Robert Boyle, a chemist in the mid to late 1600's, was a frail man who was a bachelor all his life. His poor health might be attributed to the fact that he, like most other chemists of his day, tasted his own chemicals and often dosed himself (and his friends) with them to discover any potentially beneficial properties.

At this time, chemistry was just breaking free of alchemy and the search for the elixir to life and the transmutation of lead into gold. Boyle was one of the first to leave behind the secrecy of alchemy and to start doing experiments using the scientific method as well as recording his results so that others could understand them. Although the experiments of these early chemists might seem simplistic to us today, their results form the foundation of chemistry.

Boyle began to study gasses and was the first to recognize that for any fixed about of gas at a fixed temperature, the volume of the gas varied inversely with pressure.

Thus at constant temperature, as pressure increases, volume decreases in a linear fashion. (figure 5.6) and thus V µ 1/P. Can you explain this using the kinetic molecular theory?

Since this is linear, we can include a proportionality constant, a to make an equation:

V = a/P or V P = a at constant T

Since a is constant for any individual gas (it varies with the type of gas) then, for any sample of gas:

V₁ x P₁ = V₂ x P₂

example:

The volume of a balloon on earth is 2.56 L at sea level (1 atm). If the atmospheric pressure on Mars is 7.50 mmHg, then has our balloon increased or decreased in size? By how much?

What would happen to our balloon on Jupiter where the atmospheric pressures can reach 1000 atm?

Jaques Charles, nearly a century later, determined the relationship between the volume of a gas and the temperature of a gas.

Charles’ law: At constant pressure, the volume of a gas varies directly and linearly with its temperature (figure 5.8). Thus: V = b T where b is a proportionality constant specific to that particular gas.

Hence, for any sample of gas, V₁ / T₁ = V₂ / T₂ at constant P

Now Charles couldn’t go too low in temperature (and we still can’t either), but when a volume vs temp graph is extrapolated to zero volume, the line intersects the temperature scale at -273.15ºC. This is the lowest temperature theoretically possible and is the zero point of the Kelvin temperature scale.

T_K = T_ºC + 273.15

We can explain the effects of temperature by referring back to the kinetic molecular theory. Temperature is simply our way of measuring the relative motion of particles in a sample. The higher the temperature, the more motion (greater the velocity of each particle) and hence the more kinetic energy. As temperature drops, kinetic energy drops and the force exerted by the gas particles on their container decreases. If this is an elastic container such as a balloon, then the balloon shrinks to maintain a constant pressure.

example:

If our same balloon, blown up at 1 atm and 22.5 ºC, is now taken to the Palmer Antarctic station where the temperature today is -25.5°C, what will it’s volume be?

A do at home demonstration: Blow up a balloon, preferably one that is spherical rather than elongated. Measure the circumference then place it in the freezer for thirty minutes. Remove from the freezer and immediately measure the circumference of the cold balloon. What should happen? Assuming that the balloon is spherical, can you estimate the temperature of your freezer from this experiment?

Avagadro’s law

About fifty years later, soon after Dalton proposed his atomic theory, Avagadro proposed another hypothesis, that at constant temperature and pressure, the number of particles in a gas sample was directly proportional to its volume.

Until Dalton proposed the existence of atoms and molecules, Avagadro couldn’t have postulated this relationship. It took another fifty years and a very charismatic chemist named Cannizzaro to convince chemists that Avagadro’s hypothesis help up to experimental scrutiny.

So, V = c n where n = number of moles of gas particles and T and P are constant.

therefore V₁/n₁ = V₂ / n₂ at constant T and P

The molar volume of gas is derived from Avagadro’s law. It is simply the volume of 1 mole of gas at 1 atm, 0ºC - what is known as standard temperature and pressure (STP). For most gasses it is close to 22.4 L/mole

Example:

If we wanted out balloon to be exactly 3.00 L in volume at sea level and 22.5ºC and it currently contains 0.105 moles of gas, how much more gas will we have to add? If this gas was nitrogen (N₂), how many grams would we have to add?