Verification and use of Boyle’s Law
Aim
This purpose of this experiment is to see how closely Boyle’s law is followed by a constant amount of air at a fixed temperature.
Background information
Boyle’s law is a well-known law of chemistry; that states that for a fixed amount of gas at a constant temperature, the volume will be inversely proportional to the applied pressure. This can be expressed as V 1/P. The ideal gas equation relates the pressure, volume, and temperature of a fixed amount of an ideal gas. The ideal gas equation is written as PV= nRT. Where P= pressure (Pa), V= volume (m3), n= number of moles, R is the molar gas constant and T is the absolute temperature . This equation is used to predict the behaviour of gases. Boyle’s Law describes the behaviour of a fixed amount of gas when its temperature is constant. This can be summarised as pV= constant. The pressure (p) of a gas can be expressed as p= pa+pg, where pa= the atmospheric pressure and pg= the gauge pressure.
P= pa+pg can be substituted into PV= nRT to obtain the equation pa V +Pg V= nRT. When the equation is it becomes: pg V=-Pa+nRT. This rearrangement makes the equation linear, in the form of y=Bx + A, with V as the independent variable (x) and pg V as the dependent variable (y), B is the gradient and A is the y-intercept.
The purpose of this experiment is to verify how closely Boyle’s law is followed by a constant amount of air at a fixed temperature. By the end of the experiment, the atmospheric pressure of, the room will be calculated. As well as the amount of gas trapped within a given volume under atmospheric pressure (pa) and the constant temperature (T).
DIAGRAM
Procedure
Set up the equipment shown in the diagram. Measure the surrounding room temperature with a thermometer. Once the temperature has been measured, it must be converted into Kelvins. Whilst the valve is opened, adjust the piston to the given starting volume. The valve must be closed once the piston has been set. The valve should be closed and not opened, until the experiment has been completed. The piston must be moved inwards to reduce the volume of gas by one or two units. The new volume and pressure must be recorded into a produced table. Gather results until the maximum pressure has been reached, or until the piston cannot be turned. The experiment will be finished once fifteen data points have been gathered. Check that the data gathered follows a trend. A statistical analysis should be carried out.
The conditions that should remain constant is the temperature of the room (which was measured using a thermometer) and the fixed amount of gas within the apparatus. The dependent variable is the pressure of the apparatus (measured using the pressure gauge) and the volume within the apparatus. As the experiment is to see how the amount of a gas under a given volume is affected by a
Results
Number of observations Volume/(10cm3) Gauge pressure (Pg)/kgcm-2 Volume/cm3 Pg x V/kg.cm
1 19.5 0 195 0.00
2 17.5 0.18 175 31.50
3 15.5 0.31 155 48.05
4 13.5 0.51 135 68.85
5 12.5 0.62 125 77.50
6 11.5 0.78 115 89.70
7 10.5 0.92 105 96.60
8 9.5 1.12 95 106.40
9 8.5 1.38 85 117.30
10 8.0 1.51 80 120.80
11 7.5 1.68 75 126.00
12 7.0 1.88 70 131.60
13 6.5 2.05 65 133.30
14 6.0 2.30 60 138.00
Table 1: Shows that as the Volume decreased the Gauge pressure would increase within the pressure gauge apparatus
Statistical analysis from calculations:
A=200.2
B=-0.989
R=-0.998
Graph
Graph 1: Shows the negative gradient of the Volume shown on piston against the pressure x volume (PgV)
Analysis:
Percentage error:
R2 = -0.998
R= 0.999
(-1-(0.999))/(-1) X 100 = 0.1%
Percentage difference:
B= -0.989kgcm-2
Pa = 0.989kgcm-2
9.81ms= acceleration due to gravity
1kg/〖1cm〗^2 = ( 1kgx 〖9.81ms〗^(-2))/(1/100 m x 1/100 m) = (9.81N x 〖10〗^4)/〖1m〗^2
1kgcm-2= 9.81 x 104Pa
Pa=0.989kgcm-2
0.989Pa x (9.81 x 104Pa) = 9.70 x 104Pa
Comparing my atmospheric pressure result with the standard atmospheric pressure:
((1.01 x 〖10〗^5 Pa)-(9.70 x 〖10〗^4 Pa))/(1.01 x 〖10〗^5 Pa) X 100 = 3.9603 = 4.0%
Value of nexperimental:
A= nRT
n= A/RT
T= 23c + 273 = 296K
A calculated = 200.2Kgcm
R= Universal gas constant = 8.314Jk-1mol-1
n= (200.2 x (9.81 x 〖10〗^(-2 )) )/(8.314〖Jk〗^(-1) 〖mol〗^(-1) x 296K )=7.98 x 〖10〗^(-3) mol
nexperimental = 7.98 x 10-3 mol
Value of ncalculated:
EVALUATION
From the results gathered from the experiment, it can be stated that the experiment was accurate and reproducible due to taking precautions to reduce error.
Boyle’s law is a well-known law of chemistry; that states that for a fixed amount of gas at a constant temperature, the volume will be inversely proportional to the applied pressure. . It predicts that: PgV = nRT – Pa x V
PgV against V is a straight line with a negative gradient and a positive y-intercept. Qualitatively the gradient that was found was negative and the y-intercept was positive.
Quantitatively:
From analyses from the graph, we can see that it is linear which suggests that the experiment was ——-.
Some of the errors we had encountered can be categorised as either random or systematic error. Systematic errors are measurements that shift from the true value by the same fraction each time and affects the accuracy. Whereas random errors will shift from the true value by random amounts and in a random direction. These errors will affect the reliability.
One of the main errors was having difficulty in reading the scales on the pressure gauge. As the gauge went up in 0.1 units, we would have to estimate the value. This means that we would measure a value that could have been in between two markings on the scale; which would lead to us gathering unprecise values and having to round up or down a decimal point. This would be classed as a random error. Random errors will have a shift in measurements from the true value by the same fraction all the time. This form of error would not affect the reliability of the experiment but may affect the overall accuracy of the results.
Another error that was encountered was the angle that the pressure gauge was read at (parallax error). This caused a few problems because depending on the angle you were reading from, you could get very different values. This can be classed as either a systematic error or a random error. It can n]be a systematic error if I always viewed the pressure gauge at that same angle and if it was a random error if I viewed the gauge at different angles each time, I took the data values. A precaution I took to prevent this was to try and view the pressure gauge at the same angle, by laying the apparatus flat onto the table and reading the value off the gauge.
We reduced the systematic errors by using equipment that was absolutely on zero. This would prevent us from having zero errors. However, even if some of the results were affected by any errors, they could have been eliminated through data analysis. So, as we created a graph through excel, we would be able to easily distinguish any anomalies by drawing a line of best fit. After that we would also calculate the gradient that would look in the change between two values and this means that any zero errors would not affect the overall result. Therefore, by eliminating any zero errors we would increase the accuracy of the experiment.