LabLulz: densitometry of hydrogen purr-oxide

Today in LabLulz, I’m going to walk through a recent preparation I did in my chemistry lab: increasing and measuring the concentration of hydrogen peroxide.

WARNING: This procedure involves heat and the end product is a powerful oxidizer. Don’t get burned and don’t get it on yourself – wear gloves, splash-resistant goggles, and an apron. I had a spill of ~15%, all over everything, including myself. It was okay, but only because I followed safety protocols. I didn’t have the apron though, and I had to get pantsless.

Hydrogen peroxide is an interesting substance; it’s formula is H2O2, meaning that it is composed of two hydrogen atoms bonded to two oxygen atoms.

Figure 1. Behold, the hydrogen peroxide molecule!

It is a powerful oxidizer, decaying into water and free oxygen. This is because the bond between the two oxygen atoms, called the peroxide bond, is unstable. Some substances which contain the peroxide bond are even explosive, like triacetonetriperoxide. Because it’s an explosive precursor, and somewhat dangerous on its own, concentrated hydrogen peroxide can be difficult to come by. The weak 3% solution found in drugstores is all that is available to DIYers, hobbyists, and other scientists outside of the mainstream chemical supply chain.

Fortunately, it is relatively trivial to increase the concentration from 3% to around 30%. There are several tutorials on the subject at YouTube (TheChemLife; zhmapper, nerdalert226) so I’m going to focus on measuring the concentration of the end product, a procedure which the videos tend to treat very qualitatively. I hope this tutorial will be informative and useful, even outside of punklabs; the process is easily generalized and density is important in many fields, including medicine and winemaking.

The concentrating procedure is pretty simple: pour about 500 mL of the 3% solution into a beaker and heat it, forcing the excess water to evaporate until there is a tenth as much liquid left (peroxide boils at 150 C, compared to 100 C for water.) There are only a couple of tricky points: the liquid must NOT boil, only steam – if it starts boiling, the peroxide will decay. Bits of dust and dirt will also cause disintegration, so the equipment must be kept very clean and free from scratches.

Okay, so after a few hours, I have about 50 mL of liquid. I drop a bit into a solution of corn starch and potassium iodide, and the mixture turns black, a positive test for oxidizers. I add a squirt to some sulfuric acid and copper wire, and the metal wire begins bubbling and the solution begins to turn blue with copper sulfate*. This reaction is faster and more vigorous than when I try it with the 3% solution, so I’ve clearly succeeded in increasing the concentration, but to what level? To answer that question, I’m going to measure the density of the solution.

Figure 2. The Densitometry Setup. Note the safety equipment. Note also the lab notebook, which is essential. Other sights include a bit of iron oxalate, tongs, and a desiccator.

Here’s my setup. I don’t have a nice buret with a stopcock, so instead I have repurposed a graduated medical pipette (I picked up a huge box of these at the Scrap Exchange). This is controlled with a valve and a syringe plunger. It’s a little drippy and derpy, not great for dispensing a planned volume, but it works fine to measure the amount that has been dispensed, which is sufficient for our purposes. The milligram scale was lent to me by a friend after armed thugs stole my old one (thanks, B!) The brown glass vial is good for containing peroxide, since light speeds up its decomposition.**

Once the room and the beaker are at the same temperature (20 deg C), I draw about 8 mL of my peroxide up into the pipette, and start adding peroxide a bit at a time. By the time I had figured out the fluidics system, I’d added about 3.0 mL, so that’s where the data start. I then would squirt a bit of peroxide into the vial, note the volume and the mass, and repeat. I took 8 different measurements this way.

Then, after I put everything away and cleaned up, I sat down with a cup of coffee for a bit of data entry.

Figure 3. Data, in analog and digital form. This is a page from my lab notebook, and the spreadsheet in gnumeric (inset).

I usually store my data in spreadsheets, and my processing and analysis with Python. Once the spreadsheet file is ready, I get started and load up my data.

$ ipython –pylab

In [1]: import xlrd
In [2]: phial = xlrd.open_workbook('densityData.xls')
In [3]: data = phial.sheet_by_index(0)
In [4]: raw_volume = data.col_values(1)[5:]
In [5]: raw_mass = data.col_values(3)[5:]

Next, I take a quick peek at the data just to make sure that everything is as expected.

In [6]: plot(raw_volume, raw_mass, 'bo')

Figure 4 Plotting the raw data.

Looking good; the data are nice and linear, meaning that the slope (and therefor the density) is well defined. But this is the raw data, which include the mass of the bottle. I also didn’t start at zero on my pipette, just wrote down the volume the liquid was at when I took each mass measurement. It doesn’t matter too much, but strictly speaking, we want to compare just the mass of the liquid in the bottle to the volume of liquid drained from the pipette. Let’s go ahead and calculate that (it’s a lot like calculating temperature anomaly.)

In [12]: volume = array(raw_volume) - 3.0*ones_like(raw_volume)
In [12]: mass = array(raw_mass) -9.988*ones_like(raw_mass) 

Much better. Now, to get some basic statistics on these data, let’s apply a linear regression.

In [13]: from scipy import stats
In [16]: (m, b, r, p, std) =stats.linregress(volume, mass)
In [17]: (m, b, r, r**2,  p, std)

Out[17]:
(1.1189534883720933,
0.067450581395348319,
0.99932418729044048,
0.99864883130369941,
7.7125664942037092e-10,
0.01680292147514929)

It’s mostly the slope, m = 1.12 g/mL, which we’re interested in.

In [16]: linFit = polyval([m,b], volume)
In [29]: plot(volume, linFit, 'r-')
In [30]: plot(volume, mass, 'bo')
In [31]: title('Mass vs. Volume for H2O2')
In [32]: xlabel('Volume (mL)')
In [33]: ylabel('Mass (g)')
In [36]: text(1.25, 4.5, 'M = %fg/mL*V + %fg'%(m,b))

Figure 4. The mass of peroxide is plotted as a function of its volume, and a linear regression applied.

Now that we have the density, we can use this graph from H2O2.com.  (It’s derived from Easton et al 1952. The paper actually reports on density measurements at 0, 10, 25, 50, and 96 degrees, so these are probably interpolated curves).  We’ll draw a horizontal line at the measured density (~1.12 g/mL) until we hit the curve corresponding to the temperature (20C). Then we draw a vertical line and read off the concentration where it crosses the horizontal axis. Result? The concentration is about 32%. (Figure 5)

Figure 5.

You may wonder why I went through so much trouble of taking multiple data points and calculating a trend line. If density is defined as mass per volume, then surely I can measure it in one go, by massing a single sample of known volume. Right? The problem is that any one such measurement might be a little wonky. Maybe one fewer drop than usual wiggled out, or a draft of air was pushing down a little on the scale. Look back at Figure 4; see the data point third from the end, visibly above the trend line? If I was only taking one measurement, I might get unlucky enough to get an outlier like that one.  By using a linear regression, I can aggregate the data, and hopefully all those small outside factors will tend to cancel out.

Another reason is that the linear regression allows us to calculate uncertainty in the slope of the line, and therefor in the density. There are good online explanations of this, so I’m just going to churn through the equations.

In [26]: N = len(volume)
In [27]: unc = std *sqrt(N/(N*sum(volume**2)-sum(volume)**2))
In [28]: unc
Out[28]: 0.005463100999105781

We can thus report the density as 1.119 +/- 0.005 g/mL. If we wanted, we could use the uncertainty in the density to calculate the uncertainty in concentration the same way we calculated the concentration estimate: plot lines at 1.119 + 0.005 g/mL for the upper bound, and 1.119 – 0.005 g/mL for the lower bound and work backwards to get a confidence interval of concentrations. In our case though, the uncertainty is so small that it’s about the width of the original line not really worth propagating.

I feel comfortable just calling this 32% peroxide. Success!

* An easier, quicker test is to add peroxide to a catalyst that causes it to decay, but I didn’t have any manganese dioxide or horseradish on hand. Also, everyone loves copper sulfate.

** This is really a moot point, since I am keeping this sample in the fridge, and there is not even a lightbulb to philosophize about. But it’s also why you buy peroxide in opaque bottles.

~~~

Easton, M., Mitchell, A., & Wynne-Jones, W. (1952). The behaviour of mixtures of hydrogen peroxide and water. Part 1.?Determination of the densities of mixtures of hydrogen peroxide and water Transactions of the Faraday Society, 48 DOI: 10.1039/TF9524800796

Graphing Out Loud: ups and downs

A while back, we started looking at a poorly thought-out article from the website C3Headlines. C3 is starting to make a name for itself as a goldmine of climate comedy- their claims have recently been addressed at Tamino and SkepticalScience.

We’re going to keep digging into C3‘s claim that carbon dioxide concentrations have been increasing linearly over the 20th century. They seemed to draw this claim by eyeballing the graph of CO2 concentrations and qualitatively describing them as linear, apparently using the inset in their first figure to compare linear, quadratic, and exponential trends. This is a faulty method: it’s an elementary fact of calculus that ANY smooth curve, when viewed appropriately, will appear linear. The point has already been made but it’s worthwhile to keep looking because there are some interesting graphical follies at play; examining them further might help us understand how and why graphs are misunderstood.

Figure 1: From C3Headlines’ article on “The Left/Liberal Bizarro Anti-Science Hyperbole”, which claims that CO2 concentrations are increasing linearly. Click to read it, if you dare…

C3‘s second graph in this article measures the change in atmospheric CO2 by calculating a month-to-month percentage change. It’s not entirely clear why they are using a percent change, rather than the standard practice of expressing rate of change as concentration change per year (like the source of their data uses). Whereas ppm/year is an absolute measure, each datum generated by the percentage-change method depends strongly upon the value of the previous month. As a measure of long-term rate of change, it is a bit questionable.

My primary concern, though, is with their use of monthly data in the first place. In my last article, we noted that, without explanation, C3 confined their focus to January CO2 concentrations. Were they consistent, they’d also look at January rates of change – of course, doing so might lead to unacceptable conclusions.

 Figure 2. Rates of CO2 accumulation have been calculated for the month of January, consistent with earlier investigation of January CO2 concentration. Over the period of observation, rates have increased at a significant (P~0.0005) acceleration of 0.11 ppm/year^2. Monthly rates throughout this article have been calculated by considering the change in CO2 between adjacent months, and assuming that a month is 1/12 of a year. Interpolated values of CO2 were used to avoid annoying data holes early in the record.

Instead, they look at the rate of change for every single month on record. Why do I find that problematic? Well, let’s look at the full record, with monthly resolution:

Graphing Out Loud: curves and lines

I love graphs – my eyes quickly glaze over at a table of numeric data, but a graph, used correctly, can quickly and easily tell the whole story.

‘Used correctly’ is the key phrase – for all their power, graphs are infamously easy to bungle, and when used incorrectly they can misinform – or lie outright.

I’m going to look at an example that touches on a few graphical and statistical concepts near and dear to my heart, as well as carbon geochemistry.

Fig. 1: An image from C3Headlines; the 3 C's are "Climate, Conservative, Consumer". Oh, and the article is titled "The Left/Liberal Bizarro, Anti-Science Hyperbole Continues". It sure would be tragic if they made obvious n00b mistakes after using such language. Click for link!

Coming from an article on the website C3Headlines, this image claims that carbon dioxide concentrations have ‘Linear, Not Exponential Growth’. thereby ‘expos[ing] the lunacy of typical left/liberal/progressive/Democrat anti-science’, The author has reached this conclusion by graphing January CO2 levels* and fitting a linear trendline to them.

Already this is a warning sign – the comparisons the author makes are entirely qualitative, apparently  based up on eyeballing the graph. However, trend lines are created by a statistical process called a linear regression, which comes with a caveat: it will fit a trend line to ANY data given to it, linear or nonlinear. Fortunately, there are also ways of evaluating how good a trend line is.