# Practical: Verification of Boyles law

### Introduction

In this practical the pressure of a sample of gas trapped in a syringe will be measured with a pressure sensor.

### Theory

Boyles law states that for a fixed mass of gas at constant temperature the pressure will be inversely proportional to the volume. This can be expressed as:

PV = nRT

Where n = the number of moles
R = molar gas constant (8.31 m2kgs-2K-1mol-1)

### Method

• Connect the pressure sensor to the interface and set up the software to measure pressure.
• Connect the syringe to the pressure sensor making sure that it is full of air.
• Make sure that everything is working by pressing the piston to see if the pressure increases.
• Measure the pressure of air as the volume is reduced in steps. To do this you can either read the values of pressure directly off the digital display or record values on a graph/table.
• Estimate the uncertainties in your measurements.
• In a spreadsheet calculate values of 1/P and plot a graph of V vs 1/P.
• Calculate the uncertainty in 1/P by using (1/Pmin -1/Pmax)/2. If you have a range of pressures then select the max and min values, if you have only one measurement of pressure for each volume then find the max and min by adding and subtracting the estimated uncertainty.

#### If using Capstone

• Switch on the sensor and start Capstone
• Choose "table and graph" from the options.
• Click hardware selection and choose pressure sensor

• Select pressure in the table header

• You are going to enter the volume by hand so create a new column "user entered data" and edit the heading to Volume (ml).

• Enter the volumes from 50 to 30 ml in steps of 2 ml
• You are going to reduce the volume in steps and measure the pressure for each step. To do this set the sampling rate to one sample every 10s, this will give you time to change the pressure.

• Prepare the graph by selecting pressure and volume for the y and x axis.
• Run the experiment changing the volume every 10 s

#### Calculating 1/V

You want to see if P is proportional to 1/V so need to calculate 1/V. First set up the calculation

• Click the calculator icon and type 1/ then choose volume from the insert data button menu

Now you can plot P against 1/V and see if it is linear.

### Conclusion and evaluation

• Did your graph support Boyles law?
• Was the intercept (0,0), if not can you think of a reason why it wasn't?
• Use the gradient of your graph to find the number of moles of air in the syringe. Does your value seem reasonable?
• Do you think that the temperature of the gas was constant throughout the experiment? Do you have any evidence to suggest that it wasn't?
• What effect would the gas in the tube have on you result?
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