Comparing uncertainties like those calculated above 'might' help you to decide which stage in an experimental procedure is likely to contribute most to the overall experimental uncertainty.
How about thermometers...?
Spirit filled thermometers are regularly used in college laboratories. They are often more precise than accurate. It is quite easy to read a thermometer to the nearest 0.2 °C. However, the overall calibration can be out by a degree or more. For example, for a thermometer reading 43 °C, if it is not of high quality the real temperature could be as high as 44 °C or as low as 42 °C.
Arithmetical procedures can lead to uncertainty...
What about Significant Figures...?
First of all, a calculation!
You want to know the circumference of a 2p coin! Using a ruler, measure its diameter. The circumference of a circle is given by πd. Now get out a calculator.
Circumference = 3.1415927 x 26.0 = 81.681409 mm
But you feel that your measurement of the diameter could be either side of the 26 mm mark depending on how you look at the ruler.
Circumference = 3.1415927 x 26.1 = 81.995568 mm
Circumference = 3.1415927 x 25.9 = 81.367250 mm
So what is the correct circumference? Of the three answers, only the values in the first two digits (81) are the same. Only these two figures convey significant information.
A significant figure is defined as a digit that we believe to be correct, or nearly so.
Figures that are not significant should not be included in a calculated value. The circumference of the 2p coin is therefore 81 mm. Note that decimal points have nothing to do with significant figure. If the answer is calculated in cm, the number of significant figures is still two (8.1).
How do I count the significant figures in a number?
Read the number from left to right and count all the digits starting with the first digit that is not zero. The examples below all have four significant figures:
- 0.06027
- 3.783
- 2.130
- 0.004083
-
6.035 x 105
Now check out the number of significant figures in the answers for each of the following:
407.8750 - 0.98 + 3.768 = 410.66
The value with the fewest decimal places (0.98) determines the number of significant figures.
6.3 x 5479 ÷ 0.0053 = 6.5 x 106
The quantity with fewest significant figures determines the number of significant figures in the answer.
4.8729 becomes 4.873 (4 sf)
4.8729 becomes 4.87 (3 sf)
3.715 becomes 3.71 or 3.72 (3 sf)
This is 'rounding off' a number to discard non-significant figures.
Get Started with Reaction Kinetics
These notes are intended to provide an introduction to Rate of Reaction. Work through these, and then refer to other available materials to build your understanding of the concepts.
Answer the questions...
- What is meant by the 'rate' of a chemical reaction?
- How does the rate of a chemical reaction change as the reaction proceeds from start to finish?
- How can we follow experimentally the changing rate of a chemical reaction as it takes place?
A chemical reaction involves one or more reactants. We are interested in how the rate of reaction depends on each of these separately.
Two experimental methods which can be employed to investigate reaction rate are:
- Continuous (Progressive) method.
- Initial Rates method.
First of all, the Continuous method...
Consider the decomposition of dinitrogen pentoxide dissolved in liquid tetrachloromethane at 30 °C.
N2O5(sol) → 2NO2(sol) + ½O2(g)
The volume of O2(g) measured at a known temperature and pressure is related to the diminishing concentration of N2O5(sol) at intervals during the experiment. The following data are obtained:
-
Plot a graph of [N2O5(sol)] against Time (hours). This is a 'concentration against time' graph.
The gradient of a tangent to the curve at any instant of time (or concentration) is the rate at that instant.
- Calculate five of these, and then plot a 'rate against concentration' graph.
From this graph, decide how the rate of reaction is related to the concentration of N2O5(sol). If doubling the [N2O5(sol)] doubles the rate of reaction, then the reaction is said to be first order with respect to N2O5(sol).
If doubling the [N2O5(sol)] causes the reaction rate to quadruple, then the reaction is second order with respect to the reactant in question. If doubling the concentration of a reactant produces an 8 times increase in rate, then the reaction is third order with respect to the reactant concerned.
It might be that the concentration against time graph was a straight line, and consequently, the rate against concentration graph is a horizontal straight line. In this case, changing the concentration of the reactant has no effect on the reaction rate. The reaction is said to be zero order with respect to the reactant.
-
What is the order of reaction with respect to the [N2O5(sol)]?
-
Write a rate equation for the N2O5(sol) decomposition reaction.
- Now examine the concentration against time curve. Work out some repeating half-lives for this reaction. Write an appropriate statement about this observation.
If there are, for example, two reactants, then how is the continuous method applied experimentally? Clearly, it is necessary to keep each reactant concentration constant in turn whilst the other is investigated. This is achieved by having a large concentration of the reactant not being investigated, so that during the reaction its concentration changes negligibly, and so remains effectively constant.
Once you have found the order of reaction with respect to each reactant, the overall order of reaction can be obtained simply by adding together these values. A rate equation can be written for the reaction. For example,
2A(g) + B2(g) → products
rate = k[A(g)]x[B2(g)]y
The idea is to find the values of x and y. It is important to remember that these values can be obtained only by experiment.
Now the Initial Rates method...
This method involves carrying out the experiment five or more times. Each reactant is investigated in turn by changing its concentration whilst keeping the other(s) unchanged. The time taken for the reaction to reach exactly the same stage (for example, the time taken for the same amount of a product to form) is measured for each experiment. A colour change, for example, might indicate this.
Here is a brief insight into this idea...
Imagine that one of the products is iodine, I2. If the same amount (volume and concentration) of sodium thiosulphate solution is present in the reaction mixture along with some starch solution, as the iodine forms it will react with the sodium thiosulphate so being removed from solution. At the instant when all of the sodium thiosulphate has reacted, the iodine then produced will immediately form a blue-black colour with the starch. The clock is stopped at this instant. Reactions of this type are often referred to as Clock Reactions.
Now try these examples to get the ideas of the initial rates method...
For the thermal decomposition of ethanal, CH3CHO
CH3CHO(g) → CH4(g) + CO(g)
the following data at 800 K are given.
-
What is the order of reaction with respect to CH3CHO(g)? Write the rate equation for the reaction.
- Calculate the rate constant for the reaction at 800 K.
-
Calculate the decomposition rate at 800 K at the instant when [CH3CHO(g)] is 0.250 mol dm-3.
Again, when two reactants participate in a reaction, the rate equation may be derived by keeping the concentration of one reactant constant while varying the concentration of the other.
The reaction
NO(g) + ½Cl2(g) → NOCl(g)
has been studied at 50 °C.
- Work out a rate equation for this reaction.
- What is the overall order of the reaction?
- Calculate the rate constant for the reation at 50 °C.
-
Calculate the rate of formation of NOCl when [NO] = [Cl2] = 0.110 mol dm-3.
-
At the instant when Cl2 is reacting at 2.21 x 10-7 mol dm-3 s-1, what is the rate at which NO is reacting and NOCl is forming?
