User:GasLaws4ever

= Gas Laws = There are only a few gases from the periodic table that exist at room temperature which are H2, N2, O2, F2, Cl2, and the noble gases. At room temperature, molecules move about 1000 miles per hour. Gases move slower at lower temperatures and faster at higher temperatures. To help us understand gas behaviors we use the kinetic molecular theory of gases which is a model of the behavior of a gas. The Gas Laws have various functions and properties.The four properties of gas include: pressure, volume, temperature, and the amount of gas. Gases obey gas laws aside from their differences in chemical properties.

Boyle’s Law
The inverse between the pressure and volume of gas is what is known as Boyle’s Law or the pressure - volume law. When pressure increases, volume decreases and vice versa. Robert Boyle created “Boyle’s Law” in 1662 to detect the diversity of volume and pressure at a constant temperature. An example of Boyle’s Law is shown below. The equation used to describe this is $$P_1 V_1 = P_2 V_2$$

Example : A sample of hydrogen gas (H2) has a volume of 7.0 L and a pressure of 3.0 atm. What is the new pressure, in atmospheres, if it’s volume decreases to 4.0 L with no change in temperature or amount of gas?

$$P_1 V_1 = P_2 V_2$$  No change in number of moles and temperature

$$P_1$$= 3.0 atm

$$V_1$$= 7.0 L

$$P_2$$= x

$$V_2$$= 4.0 L

Now plug in the variables and solve.

$$3.0(7.0) = x (4.0)$$

The answer is 5.25 atm.

Charles law
In 1787, Jacques Charles law suggests that the volume and is directly related to temperature. Since they are directly related that means that they increase and decrease together. When dealing with temperature in Gas Laws, temperature must be converted to Kelvin temperature.

The equation used to describe this is $$\frac{V_1}{T_1}= \frac{V_2}{T_2}$$

Example : A climber has a core body temperature of  37℃. He inhales 500mL air at a temperature of -7℃. What is the volume in mL will occupy her lungs?

$$V_1$$= 500mL

$$T_1$$= 37℃ + 273= 310K

$$V_2$$= $$x$$

$$T_2$$= -7℃+ 273= 266K

Now plug in the variables and solve.

$$\frac{500}{310}=\frac{x}{429}$$

The answer is 691 mL.

Gay-Lussac’s Law
Have you ever wondered why your tires look flat in the winter  when you just filled them up? This is a perfect example of Gay-Lussac’s Law and how pressure and temperature and pressure are directly related. As the temperature decreases, the gas molecules in your tires move slower and in turn the pressure is lowered. We show this relationship by using the equation:

$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$   The number of moles and volume is constant.

Example : An aerosol can is has a pressure of 3.0 atm at 70℃. It is then heated to 82℃. What is the pressure in the can at 180°F?

$$P_1$$= 3.0 atm

$$T_1$$= 70°F +273= 343K

$$P_2$$= $$x$$

$$T_2$$= 82°C+273= 255K

Now plug in the variables and solve.

$$\frac{3}{343} = \frac{x}{255}$$

The answer is 2.2 atm.

The Combined Gas Law
Concerning the Combined Gas Law, we will combine pressure, volume and temperature in the equation needed. We are able to figure out one of these as long as the other two are given and the amount of gas remains constant. The equation used to describe this is $$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$

Example : A 26.0 mL gas bubble is released in a baby's stomach at a 4.00 atm pressure and a temperature of 33℃. What is the volume in milliliters, of the bubble when it reaches 2.00 atm at a temp of 22℃? (assuming that the amount of gas does not change)

$$P_1$$ = 4.00 atm                  $$P_2$$=2.00 atm

$$V_1$$= 26.0 mL                    $$V_2$$= $$x$$

$$T_1$$= 33℃ +273 = 306 K   $$T_2$$= 22℃ +273 = 295 K

Now plug in the variables and solve.

$$\frac{4.00( 26.0)}{306} = \frac{2.00(x)}{295}$$

The answer is 50.1 mL

Avogadro’s Law
We all know that the more air we put in a balloon the more bigger it gets. In scientific terms, the number of moles (n) is directly related to volume (v).

The equation we use to explain this is:

$$\frac{V_1}{n_1} = \frac{V_2}{n_2}$$ Pressure and temperature are constant.

Avogadro's law is similar to Gay-Lussac’s Law but the constant variables are switched. Instead of  the number of moles and volume staying constant, the pressure and temperature are constant.

Example : A bounce house has a volume of 30 L with 3.0 moles of air. How much air, in liters, will occupy the bounce house if 5.0 moles of air of pumped inside?

$$V_1$$= 30 L

$$n_1$$= 3.0 m

$$V_2$$= $$x$$

$$n_2$$= 5.0 m

Now plug in the varibale and solve.

$$\frac{30}{3.0} = \frac{x}{5.0}$$

So the bounce house will contain 50 L of air.

Dalton’s Law
An example of a mixture of gases is the air you breathe because it is a mixture of mostly oxygen and nitrogen gases. Each gas exerts its partial pressure, which is the pressure it would exert if it were the only gas in the container. Dalton’s Law states that the total pressure of a gas mixture is the sum of the partial pressures of the gases in the mixture.

$$Ptot = P_1 + P_2 + P_3$$

Total Pressure of a gas mixture = Sum of the partial pressures of the gases in the mixture

Example : Suppose we have two separate tanks, one filled with helium at 4.0 atm and the other filled with argon at 8.0 atm. When the gases are combined in a single tank at the same volume and temperature, the number of gas molecules, not the type of gas, determines the pressure in a container. Then the pressure of the gases in the gas mixture would be 12.0 atm, which is the sum of their individual or partial pressures.

$$P_1$$=4.0 atm

$$P_2$$=8.0 atm

$$P_3$$=12.0 atm

Now plug in the variables and solve.

$$Ptot$$ = 4.0 + 8.0 + 12.0

The answer is 24atm.