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# Gas Laws: Boyle's Law

### 1.0 Gas Laws 1.1 Boyle's Law

A gas can be described in terms of its Pressure (P), Volume (V), and absolute Temperature (T).

1.1 Boyle's law (How V varies with P at constantT) Figure 1.1(a): Set-up to demonstrate Boyle's law (ANIM)

Questions 1.1(a): Previous and current experiences 1. What happens to the volume, V, and pressure, P, of trapped air when the piston is moved inwards?
2. Does this agree with what we observe when an inflated rubber balloon is squeezed?
3. What happens to the volume, V, and pressure, P, of trapped air when the piston is moved outwards?
4. Does the mass of trapped air change?
5. Does the temperature of trapped air change, if the piston is moved slowly?
6. How does the volume of a fixed mass of gas at constant temperature vary with pressure?

Answers to Questions 1.1a NB: Air is used to represent a gas because it is itself a mixture of gases and, physically, it behaves like a gas.

Pressure of a fixed mass of gas increases as volume decreases. But, precisely, how does it? Is the relationship linear (a straight line), or inverse (a curve)? Let us take measurements to answer this question.

Set-up Figure 1.1(b): Boyle's law apparatus (ANIM)

h represents excess pressure on the gas in mm of mercury (mmHg)

l represents volume of the gas.

Observe the animated (or video) demonstration of Boyle's law, and record at least six pairs of corresponding values of h and l.

Questions 1.1(b) 1. What happens to the height, h, of mercury column and length, l, of air column as the open limb of the U-tube is raised?
2. Plot a graph of l (vertical axis) against h.
3. We have used l to represent volume, V. How can we obtain the actual value of V?
4. Is the graph linear or inverse?
5. State the relationship between volume (V) and pressure (P) of a fixed mass of gas at constant temperature (Boyle's law).
6. Write a mathematical equation relating P and V to represent Boyle's law.

Answers to Questions 1.1b Boyle's law: Pressure of a fixed mass of gas is inversely proportional to volume of the gas if temperature is kept constant. Figure 1.1(c): Breathing motion demonstrating Boyle's law (ANIM)

In Figure 1.1(c), the outer circle represents a rigid container and the inner circle, the volume of gas contained. As P increases, V decreases and vice versa.

For calculations,

P is inversely proportional to V; or PV = Constant, k

That is,

P1V1 = P2V2 (where 1 and 2 represent initial and final values respectively).

NB: In the experiment, pressure P was changed (varied) directly by raising or lowering the free limb of the tube. As a result, V also changed. So, a change in P caused a change in V, in the same manner a change in x causes a change in y in the Cartesian plane. So, P is normally plotted on the horizontal axis.

Questions 1.1(c) A fixed amount of gas occupies 450 ml at a pressure of 760 mmHg. Determine its volume at a pressure of 1140 mmHg (1.5 atm) if its temperature does not change.

Answers to Questions 1.1c 