# Reaction Rates

In 1953, famed actress and superstar Marilyn Monroe sang, "Diamonds are a girl's best friend." The performance inspired dozens of singers and actresses for generations. In the song, Monroe sings that "these rocks don't lose their shape" while charming audiences.

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However, unfortunately for her and every one of a diamond's best friends, one day, diamonds will be no more. All diamonds on this planet will eventually turn back into graphite and disappear from every wedding band on every hand. But don't worry, this won't happen for billions of years! Although this reaction is thermodynamically favored, it is limited by its kinetics, meaning it will take a very long time.

But how do we calculate reaction rates, and what affects them? Come along, and we'll learn about reaction rates in time for you to watch a diamond slowly turn into graphite.

• Today we will be looking at reaction rates
• First, we will be looking at the rate of reaction and what that means.
• Next, we will assess how the formula for reaction rate looks and which units you will be dealing with.
• Then, we will complete a calculation together to help you get some practice.
• And finally, we will see some things that affect reaction rate, like physical state, concentration, temperature, and catalysts.

## 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.

Reaction rate is a measure of how quickly a chemical reaction will occur. Specifically, it measures a change in concentration versus a change in time.

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.

It should be noted that what we are typically calculating is the average rate of reaction. We can also calculate the instantaneous rate of reaction. However, this is done after constructing a graph of reaction rate over a given time interval. This calculation is done using the stoichiometric coefficient and the slope of the tangent line at a specific time.

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.

A homogeneous reaction has every reactant in the same state, while a heterogeneous one has reactants in different states; like a solid, and a liquid.

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

The surface area to volume ratio of a solid will decrease with an increase in size of the chunk. This means that more molecules are in the core of the chunk than on the surface. The ones in the core are surrounded by the same molecules, and don't react with anything. The reactions that occur will happen at the surface of the solid piece. If you split the chunk in half, you expose countless molecules to the surface, increasing the surface area.

Fig 1. - With an increased surface area, the reactivity of the substance increases dramatically.

This will increase the amount of molecules capable of reacting, which will increase the reactivity. Thus, having more surface area will increase the rate of reaction. This is why, when dissolving something in water, it goes quicker if you break it up with a utensil.

### 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.

When working in the lab, determining initial concentrations is very important. This is because some reactions don't proceed if the concentrations are too low. It's not because they are thermodynamically unfavored. They just don't proceed because they are too slow to react. In reality, some will react, but it is so little that we don't really observe it.

### 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.

A lot of the artificial catalysts designed by scientists are based on the enzymes which are found in the body. Life on this planet has been evolving for billions of years. That means that there is an enzyme behind every single biological process in all life on Earth. This provides excellent blueprints which scientists can use to create catalysts in the lab. Scientists have created some groundbreaking catalysts which allows life for humans to continue. However, they still fall short of what nature can achieve. Although we try hard to match it, nature is constantly proving itself as smarter than us.

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.

## Reaction Rates - Key takeaways

• The rate of reaction is a measure of the speed of reaction, which compares concentration vs. time.
• The rate equation for the general reaction $$aA + bB \rightarrow cC + dD$$ is as follows:$$\text {Rate} = - \frac {1} {a} \frac { \Delta [A] } { \Delta t } = - \frac {1} {b} \frac { \Delta [B] } { \Delta t } = + \frac {1} {c} \frac { \Delta [C] } { \Delta t } = + \frac {1} {d} \frac { \Delta [D] } { \Delta t }$$
• As the reaction proceeds, the reactants decrease, and the products increase. This is observed in the rate equation with reactants having a negative sign, and products having a positive sign.
• As a reaction occurs, the rate will decrease as the reactants begin to diminish. Therefore, the rate of reaction will be different depending on the given time interval.
• Several factors affect the rate of reaction, including the physical state of reactants, concentration, temperature, and whether a catalyst is present.

## References

1. Nivaldo Tro, Travis Fridgen, Lawton Shaw, Chemistry a Molecular Approach, 3rd ed., 2017
2. Theodore Brown, Eugene LeMay, Bruce Bursten, Catherine Murphy, Patrick Woodward, Matthew Stoltzfus, Chemistry the Central Science, 13th ed., 2014

#### Flashcards in Reaction Rates 42

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Which will increase the rate of a chemical reaction?

The rate of a chemical reaction can be increased by the physical state of reactants, the concentration, and the temperature of reaction. It can also be influenced by whether a catalyst is involved.

Enzymes increase the rate of a reaction by

Enzymes lower the activation energy of a reaction making it easier to overcome, and thus making the reaction rate faster. Enzymes are catalysts which work in living cells.

How to calculate rate of reaction

The rate of reaction is determined by comparing the change in concentration versus the change in time of a reactant (or product), multiplied by the inverse of their coefficient.
Rate = -1/a ( Δ[A] ) / ( Δt )

What is rate of reaction

Generally, the rate of reaction is how quickly the reaction happens. More specifically, it is a measure of a change in concentration versus a change in time. The more the reactants change in a given time interval, the faster they are reacting.

How does temperature affect the rate of reaction

Temperature can affect the speed of a reaction by influencing the amount of energy involved. If reactants are higher in energy (higher temperature), they may be able to overcome the reaction barrier quicker, which will speed up the rate of reaction.

## Test your knowledge with multiple choice flashcards

What is the rate of reaction?

In the rate equation for a reacting species, why does the expression have a positive sign?

In a typical reaction, as the reactants are consumed, what will happen to the rate?

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