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C6 D) Calculating Rate of Reaction from Graphs
C6 D) Calculating Rate of Reaction from Graphs
Click here for a printable version of the graphs in this section.
In the previous sections, we have looked at rate of reaction graphs that have plotted time on the x axis and mass lost or volume of gas produced on the y axis. Two examples of these graphs are shown below.
In the previous sections, we have looked at rate of reaction graphs that have plotted time on the x axis and mass lost or volume of gas produced on the y axis. Two examples of these graphs are shown below.
The steeper the curve is, the greater the rate of reaction is. The gradient of the curve will tell us how steep the curve is, thus giving us the rate of reaction. If we have mass lost on the y axis, the gradient will tell us how much mass is lost per second. If we have volume of gas produced on the y axis, the gradient will tell us the volume of gas produced per second.
The formula for working out gradient is shown below:
The formula for working out gradient is shown below:
A greater value for the gradient means a greater rate of reaction. And a lower value for the gradient means a slower rate of reaction.
The rate of reaction for all reactions is the fastest at the start, and then the rate of reaction slows down over time. This is because at the start of the reaction there are lots of reactants in the reaction vessel (a high concentration), which means that there will be more frequent collisions between the reactants and therefore a high rate of reaction; this is why the start of the curve is very steep. As time goes on, there will be fewer reactants in the reaction vessel as some of the reactants have been used up in reactions (a lower concentration). This means that there will be less frequent collisions and therefore a slower rate of reaction, which is represented by the curve becoming less steep/ flatter. Eventually all of the reactants will have reacted, which will mean that no more reactions will take place – this is the horizontal part on the rate of reaction curve.
The rate of reaction for all reactions is the fastest at the start, and then the rate of reaction slows down over time. This is because at the start of the reaction there are lots of reactants in the reaction vessel (a high concentration), which means that there will be more frequent collisions between the reactants and therefore a high rate of reaction; this is why the start of the curve is very steep. As time goes on, there will be fewer reactants in the reaction vessel as some of the reactants have been used up in reactions (a lower concentration). This means that there will be less frequent collisions and therefore a slower rate of reaction, which is represented by the curve becoming less steep/ flatter. Eventually all of the reactants will have reacted, which will mean that no more reactions will take place – this is the horizontal part on the rate of reaction curve.
The Different Rates of Reactions
There are two different types of rates of reactions that we can work out from a rate of reaction graph. These are the mean rate of reaction for a certain period of time and the rate of reaction at a particular time. The process in working each of these out is slightly different.
Mean Rate of Reaction
We work out the mean rate of reaction for a certain period of time by working out the overall change in the y values (mass lost or volume of gas produced) and the time taken (the change in the x values). We then sub the values into the gradient formula, which is shown below:
There are two different types of rates of reactions that we can work out from a rate of reaction graph. These are the mean rate of reaction for a certain period of time and the rate of reaction at a particular time. The process in working each of these out is slightly different.
Mean Rate of Reaction
We work out the mean rate of reaction for a certain period of time by working out the overall change in the y values (mass lost or volume of gas produced) and the time taken (the change in the x values). We then sub the values into the gradient formula, which is shown below:
Let’s now have an example.
We have the rate of reaction graph below.
We have the rate of reaction graph below.
Work out the mean rate of reaction between 5 and 9 seconds.
We work out the mean rate of reaction by using the formula below.
We work out the mean rate of reaction by using the formula below.
The change in y and the change in x are the changes between 5 and 9 seconds. Therefore, we should locate 5 and 9 seconds on the graph. At 5 seconds, the volume of gas is 10 cm3. At 9 seconds, the volume of gas is 13 cm3.
I am now going to label these points up as point 1 and point 2.
We now sub these values into the gradient formula.
The gradient is 0.75.
The final step is to work out the units, which we do by looking at the units that the change in y and the change in x were measured in. The change in y was the volume of gas measured in cubic centimetres (cm3) and the change in x was time measured in seconds. This means that the units for our gradient is cubic centimetres per second (cm3/s). Therefore, the mean rate of reaction between 5 and 9 seconds is 0.75 cm3/s.
Rate of Reaction at a Particular Time
We are now going to have a look at working out the rate of reaction at a particular time. We are able to work out the rate of reaction at a particular time by drawing a tangent to the curve at the particular time that we are interested in. A tangent is a line that touches a curve at a particular point. The tangent will have the same gradient as the curve at the point where the tangent touches the curve. Let’s look at an example.
We have the rate of reaction graph below.
We are now going to have a look at working out the rate of reaction at a particular time. We are able to work out the rate of reaction at a particular time by drawing a tangent to the curve at the particular time that we are interested in. A tangent is a line that touches a curve at a particular point. The tangent will have the same gradient as the curve at the point where the tangent touches the curve. Let’s look at an example.
We have the rate of reaction graph below.
Estimate the rate of reaction at 2 minutes.
The first step in estimating the rate of reaction at 2 minutes is to draw a tangent to the curve at 2 minutes; we draw a straight line that touches the curve at 2 minutes. We should draw quite a long tangent on the graph. My tangent is shown on the graph below.
The first step in estimating the rate of reaction at 2 minutes is to draw a tangent to the curve at 2 minutes; we draw a straight line that touches the curve at 2 minutes. We should draw quite a long tangent on the graph. My tangent is shown on the graph below.
The gradient of the tangent that we have just drawn will be the rate of reaction at 2 minutes. We work out the gradient of the tangent by using the formula below.
In order to use the gradient formula, we need to find 2 nice points on the tangent. By nice points, I mean points that are on major or minor gridlines on the graph. This is so that we can find exact points and not estimates. Also, we should choose points that are quite far away from each other. The points that I have chosen are a time of 0 minutes and a mass loss of 1.2 g, and a time of 4 minutes and a mass loss of 3.2 g. These points are shown on the graph below.
I am now going to label these points up as point 1 and point 2.
The next step is to sub these values into the gradient formula.
The gradient is 0.5.
The final step is to work out the units, which we do by looking at the units that the change in y and the change in x were measured in. The change in y was mass lost measured in grams (g), and the change in x was time measured in minutes. This means that the units for our gradient is grams per minute (g/min). Therefore, the rate of reaction at 2 minutes is 0.5 g/min.
The final step is to work out the units, which we do by looking at the units that the change in y and the change in x were measured in. The change in y was mass lost measured in grams (g), and the change in x was time measured in minutes. This means that the units for our gradient is grams per minute (g/min). Therefore, the rate of reaction at 2 minutes is 0.5 g/min.
There will be a range of acceptable answers when we are measuring the rate of reaction at a particular time. For example, the range of acceptable answers for this question may be values between 0.35-0.65 g/min.