Question

For each of the following solutions, calculate the normality. a. $25.2\mathrm{mL}$ of $0.105\mathrm{M}\mathrm{HCl}$ diluted with water to a total volume of $75.3\mathrm{mL}$ b. $0.253M{\mathrm{H}}_3{\mathrm{PO}}_4$ c. $0.00103M\mathrm{Ca}(\mathrm{OH}{)}_2$

Short answer

The normalities of the given solutions are: a. $0.105N$ for HCl solution. b. $0.759N$ for H3PO4 solution. c. $0.00206N$ for Ca(OH)2 solution.

Step-by-step solution

Calculate the moles of HCl present

To begin, we need to find out the moles of HCl in the given volume of the solution. We can do this using the formula: moles = molarity × volume Moles of HCl = $0.105\mathrm{M}\ast 0.0252\mathrm{L}=0.002646\mathrm{mol}$

Calculate Normality

As we know, normality is the concentration of a solution in terms of the moles of solute per liter of the solution. Since HCl has only one ionizable hydrogen atom, the normality is equal to the molarity. Normality of HCl solution = 0.105 N b. H3PO4 solution

Determine the number of H+ ions released

H3PO4 can release 3 H+ ions during its reaction. Therefore, the number of equivalent moles is 3 times its molarity.

Calculate Normality

Normality of H3PO4 solution = molarity × number of equivalent moles Normality = $0.253\mathrm{M}\ast 3=0.759N$ c. Ca(OH)2 solution

Determine the number of OH- ions released

Ca(OH)2 can release 2 OH- ions during its reaction. Therefore, the number of equivalent moles is 2 times its molarity.

Calculate Normality

Normality of Ca(OH)2 solution = molarity × number of equivalent moles Normality = $0.00103\mathrm{M}\ast 2=0.00206N$ In conclusion: a. The normality of the HCl solution is 0.105 N. b. The normality of the H3PO4 solution is 0.759 N. c. The normality of the Ca(OH)2 solution is 0.00206 N.

Key concepts

Molarity vs Normality

Molarity and normality are both measures of concentration, but they highlight different aspects of a solution. Molarity (M) is defined as the number of moles of solute in one liter of solution. It's a straightforward way to understand concentration by focusing purely on the amount of the solute.
On the other hand, normality (N) considers the reactive capacity of a given compound. It tells us how many equivalents of a solute are present in one liter of solution. The notion of reactivity is important in normality, as it often relates to acid-base reactions or redox processes.
If you have a compound that has only one acidic or basic group (like HCl), molarity and normality will be the same because one mole of the compound yields one equivalent. But with compounds that can donate or accept more than one proton, or participate differently in a reaction, the normality will be greater than their molarity. For example:

• For HCl, with one hydrogen ion per molecule, molarity and normality are equal.
• For H₃PO₄, which can release three hydrogen ions, normality is three times its molarity.

This difference between molarity and normality is crucial in chemistry for accurately preparing and using solutions in reactions.

Solution Preparation

Preparing solutions in chemistry requires careful calculations to ensure the desired concentrations and properties of the solution. When making solutions from a concentrated sample or by diluting a more concentrated solution, it is essential to know both the initial and the final concentrations.
For instance, let's consider preparing a titular HCl solution. You start with a known concentration and volume and dilute it with water to reach the final desired volume and concentration. This example illustrates that dilution changes the concentration but keeps the amount of solute constant.
We use the formula for moles to calculate how much substance we have: $$\text{moles}=\text{molarity}\times \text{volume}$$When you perform a dilution, the equation $$M_1{V}_1=M_2{V}_2$$helps to figure out the new concentration after adding more solvent. Here, $M_1$ and $V_1$ are the initial molarity and volume, while $M_2$ and $V_2$ are the final molarity and volume. This equation is useful in labs anytime you need to dilute a solution to a specific concentration.

Acid and Base Reactions

Acid and base reactions are central to many chemical processes and affect the calculations involving normality. When an acid reacts with a base, they typically form water and a salt in a neutralization reaction.
These reactions depend on the transfer of protons (H⁺ ions) from acids to bases. As such, knowing how many hydrogens an acid can donate (or base accept) is crucial. This is where normality's focus on equivalents becomes handy.
For instance, in the case of HCl reacting with NaOH:$$\text{HCl}+\text{NaOH}\to {\text{H}}_2\text{O}+\text{NaCl}$$each mole of HCl provides one equivalent for each NaOH molecule, illustrating a one-to-one reaction equivalence. However, with H₃PO₄ which can donate three protons:$${\text{H}}_3{\text{PO}}_4+3\text{NaOH}\to 3\text{NaCl}+3{\text{H}}_2\text{O}$$it requires three equivalents of base to react completely with one mole of H₃PO₄. This is why understanding equivalent weights and normality becomes essential when predicting and balancing reactions between acids and bases.