Required Practical: Investigating Gas Laws (AQA A Level Physics): Revision Note

Required practical: investigating gas laws

Investigating Boyle's law

• The overall aim of this experiment is to investigate 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 calliper = 0.02 mm

Method

1. Before setting up the apparatus as shown in the diagram the inside diameter, d of the syringe needs to be measured using a vernier calliper after removing the plunger. Remember to take at least three repeat readings and find an average.

2. Determine the lowest volume of air visible by pushing the syringe upwards to remove as much air as possible.

3. At this lowest volume, 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).

4. Set up the apparatus as shown in the diagram and ensure the temperature of the room remains constant throughout the experiment.

5. Record the volume shown on the syringe before adding the masses and the mass holder.

6. 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 before reading volume to ensure the temperature is kept constant (since work is done against the plunger when the volume increases).

7. Record the value of the new volume from the syringe scale.

8. Repeat the experiment by adding two 100 g masses at a time up to eight to ten readings. This is so a significant change in volume can be seen each time.

9. 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:

$pV=\mathrm{constant}$

• This means the pressure must be calculated from the experiment

• The exerted pressure of the masses is calculated by:

$p=\frac{F}{A}$

• 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:

$A=\frac{\pi d^2}{4}$

• 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:

1. Plot a graph of $p$ against $\frac{1}{V}$ and draw a line of best fit.

2. 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 ($pV=\mathrm{constant}$).

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 lubricate it, so the only force applied is from the masses pulling the syringe downward

• 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

  • Due to the nature of this experiment setup, it is prone to many random errors

    • Take repeat readings to reduce their effect

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 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

1. 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 in the tube.

2. Set up the apparatus as shown in the diagram. Add a drop of sulfuric acid halfway up the tube (the gas below this drop is being studied) to ensure no gas escapes.

3. 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.

4. Allow the temperature to drop down to 95 °C, then read the height of the gas (this is up to the bottom of the sulfuric acid) using the ruler.

5. Record the height of the gas as the temperature decreases in increments of 5 °C. Make sure at least eight readings are taken.

• An example table of results might look like:

Analysing the results

1. Plot a graph of the height of the gas in the capillary tube in cm and the temperature of the water in °C.

2. Draw a line of best fit.

3. Calculate the gradient.

   

4. 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 $T_0$, the equation of the graph can be written as

$h=mT\hspace{0.17em}+\hspace{0.17em}c$

• Comparing this to the equation of a straight line: $y=mx\hspace{0.17em}+c$

  • $y=h$

  • $x=T$

  • gradient = $m$

  • y-intercept = $c$

• $c$ cannot be determined directly, as temperatures this low would cause the water to freeze

  • The straight line equation can be used for two sets of values to determine absolute zero, $T_0$

• Write the equation with $c$ as the subject at $T_0$ and any temperature $T_1$ and height $h_1$ from the experimental data:

$c=h_0-m{T}_0$

$c=h_1-m{T}_1$

$h_0-m{T}_0=h_1-m{T}_1$

• At absolute zero, $h_0=0$

$-m{T}_0=h_1-m{T}_1$

$T_0=T_1-\frac{h_1}{m}$

• 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

• If this value is close to the accepted value of –273 °C then the experiment shows that volume and temperature are directly proportional at constant pressure

Evaluating the experiment

• Systematic Errors:

  • Make sure the capillary tube is secured close to the ruler and properly aligned to get an accurate value for the height of the gas

    • Otherwise, the reading taken will be slightly out each time

• Random Errors:

  • Take temperature and height readings at eye level to avoid a parallax error

  • Stir the water well so it and the gas are the same temperature throughout the beaker

Safety considerations

• Do not spill boiling water onto your skin or electrical equipment 

• Protect the workbench from the boiling water by using a heat proof mat