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.