# Statistics and Chemistry Lesson of the Day – Illustrating Basic Concepts in Experimental Design with the Synthesis of Ammonia

To summarize what we have learned about experimental design in the past few Applied Statistics Lessons of the Day, let’s use an example from physical chemistry to illustrate these basic principles.

Ammonia (NH3) is widely used as a fertilizer in industry.  It is commonly synthesized by the Haber process, which involves a reaction between hydrogen gas and nitrogen gas.

N2 + 3 H2 → 2 NH3   (ΔH = −92.4 kJ·mol−1)

Recall that ΔH is the change in enthalpy.  Under constant pressure (which is the case for most chemical reactions), ΔH is the heat absorbed or released by the system. Knowing that iron is used as a catalyst in many chemical reactions, a chemist thinks that iron can also catalyze the Haber process.  Thus, she hypothesizes that the catalyst can decrease the reaction time for a given amount of ammonia produced.  To use experimental design’s terminology,

• the experiment seeks to determine if there is cause-and-effect relationship between the presence of iron and reaction rate in the Haber process
• the experimenter hypothesizes that the presence of iron results in a smaller amount of time needed to produce a unit of ammonia
• the explanatory variable (or factor) is iron as a catalyst
• the 2 levels of this binary factor are presence or absence in the Haber process
• the response variable is the reaction time
• the experimental unit is the mixture of nitrogen gas and hydrogen gas in a reaction vessel

Since there is 1 binary explanatory variable in this experiment, there are 2 treatments, and each treatment is simply each level of the factor.

There are 20 reaction vessels in this experiment: 10 vessels have no iron catalyst (this is the control group), and the other 10 vessels have the iron catalyst (this is the experimental group). The control group in this experiment is a negative control group; no result is known in advance, and the results from the experiment group must be compared to the results from the control group in order to establish any cause-and-effect relationship between the presence of the iron catalyst and reaction time.

• To control for any confounding variables, the reactions are performed using the same reaction vessels under the same pressures and temperatures.  The nitrogen and hydrogen are mixed thoroughly as individual reactants before being put into the vessel; this ensures that a random sample of molecules from nitrogen gas and hydrogen gas are put into each group.  The same number of moles of nitrogen and hydrogen are used as reactants in both vessels.
• There are 10 vessels in each treatment to introduce replication.  The average reaction times between the 2 treatments will be compared to each other, and the average is a better estimate of the true reaction in each treatment if there are more replicates (i.e. a large sample size).
• Choosing the number of levels for the factor is obvious and trivial in this experiment; there is only 1 factor, and it has 2 levels.
• This is a completely randomized design with 1 factor.  The experimental units are randomly assigned to each treatment.
• The difference in the reaction times between the 2 groups can be tested for statistical significance with an independent 2-sample t-test or an F-test under a single-factor ANOVA model – recall that the results between these 2 tests are equivalent.

The experiment shows that the vessel with iron produces ammonia with a significantly small amount of time.  Thus, the results of this experiment provides evidence to suggest that the presence of the iron catalyst causes a higher reaction rate.  (I’m careful with the wording in this last sentence because this inductive conclusion cannot be proven; it can only accumulate evidence to support the underlying theory, and the theory becomes stronger as more evidence in favour of it is collected.)

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