Question

What is the \(\mathrm{pH}\) of a solution in which \(10.0 \mathrm{~mL}\) of \(0.010 \mathrm{M} \mathrm{Sr}(\mathrm{OH})_{2}\) is added to \(10.0 \mathrm{~mL}\) of \(0.010 \mathrm{MHCl} ?\) (a) \(2.30\) (b) \(1.50\) (c) \(11.70\) (d) \(7.00\)

Short answer

The pH of the solution after reaction is (d) 7.00.

Step-by-step solution

Determine the reaction

Write down the balanced chemical reaction for the neutralization between Sr(OH)2 and HCl. The reaction is: \( \mathrm{Sr(OH)_2 + 2HCl \rightarrow SrCl_2 + 2H_2O} \).

Calculate the moles of Sr(OH)2 and HCl

Calculate the number of moles of Sr(OH)2 and HCl using the concentration and volume. For Sr(OH)2: Moles = \(0.010 \, M\) x \(0.010 \, L\) = \(1.0 \times 10^{-4} \, moles\). For HCl: Moles = \(0.010 \, M\) x \(0.010 \, L\) = \(1.0 \times 10^{-4} \, moles\).

Determine the limiting reactant

Since Sr(OH)2 reacts with HCl in a 1:2 ratio and the moles of both reactants are equal, after reaction, both reactants will be completely consumed. No excess of either reactant will be there, so the solution will be neutral, and the pH will be 7.00.

Key concepts

Neutralization Reaction

Understanding how an acid and a base react to form salt and water is crucial in chemistry, especially when working with pH calculations. This type of reaction is known as a neutralization reaction. When an acid, such as hydrochloric acid (HCl), comes into contact with a base like strontium hydroxide (Sr(OH)₂), they react to neutralize each other's properties. The general equation for a neutralization reaction can be written as:

Acid + Base → Salt + Water
In the provided exercise, when aqueous solutions of Sr(OH)₂ and HCl are mixed, they undergo a neutralization reaction. The balanced chemical equation is:
Sr(OH)₂ + 2HCl → SrCl₂ + 2H₂O
This indicates that one mole of strontium hydroxide reacts with two moles of hydrochloric acid to produce one mole of strontium chloride and two moles of water. An understanding of the stoichiometry of this reaction is important to predict the outcome and pH of the solution.

Limiting Reactant

In any chemical reaction, the limiting reactant is the substance that is totally consumed first, thus determining the maximum amount of product that can be formed. Analyzing the limiting reactant is a foundational skill in chemistry that prevents wastage of chemicals and helps in figuring out the efficiency of reactions. The concept applies here, as we look at the stoichiometry of the neutralization reaction between Sr(OH)₂ and HCl. Even though both reactants have equal moles in this particular problem, the stoichiometry is 1:2. This might suggest that one reactant could be the limiting reactant.

However, given that the volumes and concentrations of Sr(OH)₂ and HCl are the same and the ratio needed is as per the balanced reaction, both reactants are actually perfectly stoichiometric. Consequently, there is no limiting reactant in this scenario, and the reaction will proceed until both reagents are completely consumed, leaving us with a neutral solution.

Moles Calculation

The heart of stoichiometry in chemistry lies in the moles calculation. A mole is a unit that represents a given number of particles, atoms, ions or molecules, usually Avogadro's number (6.022 × 10²³). It allows chemists to count these particles in a substance by weighing it, as masses are more practical than counting individual particles.

To find the number of moles in a solution, you multiply its molarity (moles per liter, M) by its volume in liters (L). In the exercise, the calculations were:

Moles Sr(OH)₂ = 0.010 M × 0.010 L = 1.0 × 10⁻⁴ moles
Moles HCl = 0.010 M × 0.010 L = 1.0 × 10⁻⁴ moles
These calculations allow us to understand the quantities of reactants at play and help determine how a reaction proceeds. Moles are directly related to the numbers of particles and thus to the chemical equation that describes the reaction.

Stoichiometry

The term stoichiometry pertains to the quantitive relationships between the substances as they participate in chemical reactions. It is founded on the conservation of mass and the concept of moles, enabling the use of balanced chemical equations to calculate the masses or volumes of reactants and products involved in a chemical reaction. In the context of this problem, once the balanced equation is written and moles are calculated, stoichiometry allows us to understand the proportions in which the reactants combine and the amounts of products formed.

For the neutralization of Sr(OH)₂ with HCl, we use the stoichiometric coefficients from the balanced equation to establish that it takes two moles of HCl to react with one mole of Sr(OH)₂. Since the moles of both reactants are in the ratio required by the equation, they will perfectly react with no excess, leading to a neutral solution. Understanding stoichiometry not only helps us predict the amount of product but also informs us about the pH of the resulting solution after the reaction, as demonstrated in the exercise.