. When a strong acid reacts with a strong base, the result is a neutralization reaction, where the products are typically water and a salt.

In terms of the chemical equation for the reaction between a strong acid like \( HNO_3 \) and a strong base, it generally looks like this:
\[\text{Acid} + \text{Base} \rightarrow \text{Water} + \text{Salt}\].
Because both reactants are strong, meaning they fully dissociate, we can assume that they react in a 1:1 mole ratio unless stated otherwise. For the exercise at hand, this assumption allows us to equate the moles of \( HNO_3 \) to the moles of the unknown base, crucial for figuring out the molarity of the unknown base and narrowing down its identity. Understanding the behavior of strong acids and bases in reactions is vital for making accurate predictions in chemistry.