Required Practical: Investigating Gas Laws
Investigating Boyle's Law
- The overall aim of this experiment is to investigate the effect of Boyle's Law
- This is the effect of pressure on volume at a constant temperature
- This is just one example of how this required practical might be tackled
Variables
- Independent variable = Mass, m (kg)
- Dependent variable = Volume, V (m3)
- Control variables:
- Temperature
- Cross-sectional area of the syringe
Equipment List
- Resolution of measuring equipment:
- Pressure gauge = 0.02 × 105 Pa
- Volume = 0.2 cm3
- Vernier Caliper = 0.02 mm
Method
Apparatus setup for Boyle’s Law
- With the plunger removed from the syringe, measure the inside diameter, d of the syringe using a vernier calliper. Remember to take at least 3 repeat readings and find an average
- Push the syringe upwards to remove the air until it reads the lowest volume of air visible
- The plunger should be replaced and the rubber tubing should be fit over the nozzle and clamped with a pinch clip as close to the nozzle as possible (this is to stop air escaping)
- Set up the apparatus as shown in the diagram and make sure the temperature of the room will remain constant throughout
- Record the volume shown on the syringe
- Add the 100 g mass holder with a 100 g mass on it to the loop of string at the bottom of the plunger. Wait a few seconds to ensure the temperature is kept constant since work is done against the plunger when the volume increases
- Record the value of the new volume from the syringe scale
- Repeat the experiment by adding two 100 g masses at a time up to 8-10 readings. This is so a significant change in volume can be seen each time
- Record the mass and volume
- An example table of results might look like this:
Analysing the Results
- Boyle’s Law can be represented by the equation:
pV = constant
- This means the pressure must be calculated from the experiment
- The exerted pressure of the masses is calculated by:
- Where:
- F = weight of the masses, mg (N)
- A = cross-sectional area of the syringe (m2)
- The cross-sectional area is found from the equation for the area of a circle:
- To calculate the pressure of the gas:
Pressure of the gas = Atmospheric pressure – Exerted pressure from the masses
- Where:
- Atmospheric pressure = 101 kPa
- The table of results may need to be modified to fit these extra calculations. Here is an example of how this might look:
- Once these values are calculated:
- Plot a graph of p against 1 / V and draw a line of best fit
- If this plot is a straight line graph, this means that the pressure is proportional to the inverse of the volume, hence confirming Boyle's Law (pV = constant)
Evaluating the Experiment
Systematic Errors:
- There may be friction in the syringe which causes a systematic error
- Use a syringe that has very little friction or lubricated it, so the only force is from the weights pulling the syringe downwards
Random Errors:
- The reading of the volume should be taken a few seconds after the mass has been added to the holder
- Otherwise, a reading will be taken when the temperature is not constant
- This experiment is prone to many random errors with the equipment and surrounding temperature
- Make sure to take repeat readings to decrease the effect of these
Safety Considerations
- A counterweight or G-clamp must be used to avoid the stand toppling over and causing injury, especially if the surface is not completely flat
Investigating Charles's Law
- The overall aim of this experiment is to investigate the effects of Charles’s law, which is the effect of temperature on volume at constant pressure
- This is just one example of how this required practical might be tackled
Variables
- Independent variable = Temperature, T (°C)
- Dependent variable = Height of the gas, h (cm)
- Control variables:
- Pressure
Equipment List
- Resolution of measuring equipment:
- 30 cm ruler = 1 mm
- 2 litre beaker = 50 ml
Method
Apparatus setup for Charles’s Law
- The capillary tube should have one open end at the top and a closed end at the bottom. This is to keep the pressure constant at atmospheric pressure. Assume the temperature of the water is the same as the temperature of the gas
- Set up the apparatus as shown in the diagram. Make sure the drop of sulfuric acid is halfway up the tube (the gas below this drop is being studied)
- Boil some water in a kettle and pour it into the beaker for the full 2 litres. Make sure the waterline is higher than the drop of sulfuric acid, therefore surrounding all the gas, and stir well
- When the temperature goes down to 95 °C, read the height of the gas (this is up to the bottom of the sulfuric acid) using the ruler
- Record the height of the gas as the temperature decreases in increments of 5 °C. Make sure you have at least 8 readings
- An example table of results might look like:
Analysing the Results
- Plot a graph of the height of the gas in cm and the temperature in °C
- Draw a line of best fit
- Calculate the gradient
- If this is a straight-line graph, then this means the temperature is proportional to the height. Since the height is proportional to the volume (V = πr2h) then this means Charles’s law is confirmed, and the temperature is proportional to the volume too
- To find a value of absolute zero T0, the equation of the graph can be written as
h = mT + c
- Comparing this to the equation of a straight line: y = mx + c
- y = h
- x = T
- m = gradient
- c = y-intercept
- Plot a graph of the height of the gas in cm and the temperature in °C
- Draw a line of best fit
- Calculate the gradient
- Since c is a constant:
h0 - mT0 = h1 - mT1
- At absolute zero, h0 = 0
- mT0 = h1 - mT1
- Picking any co-ordinate of h and t from the line of best fit, and substituting into the equation will give a value of absolute zero
- Check this value is close to the accepted value of –273°C
Evaluating the Experiment
Systematic Errors:
- Make sure the capillary tube is close to the ruler and properly aligned to get an accurate value of the height of the gas
- Otherwise, the reading taken will be slightly out each time
Random Errors:
- There can be parallax error when taking the temperature and height readings - take readings at eye level to avoid this
- Stir the water well so it is the same temperature throughout the beaker, and so the gas is the same temperature as well
Safety Considerations
- When using boiling water, make sure not to spill it onto your skin or any electrical equipment
- Make sure the bench is protected with a heat-proof mat so the boiling water does not damage the surface
Worked example
A student investigates the relationship between the temperature and volume of a column of air. They obtain the following results:Calculate the value of absolute zero from these results and its relative percentage error with the accepted value of –273.15 °C
Step 1: Plot a graph of temperature T against volume V
- Make sure the axes are properly labelled and the line of best fit is drawn with a ruler
Step 2: Calculate the gradient of the graph
- The gradient is calculated by:
Step 3: Calculate the value of absolute zero
- Where T0 is absolute zero and (T1, h1) is any co-ordinate on the line of best fit
- Using the coordinates (60, 10.6):
Step 4: Calculate its relative percentage error with the accepted value of –273.15 °C