2. 2
SERIAL DILUTIONS
● Titering
● Useful in serologic tests when estimates of the volume of antibody is
necessary.
● “Dilution fold” is constant in all tubes
● Volume transferred is constant to each successive tubes.
● Volumes transferred is constant to each successive tubes.
TOTAL VOLUME = volume being transferred + vol. of diluent already in the
tube.
= the last volume to be transferred is discarded from the
last tube.
4. 4
SPECIFIC GRAVITY
● Used when working with concentrated acids or base.
● The weight of 1 mL of any liquid
● Method of measuring density
● Ratio of mass/ volume (g/mL or mL/g)
● Concentrated commercial liquids: check labels for specific gravity &
percent purity (assay)
5. 5
Example:
HNO₃ = specific gravity 1.42 (mass weight)
= assay 70% (pure HNO₃)
1.42 g x 0.70 = 0.994 g (pure HNO₃)
1 mL 1 mL
6. 6
INTERNATIONAL SYSTEMS OF UNITS
● Systeme International d’ Unites (SI), adopted in 1960
● Established, whereby all quantitative measurements could be
expressed in standard units. Although conventional Metric
System are still frequently used today.
8. 8
Derived Quantity Derived Unit Symbol
Substance concentration Mole per cubic
meter
mol/m³
Conductance Siemens S
Resistance ohms Ω
Activity (radionuclide) Becquerel Bq
Volume Cubic meter m³
9. 9
Example: A calcium concentration is reported as 10 mg/dL. What is
the concentration in mmol/L? (MW = 40)
mmol = 10mg x 1 mole x 1000mL
L 100mL 40g L
x 1g x 1000 mmole
1000mg 1 mole
= 2.5 mmole
L
10. IONIC STRENGTH
● First step in calculations is calculation of so called ionic
strength, using following formula:
● Where C₁ is a molar concentration of pH ion present in the
solution and z₁ is its charge. Summation is done for all charged
molecules present in the solution.
Ex: What is the ionic strength for a 1.0 M NaCl solution?
Using the simple formula for ionic strength I give above
I = ½ (1*1² + 1*1²)
= 1.00 (a unitless quantity)
11. 11
Example 2
What is the ionic strength for a solution whose concentrations are
1.0 M La₂(SO₄)₃ plus 1.0 M CaCl₂
For this solution, the concentrations are:
[La³⁺] = 2.0 M
[SO₄²⁻] = 3.0 M
[Ca²⁺] = 1.0 M
[Cl⁻] = 2.0 M
I = ½ (2*3² + 3*2² + 1*2² + 2*1²)
= 18.0
12. 12
RADIOISOTOPES
A. Half-life - time required for a given amount of radioactivity to
decrease to one-half its original value.
a. The amount of radioactivity decreases by a factor of 2 for
every half-life period
b. If an isotope has a half life of 8 hours and an activity of 16 mCi
(millicuries), its activity will drop to 2 mCi in 24 hrs.
B. 1 mCi activity = 3.7 x 10⁷ disintegration/second (1000 mCi = 1 Ci)
13. 13
Number of Half-lives elapsed Fraction remaining Percentage remaining
0 1/1 100
1 ½ 50
2 ¼ 25
3 ⅛ 12.5
4 1/16 6.25
5 1/32 3.125
6 1/64 1.563
7 1/128 0.781
……. ……. …….
n 1/(2n) 100(2n)
14. 14
CALCULATING pH
● pH is the only meaningful when applied to aqueous (water-based)
solutions. To calculate the pH of an aqueous solution you need to know
the concentration of the hydronium ion in moles per liter (molarity). The
pH is then calculated using the expression.
pH = - log [H₃O⁺]
➢ Ex: Find the pH of a 0.0025 M HCl sol’n. The HCl is a strong acid and is
100% ionized in water. The hydronium ion concentration is 0.0025 M.
Thus:
pH = - log (0.0025) = -(-2.60) = 2.60
15. 15
CALCULATING THE HYDRONIUM ION CONCENTRATION FROM pH
● The hydronium ion concentration can be found from the,
pH by the reverse of the mathematical operation employed to
find the pH.
[H₃O⁺] = 10pH
or [H₃O⁺] = antilog (-pH)
example : what is the hydronium ion concentration in a solution that has
a pH of 8.34?
8.34 = - log [H₃O⁺]
- 8.34 = log [H₃O⁺]
[H₃O⁺] = 10-8.34
= 4.57 x 10-9
M
