Question

\(25 \mathrm{~mL}\) of a solution of barium hydroxide on titration with \(0.1\) molar solution of hydrochloric acid gave a titre value of \(35 \mathrm{~mL}\). The molarity of barium hydroxide solution was: (a) \(0.07\) (b) \(0.14\) (c) \(0.28\) (d) \(0.35\)

Short answer

(a) 0.07

Step-by-step solution

Write the balanced chemical equation

The reaction between barium hydroxide, \( \text{Ba(OH)}_2 \), and hydrochloric acid, \( \text{HCl} \), is: \[ \text{Ba(OH)}_2 + 2 \text{HCl} \rightarrow \text{BaCl}_2 + 2 \text{H}_2\text{O} \] This equation shows that 1 mole of \( \text{Ba(OH)}_2 \) reacts with 2 moles of \( \text{HCl} \).

Start with molarity of HCl solution

The molarity of the hydrochloric acid solution is given as \( 0.1 \text{ M} \). The volume of the \( \text{HCl} \) solution used is \( 35 \text{ mL} \), which can be converted into liters: \[ 35 \text{ mL} = 0.035 \text{ L} \].

Calculate moles of HCl used

The number of moles of \( \text{HCl} \) used in the titration can be calculated using its molarity and volume: \[ \text{Moles of HCl} = 0.1 \text{ M} \times 0.035 \text{ L} = 0.0035 \text{ moles} \].

Calculate moles of Ba(OH)$_2$ present

According to the balanced equation, 1 mole of \( \text{Ba(OH)}_2 \) reacts with 2 moles of \( \text{HCl} \). Thus, \[ \text{Moles of } \text{Ba(OH)}_2 = \frac{0.0035}{2} = 0.00175 \text{ moles} \].

Find the molarity of Ba(OH)$_2$

The volume of the \( \text{Ba(OH)}_2 \) solution is \( 25 \text{ mL} = 0.025 \text{ L} \). Therefore, the molarity of the \( \text{Ba(OH)}_2 \) solution: \[ \text{Molarity of } \text{Ba(OH)}_2 = \frac{0.00175}{0.025} = 0.07 \text{ M} \].

Key concepts

Understanding Molarity

Molarity is a crucial concept in chemistry that expresses the concentration of a solution. It is defined as the number of moles of solute per liter of solution. This measurement helps us understand how concentrated a solution is. For example, having a "0.1 M HCl" solution means there are 0.1 moles of hydrochloric acid in every liter of that solution.

To calculate molarity, you can use the equation:

• Molarity (M) = \( \frac{\text{moles of solute}}{\text{liters of solution}} \)

This equation allows you to link the quantity of a substance dissolved and the overall volume of the solution, making it easier to calculate how solutions will react in various chemical processes, such as titration.

Chemical Equations Balance the Reaction

In chemistry, a chemical equation represents the substances involved in a chemical reaction. Balancing these equations is important because it reflects the conservation of mass. Each atom in the reactants side must equal those in the products side.

A balanced chemical equation, like the one given for the reaction between barium hydroxide and hydrochloric acid, looks like this: \[ \text{Ba(OH)}_2 + 2 \text{HCl} \rightarrow \text{BaCl}_2 + 2 \text{H}_2\text{O} \]

• This means that one molecule of barium hydroxide reacts with two molecules of hydrochloric acid.
• The equation helps in understanding the quantities of each substance required and produced.

By balancing equations, we ensure that the same amounts of atoms are present before and after the reaction, complying with the law of conservation of mass.

Delve into Stoichiometry

Stoichiometry is the method chemists use to measure the relationships between substances in a reaction. It's like a recipe, ensuring that you have the correct amounts of each ingredient for a complete reaction.

Using stoichiometry involves understanding mole ratios derived from the coefficients of a balanced chemical equation. For the titration process explained:

• 1 mole of \( \text{Ba(OH)}_2 \) requires 2 moles of \( \text{HCl} \).
• This ratio guides calculations for how much of one reactant will react with a given amount of another.

With stoichiometry, you can determine unknown quantities like how many moles of a reactant are needed or produced by referencing the balanced chemical equation. It forms the foundation for titration calculations and other quantitative chemical analyses.

Acid-Base Reactions Explained

Acid-base reactions are a common type of chemical reactions where an acid reacts with a base. In these reactions, hydrogen ions (\( \text{H}^+ \)) are transferred from the acid to the base. This can result in the formation of water and a salt.

The reaction between barium hydroxide (\( \text{Ba(OH)}_2 \)) and hydrochloric acid (\( \text{HCl} \)) is a classic example of an acid-base reaction:

• The base, \( \text{Ba(OH)}_2 \), donates hydroxide ions (\( \text{OH}^- \)) to neutralize the \( \text{H}^+ \) ions from the \( \text{HCl} \).
• This results in the production of water (\( \text{H}_2\text{O} \)) and a salt, barium chloride (\( \text{BaCl}_2 \)).

Understanding acid-base reactions is essential for grasping how titrations work because they rely on the precise measurement of how much acid is required to neutralize a base, or vice versa.