CH 4 (10/23) (PG 16-20)
pH Concept and Calculation
Importance of pH
pH is a crucial measurement to easily consider a wide range of acid and base concentrations.
Definition of pH
The pH of a solution is defined by the formula:
\text{pH} = -\log[H_3O^+]Here, $H^+$ is equivalent to $H_3O^+$, thus it can also be expressed as:
\text{pH} = -\log[H^+]It is important to note that concentration should be measured in moles per liter (mol/L), but this unit is omitted when taking the logarithm.
Hydrogen Ion Concentration and Corresponding pH Values
Hydrogen ion concentrations (mol/L) and their corresponding pH values include:
[H+] = 1.0 \times 10^{-1} mol/L ⇒ pH = 1.00
[H+] = 1.0 \times 10^{-2} mol/L ⇒ pH = 2.00
[H+] = 1.0 \times 10^{-3} mol/L ⇒ pH = 3.00
[H+] = 1.0 \times 10^{-4} mol/L ⇒ pH = 4.00
[H+] = 1.0 \times 10^{-12} mol/L ⇒ pH = 12.00
The pH of pure water is 7.00, indicating that [H+] = 1.0 \times 10^{-7} mol/L.
Example Calculations for pH
Calculation for [H+] = 3.2 \times 10^{-9} M:
pH = -\log(3.2 \times 10^{-9}) = 8.49
Calculation of hydrogen ion concentration for an acid with pH = 5.3:
[H+] = 10^{-5.3} = 5.0 \times 10^{-6} mol/L
Calculation of pH for 0.250 M HClO₄ solution.
Solution Stoichiometry
Overview of Solution Stoichiometry
Prior to discussing quantitative aspects, previous discussions handled reactions qualitatively:
General equation: Reactants → Products.
With the concept of molarity, quantitative calculations become feasible in aqueous solutions. The steps for calculations include:
Volume → number of moles → number of moles → mass
Mass → number of moles → number of moles → volume
Standard Solutions
Definition and Purpose
Some solutions cannot be accurately made by weight due to solute impurity or instability.
When faced with such scenarios, one can create a solution of approximate concentration and then standardize it using a reliable standard compound that reacts with the solute.
Characteristics of a Standard Compound
A standard compound should be pure, have a known molar mass, and be chemically stable (e.g., Na₂CO₃).
This allows for high accuracy, typically yielding four or more significant figures.
Standard solutions of known concentration can also be purchased commercially.
Titration
Purpose of Titration
Titrations are employed to determine the amount or concentration of a solute in a solution by reacting it with a measured quantity of a reagent of known concentration.
Process
During a titration, if a standard is utilized, it helps standardize the unknown concentration solution. An indicator is often added to signal the equivalence point, which represents the point where the reactants have reacted in stoichiometric ratios.
At the equivalence point, the number of moles from both reactants (e.g., acid and base) is equal based on their stoichiometric ratio.
Spectrophotometry
Method Overview
Spectrophotometry is a quantitative technique for determining solution concentrations based on light-matter interactions.
The Beer-Lambert Law
The Beer–Lambert Law describes the relationship between light absorbance and the solute concentration based on the formula:
A = \varepsilon l cWhere:
A = absorbance
l = path length
\varepsilon = molar absorptivity
c = concentration
Additionally, absorbance can be expressed as:
A = -\log(T) where T denotes transmittance, defined by T = \frac{P}{P_0} (ratio of transmitted to incident light intensity).This law is linear for a given compound and path length; thus, absorbance can be calibrated to determine unknown concentrations after instrument calibration.
Sample Application of Beer-Lambert Law
Consider a solution with a molar absorptivity \varepsilon of 100 ext{ L/(mol cm)}, a path length of 1.00 ext{ cm}, and an absorbance of 1.00:
Calculate concentration c:
c = \frac{A}{\varepsilon l} = \frac{1}{100 ext{ L/(mol cm)} \times 1.00 ext{ cm}} = 0.0100 ext{ mol/L}.Calibration of the instrument is crucial to utilize the Beer-Lambert Law effectively.