"Partial pressure" in chemistry is the pressure that each gas in a gas mixture exerts on its surroundings, such as a volumetric flask, diving air tank, or atmospheric boundary. You can calculate the pressure of each gas in a mixture if you know the amount of gas, the volume it occupies, and the temperature. The partial pressures can be added together to calculate the total pressure of the gas mixture. On the other hand, the total pressure can be calculated in advance to calculate the partial pressure.
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Part 1 of 3: Understanding the Properties of Gases
Step 1. Treat each gas as an “ideal” gas
In chemistry, an ideal gas is a gas that interacts with other gases without being attracted to its molecules. Molecules that are solitary can bump and bounce like billiard balls without deforming.
- The pressure of an ideal gas increases when it is compressed in a smaller space and decreases when it expands in a larger space. This relationship is called Boyle's Law created by Robert Boyle. Mathematically, the formula is k = P x V, or simplified to k = PV, k is a constant, P is pressure, while V is volume.
- There are several possible units for pressure. One of them is Pascal (Pa). This unit is defined as the force of one newton applied to a surface of one square meter. Another unit is the atmosphere (atm). Atmosphere is the pressure of the Earth's atmosphere at sea level. A pressure of 1 atm is equivalent to 101,325 Pa.
- The ideal gas temperature rises as volume increases and decreases as volume decreases. This relationship is called Charles' Law created by scientist Jacques Charles. The mathematical formula is k = V / T, where k is the volume and temperature constant, V is the volume, and T is the temperature.
- The temperature of the gas in this equation is given in degrees Kelvin, which is obtained by adding the number 273 to the degree value in Celsius.
- The two formulas above can be combined with one equation: k = PV / T, which can also be written as PV = kT.
Step 2. Determine the quantity of gas to be measured
Gases have mass and volume. Volume is usually measured in liters (l), but there are two kinds of mass.
- Conventional mass is measured in grams, but in larger quantities the unit is kilograms.
- Because gases are very light, the units used are molecular mass or molar mass. Molar mass is the sum of the total atomic masses of each atom in the compound that makes up the gas, each atom compared to the number 12 for carbon.
- Since atoms and molecules are too small to count, the quantity of gas is specified in moles. The number of moles present in a given gas can be obtained by dividing the mass by the molar mass and denoted by the letter n.
- The constant K in the gas equation can be replaced by the product of n, the number of moles (moles), and the new constant R. Now the formula is nR = PV/T or PV = nRT.
- The value of R depends on the units used to measure the pressure, volume, and temperature of the gas. For volume in liters, temperature in Kelvin, and pressure in atmospheres, the value is 0.0821 L atm/K mol. This value can be written as 0.0821 L atm K-1 mole -1 to avoid using slashes to represent divisions in units of measurement.
Step 3. Understand Dalton's Law of Partial Pressure
This law was developed by the chemist and physicist John Dalton, who first developed the concept that chemical elements are made of atoms, Dalton's law states that the total pressure of a mixture of gases is the sum of the pressures of the individual gases in the mixture.
- Dalton's law can be written in the form of the following formula Ptotal = P1 + P2 + P3 … the amount of P to the right of the sign equals the amount of gas in the mixture.
- Dalton's law formula can be extended when dealing with various gases in which the partial pressure of each gas is unknown, but whose volume and temperature are known. The partial pressure of a gas is equal to the pressure which presupposes that the gas in that amount is the only gas in the container.
- For each partial pressure the ideal gas formula can be used. Instead of using PV = nRT, only P on the left can be used. For that, both sides are divided by V: PV/V = nRT/V. The two Vs on the right side cancel each other, leaving P = nRT/V.
- We can use it to replace each P on the right that represents a particular gas in the partial pressure formula: Ptotal =(nRT/V) 1 + (nRT/V) 2 + (nRT/V) 3 …
Part 2 of 3: Calculating Partial Pressure, Then Total Pressure
Step 1. Determine the partial pressure equation for each gas you are calculating
For this calculation it is assumed that a 2 liter flask holds 3 gases: nitrogen (N2), oxygen (O2), and carbon dioxide (CO2). Each gas has a mass of 10 g, and a temperature of 37 degrees Celsius. We will calculate the partial pressure of each gas and the total pressure of the gas mixture in the chemical flask.
- The partial pressure formula is Ptotal = Pnitrogen + Poxygen + Pcarbon dioxide.
- Since we are looking for the pressure for each gas with a known volume and temperature, the number of moles of each gas can be calculated based on its mass. The formula can be changed to: Ptotal =(nRT/V) nitrogen + (nRT/V) oxygen + (nRT/V) carbon dioxide
Step 2. Convert the temperature to degrees Kelvin
The temperature in Celsius is 37 degrees, so add 273 to 37 to get 310 degrees K.
Step 3. Find the number of moles of each gas present in the sample
The number of moles of a gas is the mass of the gas divided by its molar mass, which is the sum of the atomic masses of each atom in the mixture.
- For nitrogen gas (N2), each atom has an atomic mass of 14. Since nitrogen is diatomic (a two-atom molecule), the value of 14 must be multiplied by 2 to obtain a molar mass of 28 for the nitrogen in this sample. Next the mass in grams, 10g, is divided by 28, to get the number of moles, so the result is about 0.4 moles of nitrogen.
- For the next gas, oxygen (O2), each atom has an atomic mass of 16. Oxygen is also diatomic, so 16 times 2 gives the molar mass of oxygen in the sample 32. 10 grams divided by 32 gives approximately 0.3 moles of oxygen.
- Next is carbon dioxide (CO2), which has 3 atoms, namely one carbon atom with an atomic mass of 12 and two oxygen atoms with an atomic mass of 16. These three atomic masses are added to get the molar mass: 12 + 16 + 16 = 44. Next 10 grams is divided by 44 so the result is about 0.2 moles of carbon dioxide.
Step 4. Enter the mole values, volume, and temperature
The numbers were entered into the formula: Ptotal =(0, 4 * R * 310/2) nitrogen + (0, 3 *R * 310/2) oxygen + (0, 2 * R *310/2) carbon dioxide.
For simplicity, the units are not written. These units will be erased in the mathematical calculations, leaving only the pressure units
Step 5. Enter the value of the constant R
The total and partial pressures will be expressed in atmospheric units, so the R value used is 0.0821 L atm/K mol. This value is then entered into the equation so that the formula is Ptotal =(0, 4 * 0, 0821 * 310/2) nitrogen + (0, 3 *0, 0821 * 310/2) oxygen + (0, 2 * 0, 0821 * 310/2) carbon dioxide.
Step 6. Calculate the partial pressures for each gas
Now that all the required values are available, it's time to do the math.
- For the partial pressure of nitrogen, 0.4 moles is multiplied by a constant of 0.0821 and a temperature of 310 degrees K, then divided by 2 liters: 0.4 * 0.0821 * 310/2 = 5.09 atm, approximately.
- For the partial pressure of oxygen, 0.3 moles is multiplied by the constant 0.0821 and the temperature is 310 degrees K, then divided by 2 liters: 0.3 *0.0821 * 310/2 = 3.82 atm, approximately.
- For the partial pressure of carbon dioxide, 0.2 moles is multiplied by a constant of 0.0821 and a temperature of 310 degrees K, then divided by 2 liters: 0.2 * 0.0821 * 310/2 = 2.54 atm, approximately.
- The three partial pressures are then added together to get the total pressure: Ptotal = 5, 09 + 3, 82 + 2, 54, or 11.45 atm, more or less.
Part 3 of 3: Calculating Total Pressure, then Partial
Step 1. Determine the partial pressure formula as before
Again, assume a 2 liter flask contains 3 different gases: nitrogen (N2), oxygen (O2), and carbon dioxide (CO2). The mass of each gas is 10 grams and the temperature of each is 37 degrees C.
- The temperature in Kelvin is still the same 310 degrees and the number of moles is approximately 0.4 moles of nitrogen, 0.3 moles of oxygen, and 0.2 moles of carbon dioxide.
- The unit of pressure used is also the atmosphere, so the value of the constant R is 0.0821 L atm/K mol.
- So the partial pressure equation is still the same at this point: Ptotal =(0, 4 * 0, 0821 * 310/2) nitrogen + (0, 3 *0, 0821 * 310/2) oxygen + (0, 2 * 0, 0821 * 310/2) carbon dioxide.
Step 2. Add the number of moles of each gas in the sample to get the total number of moles of the gas mixture
Since the volume and temperature are the same for each gas sample, and each molar value is also multiplied by the same constant, we can use the distributive property of mathematics to rewrite the equation as follows:total = (0, 4 + 0, 3 + 0, 2) * 0, 0821 * 310/2.
Do the sums: 0.4 + 0.3 + 0.2 = 0.9 moles of gas mixture. The equation will be simpler, namely Ptotal = 0, 9 * 0, 0821 * 310/2.
Step 3. Calculate the total pressure of the gas mixture
Do the multiplication: 0.9 * 0.0821 * 310/2 = 11.45 moles, more or less.
Step 4. Calculate the proportion of each gas that makes up the mixture
To calculate the proportion of each gas in the mixture, divide the number of moles of each gas by the total number of moles.
- There are 0.4 moles of nitrogen, so 0.4/0.9 = 0.44 (44 percent) sample, more or less.
- There are 0.3 moles of nitrogen, so 0.3/0.9 = 0.33 (33 percent) of the sample, more or less.
- There are 0.2 moles of carbon dioxide, so 0.2/0.9 = 0.22 (22 percent) of the sample, more or less.
- Although the estimated percentage calculation above returns 0.99, the actual decimal value repeats itself. This means that after the decimal point the number is 9 which repeats itself. By definition this value is equal to 1, or 100 percent.
Step 5. Multiply the proportion of the amount of each gas by the total pressure to calculate the partial pressure
- Multiply 0.44 * 11.45 = 5.04 atm, more or less.
- Multiply 0.33 * 11.45 = 3.78 atm, more or less.
- Multiply 0.22 * 11.45 = 2.52 atm, more or less.
