Question

A 25.00-mL sample of hydrochloric acid solution requires 24.16 mL of 0.106 M sodium hydroxide for complete neutralization. What is the concentration of the original hydrochloric acid solution?

Short answer

The concentration of the original hydrochloric acid solution is \(0.1026 M\).

Step-by-step solution

Write the balanced chemical equation for the reaction

For the neutralization reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH), the balanced chemical equation is: \[HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(l)\] The stoichiometric ratio between HCl and NaOH is 1:1.

Determine the moles of NaOH

We know the volume and concentration of the NaOH solution, which can be used to calculate the moles of NaOH present in the solution. Use the following formula to find moles of NaOH: Moles = Molarity × Volume The molarity of NaOH is given as 0.106 M, and the volume of NaOH is 24.16 mL. Note that to do the calculation, you must convert mL to L by dividing by 1000. Moles of NaOH = (0.106 moles/L) × (24.16 mL × (1 L / 1000 mL)) Moles of NaOH = 0.00256656 moles

Determine the moles of HCl

According to the stoichiometric ratio, the moles of HCl and NaOH have a 1:1 ratio. Therefore, the moles of HCl is equal to the moles of NaOH. Moles of HCl = 0.00256656 moles

Calculate the concentration of HCl

We know the moles of HCl and the volume of the HCl solution (25.00 mL). We can now calculate the concentration (molarity) of HCl using the formula: Molarity = Moles / Volume Convert the volume of HCl from mL to L by dividing by 1000. Volume of HCl in L = 25.00 mL × (1 L / 1000 mL) = 0.025 L Now calculate the molarity of HCl: Molarity of HCl = (0.00256656 moles) / (0.025 L) Molarity of HCl = 0.1026 M Therefore, the concentration of the original hydrochloric acid solution is 0.1026 M.

Key concepts

Neutralization Reaction

When an acid and a base mix together, they react to form water and a salt. This process is called a neutralization reaction. In the example of hydrochloric acid (HCl) and sodium hydroxide (NaOH), the acid and base completely react to form sodium chloride (NaCl) and water (H₂O).
This type of reaction is important in chemistry because it helps to balance pH levels in various environments. Neutralization reactions are used in many applications, from treating acid indigestion to processing industrial wastes.
In the reaction between HCl and NaOH, the ions swap partners. The hydrogen ion from HCl joins with the hydroxide ion of NaOH to make water.

Stoichiometry

Stoichiometry is like a recipe that chemists use to predict the amounts of substances consumed and produced in chemical reactions. It involves using the mole ratios derived from the balanced chemical equation.
For the reaction between HCl and NaOH, the stoichiometric ratio is 1:1. This means that for every mole of HCl used, one mole of NaOH will also be used. Understanding this ratio is crucial because it allows chemists to determine exactly how much of each substance is needed to achieve complete neutralization.

• If you know the amount of one reactant, you can calculate the amount needed for the other reactant using stoichiometric principles.
• These calculations ensure that no reactants are wasted and that the reaction is fully completed.

Molarity Calculation

Molarity is a way of expressing the concentration of a solution. It is defined as the number of moles of solute per liter of solution. To find it, you divide the number of moles of solute by the volume of the solution in liters.
In the provided problem, you first calculate the moles of NaOH using its known molarity and volume. Since the reaction with HCl is in a 1:1 ratio, those moles translate directly to moles of HCl.
Finally, by knowing the volume of the HCl solution, the concentration can be calculated:

• Convert the volume from milliliters to liters first.
• Divide the moles of HCl by the volume of the solution in liters to find the molarity.

In this way, molarity helps in understanding how concentrated a solution is, facilitating the comparison of different solutions.

Balanced Chemical Equation

A balanced chemical equation is crucial because it represents the conservation of mass and the proportions of reactants and products in a reaction.
For the reaction between HCl and NaOH:\[HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(l)\]
The equation shows that one molecule of HCl reacts with one molecule of NaOH to produce one molecule of water and one molecule of salt (sodium chloride).
This balanced equation provides the stoichiometric ratio needed for stoichiometry calculations and ensures that the reaction abides by the law of conservation of mass, which states that mass in a closed system will remain constant, irrespective of the chemical reactions occurring. This is because matter is neither created nor destroyed.