What is a Gas?
Gases are a state of matter with these properties:
Particles are far apart
Particles move very fast
No definite shape
No definite volume
Gas Laws
Gas Laws are simple mathematical equations that show the relationships between pressure (p), volume (v), temperature (T), and moles (n), of gas. The basic gas laws only involve pressure, temperature, and volume. The gas laws go by the Kelvin temperature scale, because it does not have negative or zero values like Celsius does. To convert Celsius to Kelvins, just add 273 to the Celsius value.
K = C + 273
Gases are a state of matter with these properties:
Particles are far apart
Particles move very fast
No definite shape
No definite volume
Gas Laws
Gas Laws are simple mathematical equations that show the relationships between pressure (p), volume (v), temperature (T), and moles (n), of gas. The basic gas laws only involve pressure, temperature, and volume. The gas laws go by the Kelvin temperature scale, because it does not have negative or zero values like Celsius does. To convert Celsius to Kelvins, just add 273 to the Celsius value.
K = C + 273
Boyle's Gas Law (1662)
The pressure of a fixed amount of gas varies inversely with the volume at constant temperature, meaning you will get an inverse relationship every time you compare the initial (starting) volume and pressure with the new volume and pressure.
Boyle's Law
P1 (V1) = P2 (V2)
P1 and V1 equal starting values, P2 and V2 equal new values.
Ex. Using 14.3 L of N2 as the initial volume, calculate the volume that would result if the pressure was raised from 150 kPa to 250 kPa.
The pressure of a fixed amount of gas varies inversely with the volume at constant temperature, meaning you will get an inverse relationship every time you compare the initial (starting) volume and pressure with the new volume and pressure.
Boyle's Law
P1 (V1) = P2 (V2)
P1 and V1 equal starting values, P2 and V2 equal new values.
Ex. Using 14.3 L of N2 as the initial volume, calculate the volume that would result if the pressure was raised from 150 kPa to 250 kPa.
P1- 150 kPa
V1- 14.3 L P2- 250 kPa V2- ? |
150(14.3) = 250 (V2)
2145 = 250 (V2) 250 250 8.6 L = V2 |
Charles's Gas Law (1787)
The volume of a fixed mass of gas varies directly with the temperature at a constant pressure, meaning when the volume of the gas increases, the temperature does too. Temperature must be in Kelvin.
Charles's Law
V1 = V2
T1 T2
Ex. A sample of gas occupied a volume of 5.0 L at a temperature of 37.0C. If the temp were to increase by 6C, what would be the volume of the gas under this new condition?
The volume of a fixed mass of gas varies directly with the temperature at a constant pressure, meaning when the volume of the gas increases, the temperature does too. Temperature must be in Kelvin.
Charles's Law
V1 = V2
T1 T2
Ex. A sample of gas occupied a volume of 5.0 L at a temperature of 37.0C. If the temp were to increase by 6C, what would be the volume of the gas under this new condition?
V1- 5.0 L
T1- 37C -> 310K V2- ? T2- 43C -> 316K |
5 = V2
310 316 1580 = 310 (V2) 310 310 5.1 L = V2 |
Gay-Lussac's Gas Law (1802)
The pressure of a fixed mass of gas varies directly with the temperature and constant volume, meaning when the
Gay-Lussac's Law
P1 = P2
T1 T2
Ex. The gas left in a used aerosol can is at a pressure of 125.3 kPa at 17C. If the can is thrown into a fire, what will the pressure be inside of the can at 1045C?
The pressure of a fixed mass of gas varies directly with the temperature and constant volume, meaning when the
Gay-Lussac's Law
P1 = P2
T1 T2
Ex. The gas left in a used aerosol can is at a pressure of 125.3 kPa at 17C. If the can is thrown into a fire, what will the pressure be inside of the can at 1045C?
P1- 125.3 kPa
T1- 17C -> 290K P2- ? T2- 1045C -> 1318K |
125.3 = P2
290 1318 165145.4 = 290 (P2) 290 290 570kPa = P2 |
The Combined Gas Law (1802)
This law takes Boyle's, Charles's, and Gay-Lussac's laws and combines them into one.
Combined Gas Law
P1 (V1) = P2 (V2)
T1 T2
Ex. A sample of gas took up 35.0 L of space at 124C and 84.56 kPa. If the temperature increased by 16C and the pressure changed to 4.56 atm, what would the resulting volume be?
First we have to convert either Kpa's to atm's or vise versa because the pressures have to be the same unit. It doesn't matter which way you convert it, but we're goin to do atm's to kPa's.
This law takes Boyle's, Charles's, and Gay-Lussac's laws and combines them into one.
Combined Gas Law
P1 (V1) = P2 (V2)
T1 T2
Ex. A sample of gas took up 35.0 L of space at 124C and 84.56 kPa. If the temperature increased by 16C and the pressure changed to 4.56 atm, what would the resulting volume be?
First we have to convert either Kpa's to atm's or vise versa because the pressures have to be the same unit. It doesn't matter which way you convert it, but we're goin to do atm's to kPa's.
P1- 84.56 kPa
V1- 35.0L T1- 124C -> 397K P2- ? V2- 4.56 atm ->462.042kPa T1- 140C -> 413K |
4.56 atm| 101.325 kPa = 462.042 kPa
| 1 atm 84.56 (35) = 462 (V2)
397 413 1222314.8 = 183414 (V2) 183414 183414 6.66L = V2 |
Ideal Gas Law
We start using moles, n, in the ideal gas laws. R is known as the gas law, it's value is never zero. All of the units for P, V, n, and T must match the units in the R value, meaning that your P has to be in atm, V in L, n in mol, and T in K. If they don't match you must convert them.
We start using moles, n, in the ideal gas laws. R is known as the gas law, it's value is never zero. All of the units for P, V, n, and T must match the units in the R value, meaning that your P has to be in atm, V in L, n in mol, and T in K. If they don't match you must convert them.
Ideal Gas Law
PV = nRT
Just use the R that matches the pressure unit.
Ex. If 234.68 g of Cl2 was compressed at 3534 mmHg of pressure and -13.8C, what volume would it have?
PV = nRT
Just use the R that matches the pressure unit.
Ex. If 234.68 g of Cl2 was compressed at 3534 mmHg of pressure and -13.8C, what volume would it have?
P-3534 mmHg
V- ? n- 234.68g Cl2 T- 259K |
234.68 g Cl2| 1 mole = 3.31
| 70.9 g Cl2 3534 (V) = 3.31 (62.4) (259.2)
3534 (V) = 53536.20 3534 3534 V= 15.1 L |
Dalton's Law of Partial Pressures
The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases, meaning when you add together all the partial pressures of the individual gases you get the total pressure of the mixture.
Partial Pressure
Ptotal = P1 + P2 +...
Ex. Hydrogen gas is collected over water at 22.5C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa.
Ptotal = PH2 + P2 H2O
94.4 kPa = PH2 + 2.72 kPa
91.7 = PH2
The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases, meaning when you add together all the partial pressures of the individual gases you get the total pressure of the mixture.
Partial Pressure
Ptotal = P1 + P2 +...
Ex. Hydrogen gas is collected over water at 22.5C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa.
Ptotal = PH2 + P2 H2O
94.4 kPa = PH2 + 2.72 kPa
91.7 = PH2
Graham's Gas Law
This law is based on the speed of diffusion and effusion.
Diffusion- spreading of gas molecules throughout a container until evenly distributed.
Effusion- Passing of gas molecules through a tiny opening in a container.
Graham's Law
This law is based on the speed of diffusion and effusion.
Diffusion- spreading of gas molecules throughout a container until evenly distributed.
Effusion- Passing of gas molecules through a tiny opening in a container.
Graham's Law
Ex. A molecule of oxygen gas has an average speed of 12.3 m/s at a given temperature and pressure. What is the average speed of hydrogen molecules at the same conditions?
VH2 = | mO2
VO2 \| mH2
(That's supposed to be a square root sign)
VH2 = | 32.00 g/mol
12.3 m/s \|2.02 g/mol
VH2 = 3.980
12.3 m/s
VH2 = 49.0 m/s
VH2 = | mO2
VO2 \| mH2
(That's supposed to be a square root sign)
VH2 = | 32.00 g/mol
12.3 m/s \|2.02 g/mol
VH2 = 3.980
12.3 m/s
VH2 = 49.0 m/s