## 1. The speedometer of chemistry: graphs

Drivers monitor their speed with a speedometer. Easy! But for chemists, there is no direct way to measure how fast our reaction is going. The closest we have to a speedometer are **graphs**, which are of course pretty *shag* to plot.

The bright side is the wealth of information the graphs contain, if you know how to read them. In this article, you will learn about the two types of graph: **time graph** and **speed graph**.

## 2. Plotting time graph to trace product formation over time

In most experiments, we monitor the **amount of product formed** at a regular **time interval**.

Take the redox reaction between zinc and acid as an example. We can use a gas syringe to measure the **volume of hydrogen gas produced** at every minute interval.

We can plot the data collected on a graph of **volume of hydrogen gas produced** (on the y-axis) against **time** (on the x-axis). This **time graph** provides us two vital pieces of information:

- The
**y-value**at every point tells us the**amount of product**at that point in time, like how there are were 20 cm^{3}of hydrogen gas at the 2nd minute. - If you draw a
**gradient**at a point, it tells us the**speed of reaction**at that point in time. Here, the**gradient gets gentler**with time, reflecting how**reaction slows down**as**more reactants are used up**.

## 3. Comparing two time graphs

Let’s compare two experiments involving the same reaction between acid and zinc. All factors are kept the same, besides **particle size**: experiment 1 uses zinc strip, while experiment 2 uses zinc powder. There are two important observations to make from the graph:

- We can see how the pink curve representing experiment 2 has a
**steeper gradient at every point in time**. From this, we can infer that the**speed of reaction is faster**when zinc powder is used. - However, both curves plateau at the
**same y-value of 40 cm**of hydrogen gas. This is because we use the same amount of reactants in both experiments. Since the^{3}**amount of limiting reactant is the same**, the**amount of product will be equal**.

## 4. An alternative: plotting time graph to trace reactant consumption over time

Besides measuring the amount of product, we can alternatively measure **the amount of reactants left behind** at a regular **time interval**.

For example, when we heat copper(II) oxide and carbon, we can trace the **loss of reactants** by measuring a **decrease in mass** at 1-minute interval. This is because we lose the carbon and oxygen atoms in the reactants as carbon dioxide gas, which escapes into the air.

With the measurements, we can plot a time graph of **mass of reaction mixture left** (y-axis) against **time** (x-axis). Like the other time graph, this offers two vital pieces of information:

- The
**y-value**at every point tells us the mass of reaction mixture left. - If you draw a
**gradient**at a point, the absolute value tells us the**speed of reaction**at that point in time.

## 5. Clock experiments measure the time a reaction takes to complete

For the time graphs that we have talked about, time is the independent variable. We measure the dependent variable: the amount of reactants or products.

However, for **clock experiments**, we instead vary reaction conditions and **measure the time taken for a reaction to complete**.

For example, we can change the temperature of the reaction between sodium thiosulfate and hydrochloric acid. For every temperature, we find the time taken for the yellow sulfur product to cloud the hitherto colourless solution completely.

## 6. Plotting speed graph to see how speed changes with reaction conditions

Temperature | Time/ s | Inverse of time/ s^{-1} |
---|---|---|

30 | 55.46 | 1 ÷ 55.46 = 0.01803 |

40 | 40.01 | 1 ÷ 40.01 = 0.02499 |

50 | 24.50 | 1 ÷ 24.50 = 0.04086 |

60 | 14.50 | 1 ÷ 14.50 = 0.06897 |

We then process the data by calculating the **inverse of time taken **= 1 ÷ time. This inverse gives a good indication of the **speed of reaction**

Finally, we plot the **inverse of time taken **(y-axis) against the **reaction condition** (x-axis). We shall call this the **speed graph**, as it gives us an indication of the speed of reaction most directly.