# UNDERSTANDING DILUTIONS OF AQUEOUS SOLUTIONS (DOC) by pptfiles

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```									                             Molarity and Dilution of Solutions
PURPOSE                                          rev 02/26/07

    Understand the concept of a solution’s concentration and molarity
    Calculate the molarity of a diluted solution
    Use the concept of dilution factor to calculate a serial dilution factor dilution factors
    Demonstrate proper use of volumetric glassware
    Demonstrate correct laboratory use of a spectrophotometer

INTRODUCTION TO MOLARITY AND DILUTIONS OF SOLUTIONS

Two ―species‖ exist in any solution. First, a solution has a solute — a dissolved solid or liquid — and
second a solvent — the liquid in which the solute is dissolved. Water is a very common universal
solvent. Solutions with water as the solvent are commonly referred to as aqueous solutions.

Solutions with uniform distribution of solute throughout the solvent are classified as homogenous
mixtures. In other words, in a homogenous mixture, every ―portion‖ of solution contains exactly the
same number of moles of solute per volume of solvent.

1.     Molarity

A chemist must often determine a solution’s concentration — the amount of solute in a solution. The
most common measurement of concentration in chemistry is molarity (M). A solution’s molarity tells
us the number of moles solute per liter of solution.

molarity (M) =      moles of solute (moles                         (Equation 1)
volume of solution (L)

An aqueous solution of known molarity is prepared by adding solute to a known volume of solvent. We
can easily calculate the moles of solute needed to achieve a desired molarity be manipulating Equation
1. In addition, the volume of solvent can be determined knowing desired molarity and moles of solute
required.

moles of solute (mol) = molarity of solution (M) x volume of solution (L)

volume of solvent (L)     = moles of solute (mol)
molarity of solution (M)

How many grams of sodium hydroxide are need to prepare 0.500 L of a 2.00 M solution?

moles of NaOH needed = 0.500 L x 2.00 M
= 1.00 mol NaOH

1.00 mol NaOH       40.00 g NaOH       = 40.0 g NaOH are needed to prepare solution.
mol NaOH

(Figure     1)

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2.     Dilution

Sometimes chemists encounter strong solutions. Chemists can weaken the concentration of a
solution by adding more solvent—a process known as dilution. After dilution, the quantity of solute
remains the same, but the volume of solution has increased, thereby reducing the solution’s molarity.

Because the number of moles of solute does not change, we can apply the derived equation above
and arrive at a useful dilution equation, where M1 and V1 are the solution’s molarity and volume
before dilution, and M2 and V2 are the solution’s molarity and volume after dilution.

M 1 x V1 = M 2 x V2                               (Equation 2)

It is important to remember that the units for volume must remain consistent (V1 and V2 have same
volume units) in this equation. (Note: You may see dilution equation represented as C 1V1 = C2V2 ,
where C stands for ―concentration.‖)

We can easily manipulate Equation 2 to determine any one of the missing four variables.

Let’s work some more sample problems.

How would you prepare 250.0 mL of a 0.500 M solution from a 6.00 M stock solution of HCl?

6.00 M   x   V1        = 0.500 M x 250.0 mL
V1        = 20.8 mL

(Figure 2)

2.0 mL of 0.3234 M CuSO 4 solution is diluted to 50.0 mL. What is solution’s final concentration?

M1       x           V1     =   M2 x       V2
0.3234 M    x        0.00200   =   M2 x     0.0500
0.0128    =   M2

Final concentration is 0.0128 M

(Figure 3)

2.1 Dilution Factors

When a solution is diluted several times — it is known as a serial dilution. A chemist can utilize
dilution factors as a tool to keep track of a diluted solution’s final concentration.

dilution factor    =    total volume of diluted solution               (Equation
3)
original volume of diluted solution

Serial dilutions allow a solution to be greatly diluted using smaller volumes of solvent—in other words,
when the volume of solvent needed is far too large for one container in a lab.
With each new dilution, the overall dilution factor increases multiplicatively. We can calculate this
overall dilution factor by simply multiply the dilution factors of each intermediate step.

overall serial dilution factor (DF) = DF1 x DF2 x DF3          …   x DFn         (Equation 4)

A sample problem will illustrate Equation 4.

10.0 mL of stock solution is diluted to 50.0 mL, producing solution A. 20.0 mL of solution A is then
diluted to 100.0 mL, resulting in solution B. 15.0 mL of solution B is then dilted to 25.0 mL, arriving at
solution C. What is the overall dilution factor?

overall dilution factor   = 50.0 mL      x    100.00 mL       x     25.0 mL
10.0 mL           20.0 mL               15.0 mL

= 5.00 x 5.00 x 1.67
= 41.7

The overall dilution factor is 41.7.

(Figure 4)

3.   Volumetric Glassware

In the laboratory, solutions are prepared using volumetric glassware. Volumetric flasks are the
containers used when diluting solutions. Volumetric pipets are used to deliver known volumes of
liquid during dilutions.

pipet           pipet
(Figure 5)

Note the etched line on the thin upper neck of the volumetric flask and pipet. When the glassware is
filled with liquid to the etched line, the volume of solution in the glassware is exactly the amount
specified for that piece of glassware. A pipet must be properly cleaned and rinsed before usage.

The following steps are necessary so that your pipet does not contaminate the solution during use.

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1. Wash your pipet with soapy water and then rinse with distilled water.
Make sure the pipet drains completely by filling it with distilled water and dispensing several
times into a beaker.
2. Blow out as much water as possible using the pipet bulb and wipe the pipet tip.
Do not use your mouth to blow water out of the pipet!
3. Pour a small portion of the solution you will be dispensing into a clean beaker and place
a smaller waste beaker nearby.
4. Keeping the pipet vertical, immerse the tip into the solution and fill the pipet ¼ full using
the pipet bulb.
5. Remove the bulb, quickly placing your forefinger over the stem hole, and remove the
pipet from the solution.
Wipe the pipet tip clean with a tissue after removal.
6. Place the pipet in a horizontal position and rotate, allowing inside surfaces to be wetted
by solution.
Do not allow the solution to touch your finger closing the stem hole.
7. Return pipet to vertical position and drain the solution in the waste beaker.
Blow out as much solution as possible, using the bulb.
8. Repeat steps 4-7 to complete the rinsing process. The pipet is now ready for usage.
.

(Figure 6)

Now that your pipet is properly cleaned and prepared, follow these steps to ensure proper usage.

1. In the vertical position, depress the pipet bulb fully, immerse the pipet in the solution,
release pressure on the pipet bulb, and allow solution to fill pipet.
The pipet will fill with solution as you slowly decrease pressure on the bulb. You want the
solution to stop solution in the pipet just above the etched line. You do not want the solution to
overfill the pipet and go into the pipet bulb.
2. Remove the bulb and quickly place your finger over the stem hole to keep the solution in
the pipet.
Gently rotate the pipet on your finger, reducing pressure to allow the solution to be lowered to
8.     the desired level.
3. Place the pipet in the volumetric flask and release your finger so the solution will run out
freely.
When the pipet is empty, gently touch the tip to the side of the flask to dispense any remaining
solution.

Note: ―To deliver‖ (TD) pipets take into account the very small amount of solution left in the pipet. In
other words, ―leaving‖ this small amount of solution is okay—you should not blow out the
remaining solution in the tip of a TD pipet.

(Figure 7)

4.    Spectrophotometer

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The spectrophotometer is a commonly used analytical tool for chemists working with solutions. A
spectrophotometer measures how much light passes through a solution and — if the solute is colored
— this measurement can indicate the solution’s concentration.

When using a spectrophotometer, the solution is placed in a cuvette, a specially designed plastic
tube. The light source is a tungsten lamp that can shine specific wavelengths of light through the
solution. As the light passes through the solution, any light absorbing particles (i.e., any colored
particles) absorb their corresponding wavelength of light, and the remaining light goes through the
sample. The spectrophotometer can measure percent transmission (%T), the amount of light
transmitted through the cuvette, as well as absorbance (A), the amount of light absorbed before
reaching the other side of the cuvette. See Figure 8 for diagram of spectrophotometer

Spectrophotometer                               diagram of spectrophotometer
(Figure 8)

The mathematical relationship expressing the usefulness of a spectrophotometer is referred to as
Beer’s Law, where A is the solution’s absorbance (no units),  is the molar absorptivity constant
(L/mol  cm), b is the path length of the light (cm) and c represents the solution’s concentration
(mol/L).
A =  bc                                      (Equation 5)

You can see from Beer’s law that absorbance is proportional to concentration. In other words,
absorbance will be higher for a solution containing more light absorbing ions.

The spectrophotometer measures % transmission more accurately because it is calculated from a
linear function, in contrast to a logarithmic function for calculating absorbance. Nonetheless, we can
easily calculate absorbance from % transmission using the following mathematical relationship:
A = 2.000 - log (%T)                                    (Equation 6)

Let’s practice using Equation 6. 45.1% transmission of a 5.00  10 M tartrazine solution. What is
-5
A spectrophotometer indicates
the solution’s absorbance value?
A = 2.000 - log (%T)
A = 2.000 - log (45.1)
A = 0.346
Absorbance is 0.346

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Experimental Procedure
In this experiment, you will prepare a ―stock‖ solution of copper sulfate (CuSO 4 ) determine its molarity
by calculation. and absorbance by using spectrophotometer. You will then create several dilutions of
this ―stock‖ solution, measuring the absorbance for each. For the second half of the lab, you will
practice making serial dilutions, again from the stock solution. The overall purpose of the lab is to
compare conclusions you make from your experimental data to theoretical calculations based on the
equations discussed above.

This lab requires the following apparatus and reagents, which should be prepared in advance:

    Turner Model SP-830 Spectrophotometer
    one 100.0 mL volumetric flask
    four 50.0 mL volumetric flasks
    three 25.0 mL volumetric flasks
    one of each of the following pipets: 5.00, 10.00, 15.00 and 20.00 mL
    a pipet bulb
    five spectrophotometric cuvettes
    12 to 15 grams of anhydrous copper sulfate (CuSO 4)

A.       Preparing Stock Solution

First, you must create a known molarity copper sulfate solution:

1. Clean a 100 mL volumetric flask, rinse with deionized water, and determine the mass to the
nearest 0.001 gram, and record on data sheet.
2. Obtain 12 to 15 grams of anhydrous CuSO 4, place CuSO 4 in the flask, determine mass,
and record mass on data sheet..
3. Determine mass of CuSO 4 in the flask and record mass on data sheet
4. Fill the flask with 60 mls of deionized water, plug flask with stopper, and invert rapidly to
completely dissolve the CuSO4.
5. Use dropper and small beaker to fill flask with deionized water until the meniscus just
touches etched mark on the neck of the flask, and rapidly invert to insure complete mixing
6. Calculate the number of moles of CuSO 4, determine the molarity of the stock solution, and
record on data sheet.

Now you will calibrate your spectrophotometer and determine absorbance of your ―stock‖ solution:

7. Set the spectrophotometer to the assigned ―analytical wavelength‖ for the ―stock‖ solution.
8. Place a cuvette filled ¾ with deionized water into the spectrophotometer and calibrate to
100% transmission as demonstrated by your instructor.
9. Fill cuvette ¾ full with ―stock‖ solution, measure % Transmission and record on data sheet.
10. Calculate absorbance of the stock solution using Equation 6 and record on data sheet.

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B.         Preparing Dilutions, Measuring % Transmission and Creating Calibration Graphs

Now you will prepare five dilutions of your ―stock‖ solution:

1.    Clean five 50 mL volumetric flasks, rinse with deionized water, and label flasks #1 – #5.
2.    Refer to Figure 6 and 7 to review instructions for cleaning and using volumetric pipets.
3.    Clean and rinse the following four volumetric pipets: 5, 10, and 20 mL.
4.    Pre-rinse each pipet with a very small sample (10 mLs max.) of ―stock‖ solution.
5.    Referring to Table 1 below, use the cleaned and pre-rinsed pipets to prepare five dilutions.

Flask        volume of stock solution          total volume of solution
1            5.00 mL                           50.00 mL
2           10.00 mL                           50.00 mL
3           15.00 mL                           50.00 mL
4           20.00 mL                           50.00 mL
(Table 1)
Perform several molarity and dilution calculations then measure % Transmission each dilution:

6.    Calculate the molarity for each dilution using Equation 2 and record on data sheet.
7.    Calibrate the spectrophotometer to 100% transmission with deionized water as before.
10.    Measure and record % transmission for each dilution and record on data sheet.
11.    Using Equation 6, determine absorbance for each dilution and record on data sheet.

After calibrating the spectrophotometer and measuring % transmission for each dilution, you will
create a graphs to represent your data:

12. For your graph, plot absorbance (y-axis) versus molarity (x-axis), and produce a ―best
fit‖ trendline (see sample graph, Figure 9).

Absorbance versus Molarity
Absorbance

y = mx + b

Molarity (mol/L)

(Figure 9)

Next, you will compare your data to theoretical calculations of molarity
13. For each dilution, determine the ratio of the absorbance of ―stock‖ solution to absorbance
of the diluted solution. For example, to obtain this ratio for the first dilution, simply divide the
stock solution’s absorbance by the absorbance of the first dilution and record on data sheet.
14. Compare these absorbance ratios to the calculated dilution factors and explain your results.

C.     Performing Serial Dilutions and Measuring % Transmission

In this phase of the lab, you will prepare a serial dilution with ―stock‖ solution:

1. Clean and rinse three 25.00 mL volumetric flasks. Label the flasks A, B and C.
2. Prepare Solution A by dispensing 5.00 mL of stock solution with a properly prepared 5 mL
pipet into flask A. Dilute by filling flask A to the etched mark with deionized water. Mix
thoroughly by plugging flask and inverting at least five times.
3. Prepare Solution B by dispensing 10.00 mL of solution A with a prepared 10 mL pipet into
flask B. Dilute by filling flask B to the etched mark with deionized water. Again, mix well.
4. Prepare Solution C by dispensing 15.00 mL of solution B with a prepared 15 mL pipet into
flask C. Dilute by filling flask C to the etched mark with deionized water. Mix as before.
5. Using spectrophotometer, measure % Transmission of solution C and record on data sheet.
6. Calculate and the absorbance of solution C using Equation 6 and record on data sheet.

Finally, you will calculate molarity and compare with molarity based on your graph.:

7. Using Equation 2, calculate the molarity of solution A, B and C.
8. Using your graph, interpolate or calculate using y = mx + b the experimentally derived molarity
for solution C and calculate the % error between your calculated and experimental values and
record on the data sheet.

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___________________________________________________                                                      _______ _________________
Name (Partner):                                                                                                Section: Date:

Data Sheet Molarity and Dilutions

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------
-----------------

A. PREPARE STOCK SOLUTION
Chemical Formula of “stock” compound                                                    Copper Sulfate Anhydrous
Molar Mass of “stock” compound                                                                                                        gr/mole
Mass of flask + “stock” compound                                                                                                           grams
Mass ―stock‖ compound                                                                                                                      Grams
Moles ―stock‖ compound                                                                                                                      Moles
Molarity ―stock‖ compound solution                                                                                                                 M
Analytical wavelength “stock” solution                                                               625                                     nm
―Stock‖ Solution % Transmission                                                                                                               %
―Stock‖ Solution Absorption                                                                                                                    A

B. PREPARE DILUTIONS, CALCULATE MOLARITY &
ABSORPTION
Volume “Stock”                 Final Volume                      Molarity of                Measured
Solutions                                                Transmission.
#               (mL)                                                          (mols/L)                                             Absorbtion
(mL)                                                        (%)
1
2
3
4

B. COMPARE ABSORBANCE RATIOS TO MOLARITY

Dilution         Absorption (Abs) Ratio                    Calculated Dilution                       % Difference
#               ―stock‖/dilutions #                        Factor (DF)                     (( Abs Ratio - DF)/DF)*100
1

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2
3
4

How do the absorbance ratios (stock solution/diluted solutions) compare to the calculated dilution
factors? Explain ?
_______________________________________________________________________________________________
___
__________________________________________________________________________________________

_______________________________________________________________________________________________
___
__________________________________________________________________________________________

C. CALCULATING MOLARITY AND DILUTIONS FACTOR

%
Experimentally measured % transmission for third dilution – solution C

Experimentally calculated absorbance for third dilution – solution C

Calculated molarity first dilution – solution A                                    M

Calculated molarity second dilution – solution B                                   M

MOLARITY         Calculated: molarity third dilution – solution C                                   M

Experimental: molarity third dilution – from solution C and graph                  M

% Error: experimental versus calculated molarity of solution C                     %

_____________________________________________________________________________
Name:                                           Section:     Date:

Post Laboratory Problems—Molarity and Dilutions
1. A stock potassium dichromate solution (K 2Cr2 O7; MM=294.2 g/mol) is prepared for dilution by
dissolving 25.0 grams of K2Cr2O7 in a 500.0 mL volumetric flask. Then, 15.00 mL of the stock
K2Cr2O7 solution is placed in a flask and diluted to a final volume of 100.0 mL. Calculate the
molarity of the solution.

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2. How would you prepare 500.0 mL of a 0.750 M solution using the following chemical compounds:

a. Sulfuric acid (H2SO4) from 18.0 M concentrated liquid

b. Sodium carbonate (Na2 CO3 )

3. A solution of ethanol (C2H5OH) (d = 0.795 g/mL) and water (H2O) is prepared by placing 30.0 mL
of ethanol in a 250.0 mL volumetric flask and diluting with water to the flask etched mark.

a.   What is the molarity of the ethanol in this solution?

b.   Next, 25.0 mL of the solution above is diluted to a final volume of 500.0 mL. What is
the dilution factor associated with this solution?

c.   What is the new molarity of the diluted solution?

4. Why does a spectrophotometer measure % transmission more accurately than absorbance?

5. Define the following terms associated with Molarity and Dilution Factors:

   Solution:

   Solvent:

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   Solute:

   Absorbance

   Transmission:

   Dilution:

   Spectrophotometer:

   Serial Dilution:

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