The method and the results are on the ideal gas law lab. Do the analysis yourself first, then check the answers below.
Quick answer: An ideal gas is a collection of tiny, randomly moving particles whose average kinetic energy is proportional to the kelvin temperature. These answers go with the AP Physics 2 lab on ideal gas law: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
The sample data show a nearly constant product pV, so p varies as 1/V within experimental error. The gradient of the graph equals nRT, which gives a small amount of air of the order of 10⁻³ mol, as expected for a few tens of millilitres at atmospheric pressure.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 9
The air in the tube and sensor also belongs to the gas sample. Without the extra 3 mL the volume is too small, and the graph would not pass through the origin. V total = reading + 3 mL.
Question 2 Check the product
The products are 2323, 2327, 2317, 2329, 2313, 2328 kPa·mL, with a mean of 2323 kPa·mL. They vary by less than 1%, so pV is constant within error and Boyle’s law is supported.
Question 3 The graph
The points lie on a straight line through the origin. This shows p ∝ 1/V, so pV is constant at constant temperature and amount.
Question 4 Gradient
Using the first and last points: (101.0 − 48.5)/(0.04348 − 0.02083) = 2318 kPa·mL. The least-squares fit gives 2325 kPa·mL.
Question 5 Amount of air
slope = nRT, and 1 kPa·mL = 1 × 10⁻³ J. So nRT = 2325 × 10⁻³ J. n = 2.32/(8.31 × 294) = 9.5 × 10⁻⁴ mol.
Question 6 Temperature control
Quick compression warms the gas and quick expansion cools it, so the temperature must be allowed to return to the room temperature. Waiting lets heat flow between the gas and the surroundings. Constant T is required for p ∝ 1/V.
Question 7 Improvement
Use a lubricated syringe to cut leaks, take more points, repeat the series to average out random error, and use a water bath for steady temperature. Repeating gives a smaller uncertainty in the gradient.
