Ch. 1: Chemical Measurements

Outline:

• 1-1 SI Units

• 1-2 Concentrations in Chemistry

• 1-3 Preparing Solutions

• 1-4 Stoichiometry & Gravimetric Analysis

• 1-5 Introduction to Titrations

• 1-6 Titration Calculations

Scale of MeasurementsThe possible scale of measurements in analytical chemistry is astounding, ranging from the atomic level to the size of galaxies!

(a) Carbon-fiber electrode with a 100-nanometer-diameter (100 × 10−9 meter) tip extending from glass capillary. The marker bar is 200 micrometers (200 × 10−6 meter). [From W.-H. Huang, D.-W. Pang, H. Tong, Z.-L. Wang, and J.-K. Cheng, Anal. Chem. 2001, 73, 1048.] (b) Electrode positioned adjacent to a cell detects release of the neurotransmitter, dopamine, from the cell. A nearby, larger counterelectrode is not shown. (c) Bursts of electric current detected when dopamine is released. Insets are enlargements. [From W.-Z. Wu, W.-H. Huang, W. Wang, Z.-L. Wang, J.-K. Cheng, T. Xu, R.-Y. Zhang, Y. Chen, and J. Liu, J. Am. Chem. Soc. 2005, 127, 8914.]

An electrode with a tip smaller than a single cell allows us to measure neurotransmitter molecules released by a nerve cell in response to a chemical stimulus. Neurotransmitter molecules released from one vesicle (a small compartment) of a nerve cell diffuse to the electrode, where they donate or accept electrons, thereby generating an electric current measured in picoamperes (10−12 amperes) for a period of milliseconds (10−3 seconds).

SI Units

SI Derived Units

Unit prefixes

Converting between units

Careful with your units! *

In 1999, the $125 million Mars Climate Orbiter spacecraft was lost when it entered the Martian atmosphere 100 km lower than planned.

The navigation error would have been avoided if people had written their units of measurement. Engineers who built the spacecraft calculated thrust in the English unit, pounds of force. Jet Propulsion Laboratory engineers thought they were receiving the information in the metric unit, Newtons.

Nobody caught the error.The spacecraft was meant to enter an orbit 226 km above Mars’ surface. However, human error had the craft enter in at a much closer orbit of 57 km. On September 23, NASA lost communication with the orbiter., and one month later it was determined that the orbiter had disintegrated in the atmosphere.

Chemical Concentrations *Concentration: An expression of the quantity per unit volume or unit mass of a substance or how much solute per given volume (or mass) of solvent.

Solute: minor speciesSolvent: major species

Concentrations, as you well know, are normally expressed in terms of: molarity (M = mol L-1) or molality (m = mol solute per kg of solvent).

Electrolytes are substances that dissolve into ions in solution, and are classified as strong and weak. The formal concentration (F) is equivalent to molarity for only strong electrolytes.

Many students have concentration problems of two types: one pictured above, and one in handling their units during calculations! Lolz.

Other expressions for compositionVery often, the composition of one pure substance in a material or mixture is given by the per cent composition, which is normally expressed in terms of weight or volume.

Be sure you can convert from wt% to molarity!

Another common expression for composition is to use either parts per million (ppm) or parts per billion (ppb).1 ppm = 1 μg / 1 mL ≈ 1 μg / 1 g (for H2O)

Atmospheric CO2 now stands at approximately 380 ppm, which means that there are:

380 μg of CO2 per litre of air

weight% =msolute

msolvent

×100%

volume% =VsoluteVsolvent

×100%

ppm =msubstance

Vsample×106 ppb = msubstance

Vsample×109

Try these calculations:

37 wt% HCl, ρ = 1.19 g mL-1

What is the molarity of HCl?[H+] = 12.1 M

What is the molality of HCl?b = 16.1 m

Preparing Solutions *One of the most important pieces of laboratory glassware for preparing solutions is the volumetric flask. Typically, a solid (or liquid) reagent or standard is quantitatively transferred into the flask, followed by dilution to the mark on its narrow neck.

1. Add reagent, swirl and invert several times.

2. Dilute such that the meniscus rests just above the 500 mL marker

3. Make sure that the flask is very clean, as water droplets can stick to the upper neck, making the dilution less accurate

Dilution *Once you make a solution in a volumetric flask, you may be required to produce solutions of lower concentrations (i.e., diluting the sample).

A simple formula for conducting dilutions is:

In other words, to make up a specific volume of a diluted solution (Vdil) with a known concentration (Mdil) from a solution with a known concentration (Mconc), we would need a precise volume of the initial concentrated solution (Vconc).

Note that both sides of this equation give units of moles!

M conc ×Vconc = M dil ×Vdil

For instance:The HCl (conc) that is used in the lab is typically 12.1 M. What volume of HCl (conc) would one need to make a 0.100 M solution by diluting to 1.000 L?

(12.1 M) × (x L) = (0.100 M) × (1.000 L)

x = 0.00826 L = 8.26 mL

Gravimetric Analysis*Gravimetric analysis is a chemical analysis based upon the accurate weighing (massing) of a final product. This final product may be the pure substance for which we are conducting the analysis, or may be another pure substance which contains the element/compound that we are analyzing for.

Sample analysis: How much iron is there in an iron supplement tablet? *

1. Tablets containing FeC4H2O4 (iron (ii) fumarate) are ground and mixed with 150 mL of 0.100 M HCl to dissolve the Fe2+. The solution is the filtered to remove bits of particulate matter from the tablet.

2. The Fe2+ is oxidized to Fe3+ using an excess (XS) of H2O2.

3. The Fe3+ is reacted with NH4OH to produce a hydrous iron (III) oxide (FeOOH·xH2O), which is then heated at 900 oC to produce solid iron oxide (Fe2O3).

Titrations & Volumetric Analysis

Volumetric analysis is a chemical analysis based on accurate measurement of a volume of reagent that reacts with the analyte. Most often, this is accomplished via titration, where the reagent solution (the titrant) is added to the analyte.

The titrant is usually delivered via a buret, and one monitors the difference between the initial and final volume markings.

The equivalence point is reached when the amount of titrant added is exactly equal to the amount of analyte in the receiving flask. This point is actually a theoretical point - in fact, we never reach this, but rather hit the end point; the closer the end point is to the theoretical equivalence point, the better the result!

Finding the end pointThe end point is usually indicated by a change in physical property of the solution, which may include:

1. a colour change (by eye or spectrophotometric - this may arise from the substances themselves, or the presence of a reactive indicator

2. a change in current or voltage (potentiometric)

3. precipitation or dissolution of a substance

In the case above, the first trace of purple colour (i.e., excess MnO4-) signifies the end point.

Titration errors and standards

The difference between the end point and equivalence point is known as the titration error (or titration uncertainty), and is a fact of life! A rough estimate of the titration error can be obtained by running a blank titration, where the exact same procedure is conducted without the presence of the analyte (e.g., drip the MnO4- titrant into solution without the oxalic acid, and see how many drops are needed to actually make the colour change happen).

All titrations strive for accuracy, and the titrants are almost always made up of very pure substances (i.e., 99.9% or higher - known as analytical grade reagents). If the pure reagent is dissolved in a known volume to produce a solution of known concentration, this is called the primary standard.

In cases where primary standards are not available (e.g., titrations involving concentrated HCl), the titrant is prepared with an approximately known concentration, and then used to titrate against a pure analyte or primary standard in order to determine the precise concentration. This is known as standardization, and this type of titrant is called a standard solution.

Direct, back and gravimetricThere are numerous styles of titrations. The most common is the direct titration, in which titrant is added to the analyte until the completion of the reaction.

One may also perform a back titration, which is useful in instances when its end point is somewhat clearer than the endpoint for the direct titration. In this case, a known excess of reagent is added to the analyte solution, and a second standard reagent is use to titrate the excess reagent. One may also use a back titration in some cases where the end point is overshot during a direct titration (but not always!).

Finally, a gravimetric titration involves the delivery of the titrant from a pipette, and the careful monitoring of titrant concentration as moles of reagent per kg of solution (molality). The precision with a buret is ca. 0.3%, but with a good analytical balance this drops to 0.1%There are numerous styles of titrations. The most common is the direct titration, in which titrant is added to the analyte until the completion of the reaction.

One may also perform a back titration, which is useful in instances when its end point is somewhat clearer than the endpoint for the direct titration. In this case, a known excess of reagent is added to the analyte solution, and a second standard reagent is use to titrate the excess reagent. One may also use a back titration in some cases where the end point is overshot during a direct titration (but not always!).

Titration calculations*

The concentration of Ca2+ in urine can be determined via the following analysis:

1. Precipitate Ca2+ with oxalate in basic solution.

2. Wash with cold water to remove oxalate, and then dissolve the solid in acid to obtain Ca2+ and H2C2O4 in solution.

3. Heat the solution to 60 oC and titrate the oxalate with KMnO4 until the purple endpoint is observed.

There are numerous styles of titrations. The most common is the direct titration, in which titrant is added to the analyte until the completion of the reaction.

One may also perform a back titration, which is useful in instances when its end point is somewhat clearer than the endpoint for the direct titration. In this case, a known excess of reagent is added to the analyte solution, and a second standard reagent is use to titrate the excess reagent. One may also use a back titration in some cases where the end point is overshot during a direct titration (but not always!).

Summary

The major areas covered in this lecture:

• SI Units - be able to use derived units, and interconvert

• Expressions for concentration - molarity and molality are the most common

• Gravimetric analysis - considerations of stoichiometry and masses of starting reagents and end products are crucial!

• Volumetric analysis - volume of titrant needed for a stoichiometric reaction of the analyte is the key point here

• Titrations - the use of primary standards, the meaning of equivalence point and end point, and direct and back titrations

There are numerous styles of titrations. The most common is the direct titration, in which titrant is added to the analyte until the completion of the reaction.

One may also perform a back titration, which is useful in instances when its end point is somewhat clearer than the endpoint for the direct titration. In this case, a known excess of reagent is added to the analyte solution, and a second standard reagent is use to titrate the excess reagent. One may also use a back titration in some cases where the end point is overshot during a direct titration (but not always!).