Question

In a titration experiment, \(20.4 \mathrm{~mL}\) of \(0.883 \mathrm{M} \mathrm{HCOOH}\) neutralizes \(19.3 \mathrm{~mL}\) of \(\mathrm{Ba}(\mathrm{OH})_{2} .\) What is the concentration of the \(\mathrm{Ba}(\mathrm{OH})_{2}\) solution?

Short answer

The concentration of \( \mathrm{Ba(OH)_2} \) is approximately 0.467 M.

Step-by-step solution

Write the Balanced Chemical Equation

The first step is to write the balanced chemical equation for the reaction. The reaction between formic acid (\( \mathrm{HCOOH} \)) and barium hydroxide (\( \mathrm{Ba(OH)_2} \)) is as follows: \[ 2 \mathrm{HCOOH} + \mathrm{Ba(OH)_2} \rightarrow 2 \mathrm{H_2O} + \mathrm{Ba(CHO_2)_2} \] In this equation, 2 moles of \( \mathrm{HCOOH} \) react with 1 mole of \( \mathrm{Ba(OH)_2} \).

Calculate Moles of Formic Acid

Next, calculate the number of moles of \( \mathrm{HCOOH} \) present in the solution. Use the formula: \[ \text{Moles of } \mathrm{HCOOH} = \text{Volume in L} \times \text{Concentration in M} \] \[ \text{Moles of } \mathrm{HCOOH} = 0.0204 \, \text{L} \times 0.883 \, \mathrm{M} = 0.0180 \, \text{moles} \]

Use Stoichiometry to Find Moles of Ba(OH)2

Use the stoichiometry from the balanced equation to find the moles of \( \mathrm{Ba(OH)_2} \). According to the equation, 2 moles of \( \mathrm{HCOOH} \) react with 1 mole of \( \mathrm{Ba(OH)_2} \). Therefore, divide the moles of \( \mathrm{HCOOH} \) by 2:\[ \text{Moles of } \mathrm{Ba(OH)_2} = \frac{0.0180 \text{ moles}}{2} = 0.0090 \text{ moles} \]

Calculate the Concentration of Ba(OH)2

To find the concentration of \( \mathrm{Ba(OH)_2} \), divide the moles of \( \mathrm{Ba(OH)_2} \) by the volume of the \( \mathrm{Ba(OH)_2} \) solution in liters: \[ \text{Concentration of } \mathrm{Ba(OH)_2} = \frac{0.0090 \text{ moles}}{0.0193 \, \text{L}} \approx 0.467 \, \mathrm{M} \]

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that allows us to quantitatively analyze chemical reactions. It involves the use of ratios provided by the balanced chemical equation to determine the amount of reactants and products involved in a reaction. In the titration problem we're discussing, stoichiometry helps us find out how many moles of each chemical are participating in the reaction.
It essentially acts like a recipe in cooking, where knowing the proportions of ingredients ensures that the outcome is as expected.
For our problem, the stoichiometric ratio is determined from the balanced equation:

• 2 moles of formic acid (\( \mathrm{HCOOH} \)) react with 1 mole of barium hydroxide (\( \mathrm{Ba(OH)_2} \)).
• Understanding this ratio allows us to calculate the moles of one reactant if we know the moles of another.

This powerful tool of stoichiometry is crucial for making sense of the quantities involved in chemical reactions.

Balanced Chemical Equation

The balanced chemical equation is integral for any stoichiometric calculation as it provides the precise relationships between the reactants and products. In a chemical reaction, atoms are neither created nor destroyed; they merely rearrange, adhering to the Law of Conservation of Mass.
For our exercise, the balanced equation is:

• \[ 2 \mathrm{HCOOH} + \mathrm{Ba(OH)_2} \rightarrow 2 \mathrm{H_2O} + \mathrm{Ba(CHO_2)_2} \]
• This shows that two molecules of \( \mathrm{HCOOH} \) interact with one molecule of \( \mathrm{Ba(OH)_2} \), producing water and a barium salt.

The balanced equation lets us know that there is exactly twice the amount of formic acid needed compared to barium hydroxide. This is essential for accurate calculation and helps us find out exactly what happens during the reaction.

Concentration Calculation

Calculating the concentration of a solution is a key part of understanding its composition. Concentration tells us how much solute (the substance being dissolved) is present in a given volume of solution. The most common unit used is molarity (\( M \)), which is the number of moles of solute per liter of solution.
In our titration example, the concentration of barium hydroxide (\( \mathrm{Ba(OH)_2} \)) is calculated using the formula:

• Concentration (\( M \)) = Moles of solute / Volume of solution in liters
• For \( \mathrm{Ba(OH)_2} \), using the moles calculated (0.0090 mol) and the volume given (0.0193 L), the concentration is \( 0.467 \mathrm{M} \).

This tells us how much \( \mathrm{Ba(OH)_2} \) is present and is crucial for determining how much it can react with the formic acid.

Neutralization Reaction

A neutralization reaction is a type of chemical reaction in which an acid and a base react to form water and a salt, often resulting in the neutralization of the chemical properties of the acid and base. It's the central focus of our titration problem.
In the reaction between \( \mathrm{HCOOH} \) (formic acid) and \( \mathrm{Ba(OH)_2} \) (barium hydroxide), a typical neutralization occurs:

• The hydrogen ions (\( \mathrm{H^+} \)) from the acid react with the hydroxide ions (\( \mathrm{OH^-} \)) from the base to form water (\( \mathrm{H_2O} \)).
• This process effectively "neutralizes" the solution, reducing the acidic and basic properties.
• The reaction also produces a salt, barium formate (\( \mathrm{Ba(CHO_2)_2} \)), which remains dissolved in the solution.

Understanding neutralization is crucial for comprehending how acids and bases interact and balance each other, facilitating a wide range of chemical processes.