To make 100 ml of 20 ppm Pb (for example) solution, begin by determining how many milligrams of Pb must exist in 100 g of 2% HNO_{3} to achieve the required strength. Remember that concentration is always determined by weight, but to do the calculations simply, we make the reasonable assumption that even a 1000 mg/l primary standard solution has a density very close to 1 g/ml and write:

(20 mg/1000 ml) = (X mg/100 ml)

From the left, 20 mg/1000 ml is the desired concentration of 20 ppm (assuming that 1000 ml weighs 1 kg, or that the density = 1 g/ml). On the right we have an expression involving the unknown amount of Pb to be placed in 100 ml (or g) of standard solution, making the same assumption as before. Solve for X:

X = 2 mg.

So, 2 mg of Pb in enough 2% HNO_{3} to make 100 ml of solution will yield a 20 ppm standard. From the 1000 mg/l concentration of the primary standard, we know that 2 mg of Pb is contained in 2 ml of primary standard solution.

**1000 mg/l means that you have [1000 mg Pb]/[1000 ml sol'n]. Divide numerator and denominator by1000 to get [1 mg Pb]/[1 ml sol'n].**

At this point, take the clean, dry, bottle you plan to use -- with the tightly-fitting screw cap in place -- to the balance; weigh it to four decimal places and record the results. You may wish to handle it with disposable examination gloves to avoid changing its weight with your fingerprints. Then use a pipette to deliver 2 ml of the 1000 ppm primary standard to your standard bottle.

**NOTE:** Use good pipetting technique:

**NEVER** draw liquid into a pipette by using your mouth; it is extremely unsafe practice to do so.

**ALWAYS** use a rubber bulb to charge your pipette.

**NEVER** pipette directly from the original standard container: To do so contaminates the remaining standard, and the fact that this has been done will not be apparent to subsequent users!

**ALWAYS** pour a small amount of standard into a cleaned beaker and pipette from that. Alternatively, if the amount required is relatively large (1 ml or greater), use a clean graduated cylinder.

**NEVER, EVER**, return any unused portion of standard to the original bottle! **ALWAYS** discard it!

Put the cap back on your bottle and weigh again using examination gloves if you wish (I do); record the results. Now subtract the 2 ml of liquid already added from the 100 ml desired and add this amount of 2% HNO_{3} to your standard bottle; in this case we add 98 ml. Use any convenient volumetric vessel to measure the acid -- I use a graduated cylinder. Weigh again with the cap in place and gloves on your hands, and record the results. I got these values:

Bottle + cap + Primary standard + HNO3 = 118.7415 g

Bottle + cap + Primary standard = 21.2615 g

Bottle + cap = 19.2694 g

The reason the weighing is done is because volumetric technique does not have sufficient accuracy for our purposes. In volumetric technique, much depends on ambient temperature, the skill of the operator, and the condition of the glassware, among other things; but even under the best of circumstances the accuracy possible using a weighing technique cannot be approached. The error introduced by assuming solution densities to be 1 g/ml is miniscule, occurring in the fifth decimal place or so, and certainly well below our ability to see it with the DC plasma spectrophotometer.

Now subtract the weight of the bottle + cap from each of the other two values to find out how much primary standard you actually used, and how much solution you have:

Weight of solution 99.4721 g

Weight of standard 1.9921 g

Making our now familiar assumption, these can be considered to be equivalent to volumes in milliliters and we now work the original proportionation problem in reverse to find out the concentration of the solution we actually made:

(X mg/1000 ml) = (1.9921 mg/99.4271 ml)

X = 20.0267 mg

Notice that in the numerator on the right side of the first expression, 1.9921 mg refers to the actual amount of Pb in the solution. Because the concentration of Pb in the primary standard is 1000 ppm, 1.9921 g of this liquid contains 1.9921 mg of Pb. Rounding to two decimal places, all that the DCP can see if you threaten it with a gun, we have: X = 20.03 mg. Because this is the equivalent amount of Pb contained in 1000 ml, or 1 kg, of solution, this is also the actual concentration of your standard in mg/l.

If you wish to make a standard "cocktail," that is, one having more than one element of interest, the procedure is essentially the same but with the following caveats: First, you must weigh and record the results after adding each standard material to the vessel. Concentrations are calculated in the same manner as above, assuming that each element is diluted by all of the other liquid added. Second, you calculate the amount of 2% HNO_{3} required as diluent by summing all of the standard volumes used,and subtracting from 100 ml. Third, you must be careful in designing your standards that all of the concentrations you desire are actually obtainable: Each standard is diluted not only by the 2% HNO_{3} added, but by all of the other standards added also. Using the stock standard concentrations of 1000 mg/l it is not possible to make a working standard with a total concentration of all elements greater than that value. It is therefore not possible to make a cocktail having 750 mg/l of one element and 300 mg/l of another -- the total concentration adds up to more than 1000mg/l. There do exist primary standards with concentrations higher than 1000 mg/l, and these may be purchased and used if necessary. Fourth, be very careful that the chemical compound used to make up the standard for a particular element does not also contain other elements of interest. Cr standards, for instance, are commonly made up using K_{2}Cr_{2}O_{7}, or the Na analogue, and would not be compatible with a cocktail that includes potassium (or sodium, as the case might be) as an element of interest. Some standard makers print this information on the bottle labels, but many do not, and it may require a telephone call to the manufacturer to sort the matter out.

As in the case of parts per million, parts per hundred, percent, is always reckoned by weight. In working with concentrated solutions, such as stock solutions of acid, the density of the liquid is significant and cannot be assumed to be 1 g/ml. In making a 1% nitric acid solution -- We will begin with a 1% solution for simplicity -- you will need to know both the percent concentration of the stock solution, and the density. These are printed on the bottle label. The stock that I used had these characteristics:

Percent concentration: 70.3% HNO_{3}

Density: 1.426 g/ml

The percent concentration means that we have 70.3 g of HNO_{3} in 100 g of stock solution. Using the density, we convert the "100g" of stock to more easily measured ml:

(100 g/1.426 g/ml) = 70.2 ml

We can summarize what we have done by writing:

(70.3 g HNO_{3}/100 g stock) = (70.3 g HNO_{3}/70.2 ml stock)

On the right side of this expression we make the observation that 1 g HNO_{3} is very conveniently contained in 1 ml of stock solution, to a close approximation. To make a 1% solution of HNO_{3}, we need 1 g HNO_{3} in 100 g of solution. Generally when one is making a solution measured in percent, as is this, he is not making a Swiss watch, so a 1% concentration may be considered sufficiently dilute to dispense with further density considerations, and we place 1 ml of stock solution in 99 ml of distilled/de-ionized water to make 100 ml of 1% HNO_{3}.

**Note:** There are dangers when making acid solutions:

**ALWAYS** add acid to water, **NEVER** the reverse, and **ALWAYS** wear eye protection and a lab apron when handling acid.

Increase the amounts used proportionately in order to make a larger quantity. Observe that 2 ml of this stock solution in 98 ml of distilled/de-ionized water would make 2% nitric acid, and so forth. It is generally recommended that standards and samples be diluted with, and that blanks consist of, 2% HNO_{3}.

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