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LABORATORY MATHEMATICS
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SOLUTION
• Can be defined as a homogenous mixture of two or more substances
– Solute
– Solvent
CONCENTRATIONS
A. PERCENT SOLUTIONS
3 means of expressing Percent Concentrations1. % w/v (weight/volume)2. %w/w (weight/weight)3. %v/v (volume/volume)
CONCENTRATIONS
A. PERCENT SOLUTIONS1. % w/v (weight/volume)– used as a unit of measurement when the solute
is a solid and the solvent is a liquid– Unit: grams per 100 mL
x (g)g = ----------------------------- [ x (mL) desired solution]
100 mL
CONCENTRATIONS
A. PERCENT SOLUTIONS1. % w/v (weight/volume)
What weight of glucose is needed to prepare 100 mL of a 15% w/v solution?
How to prepare the solution?
CONCENTRATIONS
A. PERCENT SOLUTIONSx (g)
g = ----------------------------- [ x (mL) desired solution] 100 mL 15 g
g = -------------- x 100 mL 100 mL
g = 15 grams
CONCENTRATIONS
A. PERCENT SOLUTIONS1. % w/v (weight/volume)
How many grams are contained in 500 mL of a 3% solution of sodium chloride?
Atomic WeightsNa = 22.99Cl = 35.45
CONCENTRATIONS
A. PERCENT SOLUTIONS2. % w/w (weight/weight)– using the weight of the final solution rather
than the volume– Unit: grams per 100 grams
x (g)g = ----------------------------- [ x (g) desired solution]
100 g
CONCENTRATIONS
A. PERCENT SOLUTIONS2. % w/w (weight/weight)Make 300 grams of a 20% w/w aqueous
solution of sodium chloride.
a. weight of the solute?b. weight of the solvent?
CONCENTRATIONS
A. PERCENT SOLUTIONS2. % w/w (weight/weight)
How many grams of water are needed to prepare 400 grams of a 0.9% w/w solution of sodium chloride?
CONCENTRATIONS
A. PERCENT SOLUTIONS3. % v/v (volume/volume)– both solute and the solvent are liquids– Unit: milliliters per 100 milliliters
x (mL)mL = ----------------------- [ x (mL) desired solution]
100 mL
CONCENTRATIONS
A. PERCENT SOLUTIONS3. % v/v (volume/volume)a. How much ethanol is needed to prepare 150
milliliter of a 15% v/v solution? How to prepare the solution?
b. Describe how to prepare 200 mL of a 5% v/v solution of methanol starting with absolute alcohol.
CONCENTRATIONS
B. MOLARITY the number of moles of solute in one liter of
solution Unit: moles/Liter
Weight of the soluteMolarity = ------------------------------- -------------------
Molecular weight x Liter of solution
CONCENTRATIONS
B. MOLARITY How many grams of sodium hydroxide are
contained in 500 milliliter of a 4 molar solution?
4 moles 40 g 1 L
g = ---------- x -------------- x 500 mL x --------------- 1 L 1 mole 1000 mL
= 80 grams
CONCENTRATIONS
B. MOLARITY
A solution contains 3.5 grams of hydrochloric acid in 1 liter. How many millimoles does it contain?
CONCENTRATIONS
C. MOLALITY the number of moles of solute in 1000 grams (1
kilogram) of solvent rather than final solution Unit: moles/1000 grams (moles/kilogram)
Weight of the soluteMolality = ------------------------------- ----------
Molecular weight x kilogram
CONCENTRATIONS
C. MOLALITY the number of moles of solute in 1000 grams (1
kilogram) of solvent rather than final solution Unit: moles/1000 grams (moles/kilogram)
What is the molality of a solution if 127 grams of sodium chloride were dissolved in 1000 grams of distilled water?
CONCENTRATIONS
D. NORMALITY the concentration is based on equivalent weight Unit: Equivalents/Liter (eq/L)
Weight of the soluteNormality = ------------------------------- -----------------
Equivalent weight x Liter of solution
CONCENTRATIONS
D. NORMALITY Equivalent Weight
The mass of an element or compound that will combine with or replace one mole of hydrogen
Is dependent on the total charge of the positive ion, or the valence, of the element
MWEW = ----------------------
Valence
CONCENTRATIONS
D. NORMALITY If the compound is an acid, an equivalent is the
quantity of substance that contains one replaceable hydrogen
If it is a base or a salt, an equivalent is the quantity of a substance that will react with one replaceable hydrogen
CONCENTRATIONS
D. NORMALITY What is the normality of a solution that
contains 150 grams of sodium chloride per liter?
Eq 150 g 1 eq 1 mole---- = ---------- x -------------- x --------------- L 1 L 1 mole 58.5 g
= 2.56 equivalent/Liter (2.56 Normal)
CONCENTRATIONS
E. CONVERSIONS Convert 5 molar sulfuric acid to normality
Eq 5 moles 2 eq---- = ------------ x -------------- = 10 equivalents/liter L 1 L 1 mole
CONCENTRATIONS
E. CONVERSIONS Convert 12 normal phosphoric acid to molarity
moles 12 eq 1 mole--------- = ------------ x -------------- = 4 moles/liter L 1 L 3 eq
CONCENTRATIONS
E. CONVERSIONS Convert 0.4 molar sodium hydroxide to %w/v
g 0.4 moles 40 g 0.1 L--------- = ------------ x -------------- x -----------------100 mL 1 L 1 mole 100 mL
= 1.6 grams/100 mL or 1.6% w/v
CONCENTRATIONS
F. DILUTIONS Simple Dilutions C1V1 = C2V2 Proportion Serial Dilutions
CONCENTRATIONS
F. DILUTIONS Simple Dilutions
a weaker solution is made from a stronger solution
Diluent + Aliquot Commonly expressed as one part of the
original solution to the total parts of final solution
CONCENTRATIONS
F. DILUTIONS Simple Dilutions
Volume of the SoluteDILUTION = ------------------------------
Total Volume
CONCENTRATIONS
F. DILUTIONS Calculate the dilution if 5 mL of serum
are diluted with 15 mL of saline solution
5 mL 1DILUTION = -------------- = ---------- = 4 = 1:4
20 mL x
CONCENTRATIONS
F. DILUTIONS Make 250 mL of a 1:5 dilution of
serum in saline solution
CONCENTRATIONS
G. V1 X C1 = V2 X C2• Involves changing a solution of known
volume and concentration (V1xC1) to one weaker concentration (V2xC2)
• Three of the four values must be known to solve the equation.
CONCENTRATIONS
1. How much 20% alcohol is required to make 1L of 10% alcohol?
CONCENTRATION
How much of a 25M stock solution would be needed to produce 500mL of a 10M solution?
Concentration
• Proportion:
Volume = ________C_________ A + B
Concentrations
A procedure calls for NaOH and water with the proportions of being 4 parts of NaOH to 6 parts of water. 100mL are needed. How much NaOH and how much water are required?
CONCENTRATIONS
H. SERIAL DILUTIONS:• Constitutes a series of dilutions of progressive,
regular increments in which each subsequent dilution is less concentrated than the preceding dilution by a constant amount, N.