Chemical Concentrations and Preparing Solutions
• Percent compositions
• Other expressions of concentrations
• How to prepare a solution
• Correction for thermal expansion
• How to calibrate volumetric glassware
• Significant figures in arithmetic operations
• Amount of analyte (solute), n = CV
◦ n = number of moles of analyte (mol)
◦ C = concentration of analyte (mol/L or M)
◦ V = volume of the solution (L)
• In dilutions:
◦ n is constant
◦ C V1= 1 V 2 2
▪ 1 denotes original solution
▪ 2 denotes diluted solution
Expressions of Concentration
• Equilibrium molarity (M): → eqm molarity of HCl in 2.0M sltn = 0M
molesof solute massof solute
• Formal concentration (F): litresof solution = FM xvolume
◦ independent of analyte composition in solution
▪ (FM = formula mass = molecular mass)
• Not to be confused with molality (m): kg of solvent
→ Molality is independent of temperature (based on weight)
→ Molarity changes with temperature
Effect of Temperature
• Water expands by 0.02%/degree nearo20°C
◦ Molarity changes by -0.02 %/ C
◦ concentration decreases as temperature increases
• Pyrex and other borosilicate glasses expandby 0.0010%/degree near room temperature.
◦ for most work, this expansion in insignificant
• Assume that the thermal expansion of a dilute solution is equal to that of pure water Correction for thermal expansion of solutions
C '= C
• Acorrection is possible because C is proportional to density: d ' d
• C and d at original temperature
• C' and d' at new temperature
• See Table 2-7 for density of water at different temperatures
Example: correcting concentration for a change in T
A0.03146 M solution was prepared when the temperature was 17°C. What is the molarity of this
solution when the
temperature is 25°C?
C ' C C ' at25 C 0.03146M
d '= d → 0.99605g/ml =0.99878g/ml → C' = 0.03141M
→ The concentration would decrease by 0.16% on the warm day
What is wrong with this demonstation of how to dilute a solution?
• Calibrated to deliver the most accurate fixed volume
• Relatively difficult to use compared to displacement pipets (i.e., micropipets)
• Have to be cleaned
Displacement pipets and syringes
• Easier to use than transfer pipets
• Require more frequent calibration than transfer pipets
◦ piston and spring need to be replaced regularly
• Less accurate than transfer pipets (1-2% uncertainty)
• calibrated to contain a volume of water at 20 C when bottom of meniscus at centre of
Calibration of a pipet
• Weigh an empty weighing bottle.
• Pipet water with a pipet into the weighing bottle.
• Note the lab temperature.
• Use Table 2-7 to convert the mass into a true volume.
Example: calibration of a pipet
If the mass of the weighing bottle is 10.313 g and it weighs 35.225 g with the pipetted water when the
temperature is 27°C, what volume was delivered by the pipet?
mass of water = 35.225-10.313 = 24.912 g
volume = mass * volume of 1 g of water at 27°C
volume = 24.912g * 1.0046mo/g