Relationships among Pressure, Temperature, Volume, and Amount
Goal: Use the pressure-volume relationship (Boyle's Law) to determine the final in liters, if it has a final pressure of atm with no change in temperature and .. The volume (V) of a gas is directly related to the number of moles (n) of the gas. Early scientists explored the relationships among the pressure of a gas (P) . the volume of a sample of gas is directly proportional to the number of moles of gas. For gases, temperature and pressure are closely related to volume, and this The ratio between volume and number of moles is therefore a constant. The ideal gas law also makes it possible to discern certain relations: thus if a gas is in a.
For example, if the initial volume was mL at a pressure of torr, when the volume is compressed to mL, what is the pressure? Plug in the values: 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.
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: Thus the mole makes if possible to compare the mass of one element or one compound to that of another.
Avogadro's law describes the connection between gas volume and number of moles. According to Avogadro's law, if the volume of gas is increased under isothermal and isobarometric conditions, the number of moles also increases.The Relationship Between Pressure and Moles
The ratio between volume and number of moles is therefore a constant. The Ideal Gas Law Once again, it is easy to see how Avogadro's law can be related to the laws discussed earlier, since they each involve two or more of the four parameters: In fact, all the laws so far described are brought together in what is known as the ideal gas law, sometimes called the combined gas law. R is known as the universal gas constant, a figure equal to 0. Like most terms in physics, this one is best expressed in metric rather than English units.
The ideal gas law also makes it possible to discern certain relations: Thus where p 1V 1 is the product of its initial pressure and its initial volume, T 1 its initial temperature, p 2V 2 the product of its final volume and final pressure, and T 2 its final temperature. Thesemore or less restate the terms of the earlier discussion, in which gases were compared to solidsand liquids; however, now those comparisonscan be seen in light of the gas laws.
First, the size of gas molecules is minusculein comparison to the distance between them, making gas highly compressible. In other words, there is a relatively high proportion of emptyspace between gas molecules. Second, there is virtually no force attractinggas molecules to one another. Third, though gas molecules move randomly, frequently colliding with one another, theirnet effect is to create uniform pressure. Fourth, the elastic nature of the collisionsresults in no net loss of kinetic energythe energy that an object possesses by virtue of itsmotion.
If a stone is dropped from a height, it rapidly builds kinetic energybut upon hitting anonelastic surface such as pavement, most of thatkinetic energy is transferred to the pavement. In the case of two gas molecules colliding, however, they simply bounce off one another, only to collide with other molecules and so on, with no kinetic energy lost.
Fifth, the kinetic energy of all gas molecules is directly proportional to the absolute temperature of the gas. Laws of Partial Pressure Two gas laws describe partial pressure. Dalton's law of partial pressure states that the total pressure of a gas is equal to the sum of its par tial pressures—that is, the pressure exerted by each component of the gas mixture. As noted earlier, air is composed mostly of nitrogen and oxygen.
Along with these are small components carbon dioxide and gases collectively known as the rare or noble gases: Hence, the total pressure of a given quantity of air is equal to the sum of the pressures exerted by each of these gases. Henry's law states that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the surface of the solution.
This applies only to gases such as oxygen and hydrogen that do not react chemically to liquids. On the other hand, hydrochloric acid will ionize when introduced to water: Inside a can or bottle of carbonated soda is carbon dioxide gas CO2most of which is dissolved in the drink itself.
But some of it is in the space sometimes referred to as "head space" that makes up the difference between the volume of the soft drink and the volume of the container. At the bottling plant, the soda manufacturer adds high-pressure carbon dioxide to the head space in order to ensure that more CO2 will be absorbed into the soda itself.
6.3: Relationships among Pressure, Temperature, Volume, and Amount
This is in accordance with Henry's law: The higher the pressure of the CO2 in the head space, the greater the amount of CO2 in the drink itself; and the greater the CO2 in the drink, the greater the "fizz" of the soda. Once the container is opened, the pressure in the head space drops dramatically.
Once again, Henry's law indicates that this drop in pressure will be reflected by a corresponding drop in the amount of CO2 dissolved in the soda. Over a period of time, the soda will release that gas, and will eventually go "flat. A fire extinguisher consists of a long cylinder with an operating lever at the top. Inside the cylinder is a tube of carbon dioxide surrounded by a quantity of water, which creates pressure around the CO2 tube.
A siphon tube runs vertically along the length of the extinguisher, with one opening near the bottom of the water. The other end opens in a chamber containing a spring mechanism attached to a release valve in the CO2 tube.
The water and the CO2 do not fill the entire cylinder: When the operating lever is depressed, it activates the spring mechanism, which pierces the release valve at the top of the CO2 tube. When the valve opens, the CO2 spills out in the "head space," exerting pressure on the water. This high-pressure mixture of water and carbon dioxide goes rushing out of the siphon tube, which was opened when the release valve was depressed.
All of this happens, of course, in a fraction of a second—plenty of time to put out the fire. Aerosol cans are similar in structure to fire extinguishers, though with one important difference.
As with the fire extinguisher, an aerosol can includes a nozzle that depresses a spring mechanism, which in turn allows fluid to escape through a tube. But instead of a gas cartridge surrounded by water, most of the can's interior is made up of the product for instance, deodorantmixed with a liquid propellant. The "head space" of the aerosol can is filled with highly pressurized propellant in gas form, and in accordance with Henry's law, a corresponding proportion of this propellant is dissolved in the product itself.
When the nozzle is depressed, the pressure of the propellant forces the product out through the nozzle. A propellant, as its name implies, propels the product itself through the spray nozzle when the latter is depressed. In the past, chlorofluorocarbons CFCs —manufactured compounds containing carbon, chlorine, and fluorine atoms—were the most widely used form of propellant. Concerns over the harmful effects of CFCs on the environment, however, has led to the development of alternative propellants, most notably hydrochlorofluorocarbons HCFCsCFC-like compounds that also contain hydrogen atoms.
When the Temperature Changes A number of interesting things, some of them unfortunate and some potentially lethal, occur when gases experience a change in temperature. In these instances, it is possible to see the gas laws—particularly Boyle's and Charles's—at work.
There are a number of examples of the disastrous effects that result from an increase in the temperature of a product containing combustible gases, as with natural gas and petroleum-based products. In addition, the pressure on the gases in aerosol cans makes the cans highly explosive—so much so that discarded cans at a city dump may explode on a hot summer day. Yet there are other instances when heating a gas can produce positive effects.
A hot-air balloon, for instance, floats because the air inside it is not as dense than the air outside. By itself, this fact does not depend on any of the gas laws, but rather reflects the concept of buoyancy. However, the way in which the density of the air in the balloon is reduced does indeed reflect the gas laws.
According to Charles's law, heating a gas will increase its volume. Also, as noted in the first and second propositions regarding the behavior of gases, gas molecules are highly nonattractive to one another, and therefore, there is a great deal of space between them. The increase in volume makes that space even greater, leading to a significant difference in density between the air in the balloon and the air outside. As a result, the balloon floats, or becomes buoyant.
Although heating a gas can be beneficial, cooling a gas is not always a wise idea. If someone were to put a bag of potato chips into a freezer, thinking this would preserve their flavor, he would be in for a disappointment. Much of what maintains the flavor of the chips is the pressurization of the bag, which ensures a consistent internal environment in which preservative chemicals, added during the manufacture of the chips, can keep them fresh. Placing the bag in the freezer causes a reduction in pressure, as per Gay-Lussac's law, and the bag ends up a limp version of its earlier self.
Propane tanks and tires offer an example of the pitfalls that may occur by either allowing a gas to heat up or cool down by too much. Because most propane tanks are made according to strict regulations, they are generally safe, but it is not entirely inconceivable that an extremely hot summer day could cause a defective tank to burst.
Certainly the laws of physics are there: Because of the connection between heat and pressure, propane trucks on the highways during the summer are subjected to weight tests to ensure that they are not carrying too much of the gas.
On the other hand, a drastic reduction in temperature could result in a loss in gas pressure. If a propane tank from Florida were transported by truck during the winter to northern Canadathe pressure would be dramatically reduced by the time it reached its destination.
One of these, common to everyone, is that which makes the car run: The other is, fortunately, a less frequent phenomenon—but it can and does save lives.
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This is the operation of an air bag, which, though it is partly related to laws of motion, depends also on the behaviors explained in Charles's law. With regard to the engine, when the driver pushes down on the accelerator, this activates a throttle valve that sprays droplets of gasoline mixed with air into the engine.
Older vehicles used a carburetor to mix the gasoline and air, but most modern cars use fuel-injection, which sprays the air-gas combination without requiring an intermediate step. The mixture goes into the cylinder, where the piston moves up, compressing the gas and air. While the mixture is still compressed high pressure, high densityan electric spark plug produces a flash that ignites it.
The heat from this controlled explosion increases the volume of air, which forces the piston down into the cylinder. This opens an outlet valve, causing the piston to rise and release exhaust gases. As the piston moves back down again, an inlet valve opens, bringing another burst of gasoline-air mixture into the chamber. The piston, whose downward stroke closed the inlet valve, now shoots back up, compressing the gas and air to repeat the cycle. The reactions of the gasoline and air are what move the piston, which turns a crankshaft that causes the wheels to rotate.
So much for moving—what about stopping?