Reaction Rates

Rate of Reaction Definition

When you watch any process occur, you are simultaneously observing two fields of chemistry. The first is the field of Thermodynamics, which covers whether something is actually possible. The second field is Kinetics, which measures how quickly something will happen. The speed of a reaction is determined by a couple of factors, which constitute the rate of reaction.

The diamond example highlights perfectly how important measuring the rate of reaction is. Even if a reaction is spontaneous (thermodynamically allowed), if the rate is too slow, then it won't be observed happening. Conversely, if a reaction is quick, then it might be too fast to observe. Ionic reactions, for example, are so quick that they have to be observed with special equipment, like spectrometers. These devices use light to detect changes in a sample. Some reactions are faster than 1.0 x 10^-12 s, which is 0.000000000001 seconds!

So, by now we've seen fast and slow reactions, but how is rate calculated? Well, fortunately, the rate calculations are simple.

Rate of Reaction Formula

We said earlier that reaction rate was a measure of concentration vs. time. Well, let's visualize what the rate of reaction formula looks like with the following reaction:

$$ H_2 (g) + I_2 (g) \rightarrow 2 HI (g) $$

In a forward reaction, the reactants are being consumed to form the products.

$$ Rate ~ = - \frac { \Delta [H_2] } { \Delta t } = - \frac { [H_2]_{t_2} - [H_2]_{t_1} } { t_2 - t_1 } $$

The reaction rate measures the changes in concentrations at times, t₁ and t₂. The negative sign in the expression represents the negative change in reactant concentration because as the reaction proceeds, the reactants disappear. A negative sign in the reaction rate will make the rate of reaction a positive expression. Using the same logic, the products' concentration will be increasing as the reaction moves forward. As such, the rate expression for the products will be positive.

To ensure that the rate is the same for every species, each species must be divided by its stoichiometric coefficient.

$$ + \frac {1} {2} \frac { \Delta [HI] } { \Delta t } $$

In the formation of HI, two moles of HI are being produced for each mole of H₂ and I₂. In other words, HI is being produced at twice the rate as the decomposition of each reactant.

To provide a general formula for the overall reaction, we will use this general reaction formula:

$$ aA + bB \rightarrow cC + dD $$

In this formula a, b, c, and d, are all stoichiometric coefficients, and A, B, C, and D are the chemical species. These can be applied to a general reaction formula as follows:

$$ \text {Rate} = - \frac {1} {a} \frac { \Delta [A] } { \Delta t } = - \frac {1} {b} \frac { \Delta [B] } { \Delta t } = + \frac {1} {c} \frac { \Delta [C] } { \Delta t } = + \frac {1} {d} \frac { \Delta [D] } { \Delta t } $$

This formula shows us that the concentration of one species can elucidate the concentration of any other species at that given time interval. This is all made possible through the stoichiometric coefficients. So, by knowing the balanced chemical equation, you can calculate the concentration of any other species.

Rate of Reaction Units

If you are ever confused about the units which can be used for reaction rate, it may be helpful to look at the formula. In the formula, concentration is being divided by time. But, in reality, it's a change in concentration vs. a change in time. How does this affect the units in the rate? Well, it doesn't. Look at this example to get a better idea (note, the calculation below involves a dimensional analysis only).

\begin{align}\text {Rate} &= \frac { \Delta Conc. } { \Delta time } \\\text {Rate} &= \frac { C_{final} - C_{initial} } { t_{final} - t_{initial} } \\\text {Rate} &= \frac { mol~L^{-1}_{final} - mol~L^{-1}_{initial} } { s_{final} - s_{initial} } \\\text {Rate} &= \frac { mol~L^{-1} } { s } \\\text {Rate} &= mol ~ L^{-1} ~ s^{-1}\end{align}

The units for reaction rate are typically mol L^-1 s^-1, but you may see them written with some other units. The important thing to note is that reaction rate measures concentration vs. time. So, they will likely always be in this form.

Rate of Reaction Calculation

Now that we're familiar with the general formula for reaction rate, we can do a rate of reaction calculation. Use the following balanced equation to determine the average rate of reaction.

$$ H_2O_2 (aq) + 3 I^- (aq) + 2 H^+ (aq) \rightarrow I_3 ^- (aq) + 2 H_2O (l) $$

In the first 10.0 seconds, the concentration of I^- decreased from 1.000 mol L^-1 to 0.868 mol L^-1. So, we know the concentration and the time interval for I^-. Now we can input it into our rate equation to determine the rate of reaction.

\begin{align}\text {Rate} &= - \frac {1} {3} \frac { \Delta [ I^- ] } { \Delta t } \\&= - \frac {1} {3} \frac { ( 0.868 ~ mol ~ L^{-1} - 1.000 ~ mol ~ L^{-1} ) } { ( 10.0 ~ s - 0.00 ~ s ) } \\&= - \frac {1} {3} \frac { (- 0.132 ~ mol ~ L^{-1} ) } { ( 10.0 ~ s ) } \\\text {Rate} &= 4.40 \times 10 ^ {-3} ~ mol ~ L ^{-1} ~ s^{-1}\end{align}

Now that we have our rate, what if we want to figure out the concentration of some other participant in the reaction? Let's try calculating the rate of change in H⁺ during the first 10 seconds.

\begin{align}\text {Rate} &= - \frac {1} {2} \frac { \Delta [ H^+ ] } { \Delta t } \\-2( \text {Rate} ) &= \frac {1} {2} \frac { \Delta [ H^+ ] } { \Delta t } \\\frac {1} {2} \frac { \Delta [ H^+ ] } { \Delta t } &= -2( 4.40 \times 10 ^ {-3} ~ mol ~ L ^{-1} ~ s^{-1} ) \\\text {Rate} &= -8.80 \times 10 ^ {-3} ~ mol ~ L ^{-1} ~ s^{-1}\end{align}

You aren't given the initial concentration of H⁺, so all you can do is calculate the rate of change for the hydrogen cations. As an exercise, try calculating the rate of change for the other species. What trends do you notice when calculating the rate of change for the products?

Factors Affecting Rate of Reaction

The rate of reaction is something which can vary a lot under different conditions. There are numerous factors affecting rate of reaction, but we will only discuss a few. These are some factors affecting rate that we will discuss:

• Physical State of the Reactants
• Concentration of Reactants
• Temperature of the System
• Catalysts

Effects of Physical State on Reaction Rate

The first factor is the physical state of the reactants.² As you know, gas molecules diffuse quickly, while solids simply just vibrate. This means that if a molecule moves around a lot, it has a higher chance of coming into contact with something which it will react with. This can be observed when assessing homogeneous vs. heterogeneous reactions.

Heterogeneous reactions are often limited by the amount of surface area on the solid, which greatly impacts the rate.

Effects of Concentration on Reaction Rate

Another factor which may affect the rate of reaction is the concentration of reactants. This may have already been obvious, since concentration is one of the variables in our rate expression. But, it is important to understand why concentration matters. If you were to add one grain of salt and one drop of water into a bucket, would the salt dissolve?

Well, it really depends on where you placed them in the bucket. Maybe if you moved it around enough, or placed each strategically, you could get them to interact. Now, what if you added 1 kg of salt and 1 L of water? Well, it's a lot more likely that they would interact with each other. This is why concentration matters when determining rate. If in a solution, there is more of one reactant, it means that there is a higher chance it will come into contact with something it's going to react with.

Fig 2. - With an increased number of molecules in solution, there is a higher chance that they will collide.

Effects of Temperature on Reaction Rate

Temperature is another factor which affects the rate of reaction. Typically, increasing the temperature will increase the speed at which a reaction occurs. This is due to the reactants having an increased energy. When they collide into each other, the increased energy means that it is easier to overcome the Activation Energy needed to react.

Catalytic Effects on Reaction Rate

There is one other factor that we will briefly mention, which are catalysts. Catalysts will decrease the activation energy of a reaction, which makes it easier to overcome. Certain catalysts, like Enzymes, also bring molecules closer together, which allows them to react faster.

Catalysts are mandatory for some reactions to occur, which makes them vital for life on Earth. Without enzymes, biological processes would occur too slowly, and life would not be possible.

We've listed a few different factors affecting rate of reaction, but there are still many more which we didn't mention. Kinetics is a very diverse field, with numerous avenues to explore. Here, we've discussed a short overview on rates and how to calculate the rate of reaction for simple reaction equations. This quickly becomes more complicated when considering integrated rate expressions and the Rate Law. That is a topic we will save for another article, so be sure to check that out. Until then, try to observe kinetics and reaction rates in everyday life.

The next time you stir sugar into coffee, or salt into water, ask yourself: why does this dissolve faster? With your new-found knowledge on kinetics, you'll no doubt answer that quickly.