# Rate of Reaction

## Rate of Reaction Revision

**Rate of Reaction **

The **rate** of a **chemical reaction** tells us **how quickly the reaction takes place **by looking at how the amount of products or reactants changes. Rates can be measured in terms of **reactants** or **products** and are often measured in** seconds**. Rate graphs can be used to show how the amount of a given substance **changes during a reaction** and can help us to **calculate** the rate of a chemical reaction.

**Rates**

Rates are used to express the** speed** or **frequency** with which a given process happens. When measuring the speeds of a process, rates are calculated by** dividing** the **change** of a given variable by the **time** in which the change has taken place.

For the mean rate of a **chemical reaction**, we measure the changes the amount of either the **reactants** or the** products** of the reaction:

**\text{Mean Rate of Reaction}=\frac{\text{Amount of Reactant Used}}{\text{Time Taken}}**

or

**\text{Mean Rate of Reaction}=\frac{\text{Amount of Product Formed}}{\text{Time Taken}}**

The **amounts of reactant used or product** formed are typically measured in either **grams \left(\text{g}\right)** or in **cubic centimeters \left(\text{cm}^{3}\right)**. The **time** over which these changes take place is almost always measured in **seconds \left(\text{s}\right)**.

The mean rate of a reaction is telling us about the **change in an amount over a given time **so its units are the **unit change in amount per the unit change in time**.

**\text{g}/\text{s}** or **\text{cm}^{3}/\text{s}**

Mean rates of reaction may also be measures in terms of **moles**, giving units of **\text{mol}/\text{s}**.

The mean rate of a chemical reaction will tell us how **quickly or slowly** that reaction takes place. If a reaction has a **low rate**, then it will happen **slowly**. Reactions with a **higher rate** will happen much more **quickly**. There are a number of factors that influence the rate, from temperature to **concentration**.

**Rate Graphs**

The rate of a chemical reaction can be investigated by constructing a** rate graph**. These **graphs **show the **amount of a given substance** in the reaction over a given amount of **time**. Rate graphs tend to be **curves**, as the rate of a chemical reaction will** change as the reaction progresses**. The shapes of these curves will depend on whether we are looking at changes in the reactants or at changes in the products.

As the amounts of reactants in the reaction will decrease over time plotting the amount of the** reactants** against time will produce a **downward sloping curve**.

If instead we look at the changes in the amount **product** during a reaction, the rate graph produced will instead display an **upward sloping curve **as the** amount of product increases with time**.

The steepness of both curves **decreases with time**.

There are a number of** similarities** between the two curves that tells us about the rate of chemical reactions.

- Both curves
**start off very steep**, with lots of of reactant used or product formed in a short time. This tells us that the rate of reaction is**fastest**at the**beginning**of the reaction. - Both curves eventually
**plateau**(become flat). The amount of reactant or product has**stopped changing**at this point and so the rate of the reaction falls to zero. This tells us that the**reaction has stopped**. - Both curves get
**less**steep as time goes on. This tells us that the rate of a reaction will**slow down as the reaction progresses**. This is due to the**decreasing**amount of**reactant**available to the reaction.

**Calculating the Rate of Reaction from a Rate Graph**

Rate graphs allow us to calculate the rate of a chemical reaction. To calculate the rate of reaction from a rate graph we must first draw a **tangent** to the curve of the graph.

**Drawing a Tangent**

To find the **gradient of a curve** we must draw a line called a **tangent**. Tangents are** straight lines** that touch curved lines but **do not cross them** at any point.

Tangents allow us to find the gradient of a curved graph by providing a straight line to help us find the changes in the y and x-axis values. Gradients calculated using a tangent represent the **gradient of the curve at the point where the two lines meet**. This allows us to calculate rates of reaction at specific times along the x-axis.

**Calculating Rates of Reaction using Tangents**

To calculate the **rate of a reaction** from a rate graph, a** tangent must first be drawn to the curve**. **Two lines** should then be drawn down from **two points along**** the tangent** to the **x-axis**. The **difference** between the points where these lines **meet the x-axis** will give us the** change in time**. Next, **two lines** should be drawn from the **ends of the tangent** to the** y-axis**. The **difference** between the two points where these lines **meet the y-axis** will give us the **difference in the amount of substance**.

Finally, we can calculate the **rate **of reaction by find the slope of the tangent. To do this we divide the change in the amount of substance by the change in time:

**\text{Rate of Reaction}=\text{Gradient of Tangent}=\frac{\text{Change in Amount}}{\text{Change in Time}}**

It is important to note that the rate calculated from this gradient is **the rate of reaction at the point on the curve at which the curve and tangent meet** and so at the corresponding time along the x-axis. To find the **rate of reaction at a given time**, a line should be drawn up from the time on x-axis and the tangent drawn so that it meets the curve where this line crosses it.

**Example: Calculating Rates of Reaction**

In a chemical reaction, \textcolor{#00bfa8}{20\text{ g}} of sodium hydrogen carbonate is produced. The reaction takes **12 minutes**. Calculate the mean rate of the reaction. Give your answer in \text{ g}\text{ s}^{-1}.

**[2 marks]**

Step 1: Convert the time into seconds.

\text{t (s)}=\text{t (min)}\times60 =\textcolor{#f21cc2}{12}\times60 =\textcolor{#008d65}{720\text{ s}}

Step 2: Calculate the mean rate. In this example the amount of product formed is measured by the mass.

\begin{aligned}\text{mean rate}&=\frac{\text{mass of product}}{\text{time}}\\\text{}\\ &=\frac{\textcolor{#00bfa8}{20}}{720}\\\text{}\\ &=\textcolor{#008d65}{0.028\text{ g}/\text{s}}\end{aligned}

## Rate of Reaction Example Questions

**Question 1:** During a chemical reaction, 5.6\text{ cm}^{3} of \text{HCl} is used up. The reaction takes 120 seconds.

Calculate the mean rate of reaction.

**[1 mark]**

\begin{aligned}\text{Rate}&=\frac{\text{Amount of Reactant Used}}{\text{Time Taken}}\\\text{}\\ &=\frac{5.6}{120}\\\text{}\\ &=0.047\text{ cm}^{3}/\text{s}\end{aligned}

**Question 2: **In another reaction, 7.9\text{ g} of sodium chloride is produced. This reaction takes 3.5 minutes.

Calculate the mean rate of reaction. Give your answer in \text{ g}\text{ s}^{-1}.

**[2 marks]**

Step 1: Convert the time into seconds.

\text{time (s)}=\text{time (mins)}\times60 ={3.5}\times60 =210\text{ s}

Step 2: Calculate the mean rate.

\text{mean rate of reaction}=\frac{\text{mass of product}}{\text{time Take}}\\ =\frac{7.9}{210}\\ =0.038\text{ g}/\text{s}

(One mark per correct step.)

**Question 3:** State whether the following graph shows a change in the reactants or products of a reaction. Explain your answer.

**[3 marks]**

The graph shows the **change in reactants**.

The **graph slopes downwards** so the **amount of substance is decreasing with time**.

**Question 4**: A student carries out a reaction to measure its rate of reaction. The student measures the mass of the product produced and plots this on a graph against time in seconds. The graph is displayed below:

Calculate the rate of this reaction. A tangent has been drawn for you.

**[3 marks]**

\text{Rate of Reaction}=\frac{\text{Change in Mass}}{\text{Change in Time}}\\\text{}\\=\frac{3.75-2.23}{52-12}\\\text{}\\=\frac{1.52}{40}\\\text{}\\=0.038\text{ g}\text{ s}^{-1}