Mean rate is change in amount over time

Definition

Rate of reaction

How quickly a reactant is used up or a product is formed, measured as the change in amount divided by the time taken.

The mean rate over a time interval is: $taken\text{mean rate} = \frac{\text{change in amount of reactant or product}}{\text{time taken}}$
The units of rate follow from what is measured, such as $cm3/s\text{cm}^3/\text{s}$ for a gas volume or $g/s\text{g/s}$ for a mass.
To follow a reaction, measure a quantity that changes as the reaction goes on, at regular time intervals.
When the time for a fixed change is measured instead, a shorter time means a greater rate.
1. For a fixed change, a relative rate can be worked out as $1time\dfrac{1}{\text{time}}$ , in $s−1\text{s}^{-1}$ .

Example

A reaction gives off $cm348\,\text{cm}^3$ of gas in the first $s60\,\text{s}$ ; calculate the mean rate over this time.
Mean rate $\dfrac{48\,\text{cm}^3}{60\,\text{s}}$ .
Mean rate $0.80\,\text{cm}^3/\text{s}$ .

Following a reaction by measuring gas volume

A reaction that gives off a gas, such as marble chips with hydrochloric acid, can be followed with a gas syringe.
Instead, the gas can be collected over water in an upturned measuring cylinder.
Start the stop clock as soon as the reactants are mixed and the bung is replaced.
Record the volume of gas at regular intervals, such as every 10 seconds, until no more gas is given off.
The gas collection method needs a closed apparatus, so the bung must fit tightly and the tube must not leak.

Practical

Marble chips and hydrochloric acid

Aim: follow how the rate changes during the reaction of marble chips with hydrochloric acid.
Apparatus: a conical flask with a bung and delivery tube, a $cm3100\,\text{cm}^3$ gas syringe, a clamp and stand, a $cm350\,\text{cm}^3$ measuring cylinder, a digital balance, a stop clock, marble chips of different sizes, dilute hydrochloric acid of different concentrations and cotton wool.

Method

Measure $cm350\,\text{cm}^3$ of dilute hydrochloric acid into the conical flask.
Weigh out a set mass of marble chips of one size.
Connect the bung and delivery tube to the gas syringe, checking that the plunger is pushed fully in.
Add the chips to the acid, replace the bung quickly and start the stop clock.
Record the volume of gas every 10 seconds until it stops changing.
Repeat with a different acid concentration or chip size, keeping the volume of acid, the mass of chips and the temperature the same.
Plot volume of gas against time for each run on the same axes, and compare how steep the lines are at the start.

Accuracy and safety

Replace the bung straight away, or some carbon dioxide escapes before it is measured.
Another method is to stand the flask on a balance with a cotton wool plug in the neck and record the loss in mass as carbon dioxide escapes.
The cotton wool lets the gas out but stops acid spray escaping, which would also lower the mass.
Wear eye protection, because hydrochloric acid is an irritant.

Following reactions by mass loss or visible change

If a gas escapes, put the flask on a balance and record the mass at regular intervals.
1. A cotton wool plug in the neck lets the gas out but stops acid spray escaping.
This method suits heavy gases such as carbon dioxide, but hydrogen is so light that the mass change is too small to measure well.
A reaction that forms a precipitate can be timed until a cross drawn under the flask disappears from view.
1. Sodium thiosulfate reacts with hydrochloric acid to form a yellow sulfur precipitate: $Na2S2O3(aq)+2HCl(aq)→2NaCl(aq)+S(s)+SO2(g)+H2O(l)\text{Na}_2\text{S}_2\text{O}_3\text{(aq)} + 2\text{HCl(aq)} \rightarrow 2\text{NaCl(aq)} + \text{S(s)} + \text{SO}_2\text{(g)} + \text{H}_2\text{O(l)}$
A reaction that changes colour can be timed until the colour change reaches the same stage each time.

Note

Choose the method from what the reaction produces: a gas suggests gas volume or mass loss, while a precipitate or colour change suggests timing a visible change.

The gradient of the graph shows the rate

Definition

Gradient

The steepness of a line on a graph, found by dividing the change in the vertical value by the change in the horizontal value.

On a graph of gas volume against time, a steeper curve means gas is given off faster, so the rate is greater.
The curve is steepest at the start, because the reactants are at their most concentrated.
The curve gets less steep as the reactants are used up, so the rate decreases.
A horizontal line means the reaction has stopped, because one of the reactants has been used up.
A graph of mass against time falls as gas escapes, and it too levels off when the reaction stops.

Common Mistake

Do not judge which reaction was faster from the height of a curve, because height shows how much product has formed, while the gradient shows the rate.

Comparing curves and drawing tangents shows how rates differ

When two curves are drawn on the same axes, the one that is steeper at the start shows the faster reaction.
If both curves level off at the same height, the same amount of product formed, so the amount of the used-up reactant was the same.
1. A curve that levels off at half the height shows that half as much of that reactant was used.
The rate at an instant is the gradient of a tangent to the curve at that time.
1. Draw a straight line that touches the curve at that point, then divide its rise by its run using two points far apart on the line.

Example

A tangent drawn at $s20\,\text{s}$ on a gas volume curve passes through $cm3)(0\,\text{s}, 10\,\text{cm}^3)$ and $cm3)(40\,\text{s}, 50\,\text{cm}^3)$ ; find the rate at $s20\,\text{s}$ .
Gradient $\dfrac{50 - 10}{40 - 0} = \dfrac{40\,\text{cm}^3}{40\,\text{s}}$ .
Rate at $cm3/s20\,\text{s} = 1.0\,\text{cm}^3/\text{s}$ .

Self review

How is the mean rate of a reaction calculated?
Name two pieces of apparatus that can collect and measure the volume of a gas.
Why is the mass-loss method unsuitable for a reaction that gives off hydrogen?
What does a horizontal section of a gas volume curve show?
How do you find the rate of a reaction at a particular time from a curve?

Mean rate is change in amount over time

Definition

Rate of reaction

How quickly a reactant is used up or a product is formed, measured as the change in amount divided by the time taken.

The mean rate over a time interval is: $taken\text{mean rate} = \frac{\text{change in amount of reactant or product}}{\text{time taken}}$
The units of rate follow from what is measured, such as $cm3/s\text{cm}^3/\text{s}$ for a gas volume or $g/s\text{g/s}$ for a mass.
To follow a reaction, measure a quantity that changes as the reaction goes on, at regular time intervals.
When the time for a fixed change is measured instead, a shorter time means a greater rate.
1. For a fixed change, a relative rate can be worked out as $1time\dfrac{1}{\text{time}}$ , in $s−1\text{s}^{-1}$ .

Example

A reaction gives off $cm348\,\text{cm}^3$ of gas in the first $s60\,\text{s}$ ; calculate the mean rate over this time.
Mean rate $\dfrac{48\,\text{cm}^3}{60\,\text{s}}$ .
Mean rate $0.80\,\text{cm}^3/\text{s}$ .

Following a reaction by measuring gas volume

A reaction that gives off a gas, such as marble chips with hydrochloric acid, can be followed with a gas syringe.
Instead, the gas can be collected over water in an upturned measuring cylinder.
Start the stop clock as soon as the reactants are mixed and the bung is replaced.
Record the volume of gas at regular intervals, such as every 10 seconds, until no more gas is given off.
The gas collection method needs a closed apparatus, so the bung must fit tightly and the tube must not leak.

Practical

Marble chips and hydrochloric acid

Aim: follow how the rate changes during the reaction of marble chips with hydrochloric acid.
Apparatus: a conical flask with a bung and delivery tube, a $cm3100\,\text{cm}^3$ gas syringe, a clamp and stand, a $cm350\,\text{cm}^3$ measuring cylinder, a digital balance, a stop clock, marble chips of different sizes, dilute hydrochloric acid of different concentrations and cotton wool.

Method

Measure $cm350\,\text{cm}^3$ of dilute hydrochloric acid into the conical flask.
Weigh out a set mass of marble chips of one size.
Connect the bung and delivery tube to the gas syringe, checking that the plunger is pushed fully in.
Add the chips to the acid, replace the bung quickly and start the stop clock.
Record the volume of gas every 10 seconds until it stops changing.
Repeat with a different acid concentration or chip size, keeping the volume of acid, the mass of chips and the temperature the same.
Plot volume of gas against time for each run on the same axes, and compare how steep the lines are at the start.

Accuracy and safety

Replace the bung straight away, or some carbon dioxide escapes before it is measured.
Another method is to stand the flask on a balance with a cotton wool plug in the neck and record the loss in mass as carbon dioxide escapes.
The cotton wool lets the gas out but stops acid spray escaping, which would also lower the mass.
Wear eye protection, because hydrochloric acid is an irritant.

Following reactions by mass loss or visible change

If a gas escapes, put the flask on a balance and record the mass at regular intervals.
1. A cotton wool plug in the neck lets the gas out but stops acid spray escaping.
This method suits heavy gases such as carbon dioxide, but hydrogen is so light that the mass change is too small to measure well.
A reaction that forms a precipitate can be timed until a cross drawn under the flask disappears from view.
1. Sodium thiosulfate reacts with hydrochloric acid to form a yellow sulfur precipitate: $Na2S2O3(aq)+2HCl(aq)→2NaCl(aq)+S(s)+SO2(g)+H2O(l)\text{Na}_2\text{S}_2\text{O}_3\text{(aq)} + 2\text{HCl(aq)} \rightarrow 2\text{NaCl(aq)} + \text{S(s)} + \text{SO}_2\text{(g)} + \text{H}_2\text{O(l)}$
A reaction that changes colour can be timed until the colour change reaches the same stage each time.

Note

Choose the method from what the reaction produces: a gas suggests gas volume or mass loss, while a precipitate or colour change suggests timing a visible change.

The gradient of the graph shows the rate

Definition

Gradient

The steepness of a line on a graph, found by dividing the change in the vertical value by the change in the horizontal value.

On a graph of gas volume against time, a steeper curve means gas is given off faster, so the rate is greater.
The curve is steepest at the start, because the reactants are at their most concentrated.
The curve gets less steep as the reactants are used up, so the rate decreases.
A horizontal line means the reaction has stopped, because one of the reactants has been used up.
A graph of mass against time falls as gas escapes, and it too levels off when the reaction stops.

Common Mistake

Do not judge which reaction was faster from the height of a curve, because height shows how much product has formed, while the gradient shows the rate.

Comparing curves and drawing tangents shows how rates differ

When two curves are drawn on the same axes, the one that is steeper at the start shows the faster reaction.
If both curves level off at the same height, the same amount of product formed, so the amount of the used-up reactant was the same.
1. A curve that levels off at half the height shows that half as much of that reactant was used.
The rate at an instant is the gradient of a tangent to the curve at that time.
1. Draw a straight line that touches the curve at that point, then divide its rise by its run using two points far apart on the line.

Example

A tangent drawn at $s20\,\text{s}$ on a gas volume curve passes through $cm3)(0\,\text{s}, 10\,\text{cm}^3)$ and $cm3)(40\,\text{s}, 50\,\text{cm}^3)$ ; find the rate at $s20\,\text{s}$ .
Gradient $\dfrac{50 - 10}{40 - 0} = \dfrac{40\,\text{cm}^3}{40\,\text{s}}$ .
Rate at $cm3/s20\,\text{s} = 1.0\,\text{cm}^3/\text{s}$ .

Self review

How is the mean rate of a reaction calculated?
Name two pieces of apparatus that can collect and measure the volume of a gas.
Why is the mass-loss method unsuitable for a reaction that gives off hydrogen?
What does a horizontal section of a gas volume curve show?
How do you find the rate of a reaction at a particular time from a curve?

5.2.1 Measuring and interpreting rate of reaction

Mean rate is change in amount over time

Following a reaction by measuring gas volume

Marble chips and hydrochloric acid

Method

Accuracy and safety

Following reactions by mass loss or visible change

The gradient of the graph shows the rate

Comparing curves and drawing tangents shows how rates differ

Review 5.2.1 Measuring and interpreting rate of reaction by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

5.2.1 Measuring and interpreting rate of reaction

Mean rate is change in amount over time

Following a reaction by measuring gas volume

Marble chips and hydrochloric acid

Method

Accuracy and safety

Following reactions by mass loss or visible change

The gradient of the graph shows the rate

Comparing curves and drawing tangents shows how rates differ

Review 5.2.1 Measuring and interpreting rate of reaction by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

5.2.1 Measuring and interpreting rate of reaction

Mean rate is change in amount over time

Following a reaction by measuring gas volume

Marble chips and hydrochloric acid

Method

Accuracy and safety

Following reactions by mass loss or visible change

The gradient of the graph shows the rate

Comparing curves and drawing tangents shows how rates differ

Review 5.2.1 Measuring and interpreting rate of reaction by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

5.2.1 Measuring and interpreting rate of reaction Revision Guide

5.2.1 Measuring and interpreting rate of reaction

Mean rate is change in amount over time

Following a reaction by measuring gas volume

Marble chips and hydrochloric acid

Method

Accuracy and safety

Following reactions by mass loss or visible change

The gradient of the graph shows the rate

Comparing curves and drawing tangents shows how rates differ

Review 5.2.1 Measuring and interpreting rate of reaction by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

5.2.1 Measuring and interpreting rate of reaction Revision Guide