The Laws of Gases Help (page 3)
In 1811, Italian physicist Amedeo Avogadro noted that when you have equal volumes of gases at the same temperatures and pressures, the gases will have equal numbers of molecules. Avogadro found that this direct relationship between the number of molecules and the volume of the sample could be written in the following way: V/n (number of molecules) = k (a constant)
V 1 / n 1 = V 2 / n 2
Temperature and pressure are unchanged and constant in Avogadro’s law.
Avogadro’s number ( L ) is a constant number of atoms, ions, or molecules in a sample. It is equal to the number of atoms in 12 grams of carbon-12 or 6.022 × 10 23 .
To give you an idea of the unthinkable number of molecules contained in Avogadro’s number, take a bunch of hazelnuts and cover the United States. To equal Avogadro’s number, you would cover it with a layer over 100 kilometers (about 70 miles) deep.
In 1662, an Irish chemist named Robert Boyle tried to figure out how gas is affected by outside factors. To test this, he bent a glass tube into a hook shape and sealed one end. Into this tube he poured mercury. Boyle discovered that the mercury pushed ahead of it a small volume of air to the end that could not escape out of the tube. Since mercury is so heavy and dense, Boyle found that the more he poured into the tube, the harder it pushed against the trapped air at the end of the tube. After adding enough mercury to push (or compress) the trapped air into ½ of its space (or volume) he realized that the more pressure pushing against a trapped volume of gas, the more it was compressed if the temperature stays the same. Boyle described pressure affect in the following way.
In Boyle’s law , when temperature is held constant, a volume of gas is inversely proportional to the pressure; V α 1/P
With further tests, Boyle found that by doubling the pressure, the volume of the gas was reduced by ½. When the pressure was tripled, the volume of gas was squashed to 1 / 3 of its original volume.
Boyle decided to multiply both sides of the equation by pressure ( P ) to get rid of the inverse 1/ P . Then, if you know two volumes and want to figure out the pressures or have two pressures and want to find the volumes, then the formula below will give the unknown values:
P 1 V 1 = P 2 V 2
See if you can figure out the amount of oxygen in a container if it has a volume of 4.0 liters. The pressure of the gas is 1470 psi when at 25 °C. If 1 atm of pressure is pushing on the volume, with no temperature change, find the volume of the oxygen.
Since a greater volume of gas can be stored at a higher pressure, many gases are stored at increased pressure.
The second of the ideal gas laws has to do with the affect of changing the temperatures of gases. This different angle of research was done in 1787 by French physicist Jacques Charles. Charles was said to be very interested in the hot air ballooning that was sweeping France as a huge sport at the time. He was known as one of the best balloonists in France. In fact, Charles was the first to use helium to inflate a balloon capable of carrying passengers.
Charles’ scientific nature caused him to use ballooning as a way to test his ideas about gases and temperature. He found that the more a gas was heated, the more its volume increased. He described this with the following equation:
V 1 / T 1 = V 2 / T 2
V 2 = V 1 × T 2 / T 1
If we think of what is happening with the atoms of the gas, it is easy to remember Charles’ law. Temperature (heat) provides energy to a sample. When atoms are energized (heated), they move around a lot. Like a happy puppy that can’t stay in one place, heated atoms get crazy wild and hit the sides of their containers harder and more often causing it to expand.
In Charles’ law , when pressure is held constant, a volume of gas is directly proportional to the Kelvin temperature; V α T
The kinetic energy (KE) increases, but the mass stays the same, so the velocity has to increase.
Kinetic energy = ½ m v 2
If we have a balloon of 1.0 liter that is flexible and can expand with increased temperature (from 20°C to 45°C), find the volume of the balloon after it is heated. (Hint: add 273 to the Celsius temperatures to get everything into Kelvin.)
T 1 = 20 + 273 = 293 K
T 2 = 45 + 273 = 318 K
V 1 = 1.0 liter, V 2 = X
1.0 liters/293 K = x liters/318 K
x = 1.0 liter × 318 K/293 K
x = 1.09 liters = V 2
Around the same time that Charles was ballooning and experimenting in France, another French scientist, Joseph Gay-Lussac, was studying the connection between temperature and gas pressure. His research added the third of the ideal gas laws. Gay-Lussac discovered that as temperature increases and kinetic energy increases, pressure increases too.
In Gay-Lussac’s law , when volume is held constant, the pressure of a gas is directly proportional to the Kelvin temperature; P α T .
It’s a case of atoms dancing wildly in a constant volume again. As the temperature increases, the pressure increases and the atoms collide with the container’s walls faster and harder. This increases the kinetic energy. The following equation describes what happens:
P 1 / T 1 = P 2 / T 2
P 2 = P 1 × T 2 / T 1 or T 2 = T 1 × P 2 / P 1
When you read the label of a pressurized spray paint can, you will probably see a warning not to let the can come in contact with heat. You can thank Gay-Lussac for this warning. If the can is heated enough, the pressure will increase and the can will explode. Besides being very dangerous, you will paint everything in sight. The take home chemistry message is, never heat a spray can !
If you have a pressurized (875 torr), room temperature (25°C) hair spray can with a volume of 15 ounces (oz.) that is in a house fire and heated to 1500°C, find the pressure inside the can before it explodes.
V 1 = 15 oz., V 2 = 15 oz. (just before it explodes)
T 1 = 27°C, T 2 = 1500°C
Remember to add 273 to get the temperature in kelvin.
T 1 = 27 + 273 = 300 K
T 2 = 1500 + 273 = 1773 K
P 1 = 875 torr
P 2 = x torr
P 2 = 875 torr × 1773 K/300 K = x torr
P 2 = 5171 torr
The pressure at this high heat is nearly 6 times what the spray can is designed to hold!
Ideal Gas Law
These three gas laws are referred to as the ideal gas laws . They were discovered by different scientists at different times, but all add up to explain the strange and amazing things that gases do in different conditions. The formula that considers all three laws is written as:
PV = n RT
where P = pressure, V = volume, n = number of moles of gas at constant pressure and temperature, R = molar gas constant (0.821 liter × atm/(kelvin × mol)), T = temperature. An ideal gas is one that meets all the rules of the gas laws. Gases that are mixtures of different molecules have some quirks that don’t follow the gas laws exactly.
Dalton’s Law Of Partial Pressures
John Dalton that we learned about in Chapter 1 as the father of the atomic theory, came up with an idea about how gas pressure works. Like Gay-Lussac, Dalton had a hobby. He was interested in meteorology; the study of the weather. While studying changes in the weather, Dalton did some experiments with vapor pressure. What he found was that, like people, gases are unique and behave in their own way when in a mixture. Each gas, for example, compresses at its own pressure. When using three different gases at a constant temperature, Dalton found that the total pressure of the three gases was equal to the sum of each of the three individual gases. This general rule became known as Dalton’s law of partial pressures.
Dalton’s law of partial pressures says that when you have more than one gas mixed with one or more different gases, the pressures of each gas will add together to give the total pressure of the mixture.
Dalton’s law is probably the easiest of all the gas laws to remember. It is written like this:
P total = P 1 + P 2 + P 3 + P 4 + P 5 + · · ·
If you have an atmosphere of mixed gases on an alien planet, composed of oxygen ( p = 0.3 atm), argon ( p = 0.1 atm), nitrogen ( p = 0.8), and neon ( p = 0.01), what is the total pressure of the atmospheric gases?
P total = P 1 (0.3) + P 2 (0.1) + P 3 (0.8) + P 4 (0.01)
P total = 1.21 atm
The total pressure of the alien atmosphere is greater than that of any of the single gases alone.
Combined Gas Law
Considering all the gas laws, then, you can figure out nearly every temperature, volume, and pressure of a gas if you know the other constants. This can be thought of as the combined gas law .
The combined gas law is made up of the general rules for temperature, volume, and pressure described in Boyle’s, Charles’, and Gay-Lussac’s laws.
It is written as:
P 1 V 1 / T 1 = P 2 V 2 / T 2
When you know five of the six values, you can figure out the missing value. If the volumes don’t change, then you can write the combined gas law as:
V 2 = V 1 × P 1 / P 2 × T 2 / T 1
V 2 = V
1 = P 1 / P 2 × T 2 / T 1 , or P 2 / P 1 = T 2 / T 1 (which is Gay-Lussac’s law)
If a bicycle tire has a volume of 0.5 m 3 at 20°C and 1 atm (760 torr), figure out the volume when taken into the mountains where the pressure is 720 torr and temperature is 14°C.
V 1 = 0.5 m 3 , T 1 = 20°C, T 2 = 14°C, P 1 = 760 tor, P 2 = 720 torr
V 2 = x
T 1 = 20 + 273 = 293 K, T 2 = 14 + 273 = 287 K
V 2 = 0.5 m 3 × 760 torr/720 torr × 287°C/293°C
0.5 m 3 × 1.056 torr × 0.980°C
V 2 = 0.52 m 3
As the temperature and pressure decrease, the tire volume is less compressed and feels mushy. To get the same riding feel on the tires, you might want to pump up the tires a bit.
Practice problems for these concepts can be found at – Chemistry and Gases Practice Test
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