Reaction Rates

• Up to this point in the course our concern with chemical equations has focused upon understanding, reactants, products, stoichiometry, and states.
• We have also looked at the energy associated with various reactions and physical processes, and we have also had a brief introduction to thinking about entropy associated with various physical processes.
• In the section on the solution process, we also began to think about the rates of the physical processes of dissolving and crystallization. The relative rates of these two processes determine whether a crystal dissolves, grows, or is in dynamic equilibrium

We are now going to begin to consider the reaction rates of the chemical reactions that we have been studying. This area of chemistry is referred to as chemical kinetics.

The rates of chemical reactions can be relatively fast, or slow, and can also be influenced by various factors, including:

• Concentrations of reactants. Generally speaking, the higher the concentration of reactants, the faster the rate of the reaction.
• The temperature. The higher the temperature, the faster the rate of the reaction.
• The presence of a catalyst. A catalyst is able to increase the rate of a reaction, although the catalyst itself is neither created nor destroyed when performing this function. Catalysts don't "cause" a reaction, they just speed it up.
• The surface area of the reactants or catalyst. Reactions that involve solids often proceed faster is the solid is a fine powder instead of big chunky bits. The physical difference between a fine powder, and big chunky bits, will be the surface area. (You typically will try to start a fire using kindling, and will not try to put a match to a large log)

"Speed"

• The speed of any activity (e.g. running, reading, cooking hamburgers, etc) involves quantifying how much you accomplish in a specific amount of time
• We can also quantify, or measure, the speed of a chemical reaction (also known as its reaction rate)

An example of a simple chemical reaction:

Let's assume that this reaction does not occur instantaneously, and therefore, it takes some time

• At the beginning of the experiment, our sample is composed 100% of the A molecules
  (Note: the start of experiments that measure reaction rates is usually referred to a "T₀")
• As time goes by, the A molecules are chemically converted into the B molecules
• Thus, over time, the number of A molecules in the sample decreases and the number of B molecules increases

The reaction rate is a measure of how quickly the A molecules (not the mass, for this is not a measure of stoichiometry) are consumed, or how quickly the B molecules are produced

• The reaction rate can be expressed by measuring the change in the number of A or B molecules per unit of time
• Numbers of molecules are quantified using moles (a convenient way to keep track of the large number of molecules in such experiments)
• Time is often seconds or minutes
• In the reaction of A -> B, the reaction rate can be determined by measuring the increase in the amount of the B molecules over time. (Note: conversely we could monitor the decrease in the levels of the A molecules). This is the average reaction rate, or "rate of reaction"

D(moles of B) = (#moles of B at end of time interval - #moles of B at start of time interval)

and

D(moles of A) = (#moles of A at end of time interval - #moles of A at start of time interval)

The following is a plot of some experimental data for this type of reaction. The plot displays time (in minutes) along the x-axis, and the number of moles of the A reactant and B product along the y-axis:

Notice a couple of things:

• As the amount of reactant A decreases, the amount of product B increases (just like the equation says!)
• The stoichiometry of the balanced equation is reflected in the concentrations of A and B: at each time point the number of moles of A plus B equals 1.0
• We started with 1.0 mole of A. According to the stoichiometry, if 0.70 moles of A have been used up in the reaction, it must mean that 0.30 moles of A remain and 0.70 moles of B have been produced (see the 40 minute time point)
• The rate of disappearance of A (or appearance of B) does not appear to be linear with time
• The reaction appears to slow down with time

We can determine the average reaction rate for each of the 10 minute intervals that data was collected:

• For the first 10 minute period, D(moles of B) = (moles of B at t = 10 min) - (moles of B at t = 0 min), and the time interval is 10 min
• The average reaction rate for the other 10 minute intervals in calculated similarly (Dt always 10 min)

Results of the calculation of the average reaction rate for the appearance of the B product:

• Note that the reaction rates have units of moles/min in these calculations (they describe the amount of the reaction in a unit of time)

How do the reaction rates for the formation of B relate to the reaction rates for the disappearance A?

• In the first 10 minutes, 0.026 moles of B were formed
• Thus, in the first 10 minutes, 0.026 moles of A disappeared, i.e. a negative reaction rate for the A component

The volume of reactions is typically held constant.

• Instead of monitoring the absolute number of moles during a reaction it is more common to monitor concentration during a reaction
• Reaction rates are therefore typically in units of M/sec, or M/min (i.e moles/L*sec, or moles/L*min)

The reaction of butyl chloride with H₂O to produce butanol and hydrochloric acid:

C₄H₉Cl(aq) + H₂O(l) -> C₄H₉OH(aq) + HCl(aq)

(A + B à C + D)

The experiment is setup in the following way:

• We start by preparing a 0.10 M solution of C₄H₉Cl in H₂O
• As soon as we mix the C₄H₉Cl in H₂O to make a 0.10 M solution we call that the T₀ timepoint and we start the clock running
• Then we measure the concentration of C₄H₉Cl at various times

Here's the raw data:

In the above graph we have determined the average reaction rate over the time period 300 - 400 sec. The general trend of the plot of [C₄H₉Cl] vs. time is not a straight line: the reaction slows down over time

• Therefore, when considering the period of time from 300 to 400 seconds, the reaction rate is faster at 300 sec and slightly slower at 400 sec
• The average reaction rate is the average over that time period

As we shorten the time period, there is less difference between the starting and ending reaction rates and the average reaction rate

• If the time period was infinitely small, the average reaction rate would be the instantaneous reaction rate for that time

• The slope of the tangent line is found by determining the rise/run for the line. Pick any two convenient time points and figure out Dt and D[C₄H₉Cl]

• In this case, at 350 sec the slope of the tangent line is approximately

• Since we are concerned with the disappearance of C₄H₉Cl, the reaction rate is the negative of the slope (i.e. -D[A]/Dt)
• Therefore, the instantaneous reaction rate at 350 sec for the disappearance of C₄H₉Cl is 1.6 x 10^-4 M/sec

In the above reaction the stoichiometry of the reaction is such that for every 1.0 mole of C₄H₉Cl reactant consumed we produce 1.0 mole of C₄H₉OH product.

What about for other reactions where the stoichiometry is not 1:1?

The reaction can be monitored by measuring the disappearance of HI(g) or by measuring the appearance of either the H₂(g) or I₂(g)

• However, one mole of either H₂(g) or I₂(g) will be produced for every two moles of HI(g) consumed
• Therefore, the rate of reaction of the consumption of HI(g) will be twice as rapid as the rate of production of H₂(g) or I₂(g)

• In other words, to correct the reaction rates for the stoichiometry we divide the rate for each component by their coefficient in the balanced equation

This general equation that describes the reaction rates normalized for the stoichiometry is termed the General Rate of Reaction or the General Rate Law