# Relationship of pressure and volume a confined gas

The gas we will use is air, and it will be confined in a syringe connected to a Gas Determine the relationship between pressure and volume of a gas and. Early scientists explored the relationships among the pressure of a gas (P) and its temperature (T), volume (V), and amount (n) by holding two of the four. In the mid 's, Robert Boyle studied the relationship between the pressure p and the volume V of a confined gas held at a constant temperature.

The pressure generated by an overlying column of fluid is thus termed the hydrostatic pressure.

### Relationships among Pressure, Temperature, Volume, and Amount

The upper boundary of the air column that gives rise to atmospheric pressure is the vacuum of space. Being rather light, the mass of a column of air with a 1 cm2 cross section is almost exactly 1 kg.

If a much heavier liquid substance is used to balance this air column, only a relatively small length would be needed. In addition, because the density of liquids does not change with height most liquids are incompressiblesuch an equivalent liquid column has a well defined upper boundary below a vacuumOne of the heaviest liquids at room temperature is mercury Hg and the height of the Hg-column that is equivalent to normal pressure mb is only mm long For this reason, columns of mercury, "hanging" in an inverted vacuum tube, can be used as practical instruments to measure atmospheric pressure see FigureLutgens and Tarbuck, If water were used instead of mercury, the height of the column equivalent to normal pressure would be The Gas Laws The example of the gas-filled balloon can also be used to explore the basic gas laws see also Appendix D, p.

In the following, lets assume that the balloon is tight, so that the amount or mass of air in it stays the same: With density being the ratio of mass per volume, the gas density of the balloon thus varies only with its volume when mass is held constant.

### Boyle's law - Wikipedia

The Temperature-Volume Law This law states that the volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature. V Same as before, a constant can be put in: Also same as before, initial and final volumes and temperatures under constant pressure can be calculated.

The Pressure Temperature Law This law states that the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature.

P Same as before, a constant can be put in: The Volume Amount Law Amedeo Avogadro Gives the relationship between volume and amount when pressure and temperature are held constant. Remember amount is measured in moles. Also, since volume is one of the variables, that means the container holding the gas is flexible in some way and can expand or contract.

## Boyle's law

If the amount of gas in a container is increased, the volume increases. If the amount of gas in a container is decreased, the volume decreases.

V As before, a constant can be put in: The Combined Gas Law Now we can combine everything we have into one proportion: The volume of a given amount of gas is proportional to the ratio of its Kelvin temperature and its pressure.

Same as before, a constant can be put in: The Ideal Gas Law The previous laws all assume that the gas being measured is an ideal gas, a gas that obeys them all exactly. But over a wide range of temperature, pressure, and volume, real gases deviate slightly from ideal.

Since, according to Avogadro, the same volumes of gas contain the same number of moles, chemists could now determine the formulas of gaseous elements and their formula masses. The idea gas law is: The balloon used by Charles in his historic flight in was filled with about mole of H2.

If the outside temperature was 21 oC and the atmospheric pressure was mm Hg, what was the volume of the balloon?