How to Calculate Partial Pressure

In chemistry, “partial pressure” is the pressure each gas in a gas mixture exerts on its surroundings, such as a laboratory sample gas cylinder, a diver’s supply tank, or the surrounding space. atmosphere. You can calculate the pressure of each gas in a mixture if you know its mass, volume, and temperature. You then add up the partial pressures to get the total pressure of the gas mixture, or you find the total pressure first and then find the partial pressure.

Table of Contents

Understand the properties of gases

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Treat each gas as an “ideal” gas. In chemistry, an ideal gas is a gas that interacts with other gases without being attracted to their molecules. Gas molecules can collide with each other and bounce like billiard balls without being deformed at all. ^{[1] X Research Source}

The pressure of an ideal gas increases as it is compressed into a smaller space and decreases as it disperses into a larger space. This relationship is known as Boyle’s Law (named after scientist Robert Boyle). The mathematical formula for this relationship is k = P x V, or more simply k = PV, where k is the constant relationship between pressure and volume, P is pressure and V is volume. accumulate. ^{[2] X Research Source}
The problem can give pressure in one of many different units. In which pascal (Pa) is defined as the force of one newton acting on one square meter. Another unit is the atmosphere (atm) which is defined as the pressure of the earth’s atmosphere at an altitude equal to sea level. A pressure of 1 atm is equal to 101.325 Pa. ^{[3] X Research Sources}
The temperature of an ideal gas increases as the volume increases and decreases as the volume decreases. This relationship is known as Charles’ Law (named after scientist Jacques Charles). The mathematical formula for this relationship is k = V/T, where k is the constant relationship between volume and temperature, V is volume, and T is temperature. ^{[4] X Research Sources}^{[5] X Research Sources}
The temperature of the gas in this equation is given in degrees Kelvin, and degrees Kelvin is calculated by adding degrees Celsius by 273.
These two relationships can be combined into a single equation: k = PV / T, or PV = kT.

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Defines the unit of mass used to measure gases. Gases have both mass and volume. Volume is usually measured in liters (l), but there are two mass forms of gases.

Conventional mass is measured in grams, or, if the mass is large enough, in kilograms.
Since most gases are usually so light, they are also measured in another form of mass called molecular mass or mp mass. The mass mp is defined as the total atomic mass of each atom in the composition of that gas, with the mass of each atom compared with the mass of carbon (which has a value of 12). ^{[6] X Research Source}
Since atoms and molecules are too small to calculate, the mass of a gas is defined in mp. The number of mp in a gas can be calculated by dividing the mass of the gas by the mass mp, and is denoted by the letter n.
We can replace any constant k in the gas equation with the product of n, the number of mps, and a new constant R. We now have the equation nR = PV/T or PV = nRT. ^{[7] X Research Sources}
The R value depends on the units used to measure the pressure, volume, and temperature of the gas. If the volume is in liters, the temperature is in Kelvin, and the pressure is in atmospheres, this value is 0.0821 L atm/K mp. You can also write 0.0821 L atm K ^-1 mp ^-1 to avoid having to use slashes of division in units of measure. ^{[8] X Research Sources}

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Dalton’s law of partial pressure. This law was introduced by chemist and physicist John Dalton, who first presented the concept that a chemical element is composed of atoms. ^{[9] X Research Source}^{[10] X Research Source} Dalton’s law states that the total pressure of a gas mixture is the sum of the pressures of each gas in the mixture.

Dalton’s law can be written as the following equation P _sum = P ₁ + P ₂ + P ₃ … with the amount of pressure P equal to the number of gases in the mixture.
The Dalton Law equation can be expanded when the problem is for gases whose partial pressure is unknown, but whose volume and temperature are known. The partial pressure of a gas is the pressure exerted by the same mass of gas in a vessel containing it alone. ^{[11] X Research Source}
For each partial pressure, we can rewrite the ideal gas equation PV = nRT to the form with only P on the left side of the equal sign. So we have to divide both sides by V: PV/V = nRT/V. The two Vs on the left side are eliminated, and in the end, P = nRT/V remains.
Then you substitute this formula for each P in the right hand side of the partial pressure equation: P _sum =(nRT/V) ₁ + (nRT/V) ₂ + (nRT/V) ₃ …

Calculate the partial pressure, then calculate the total pressure

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Determine the partial pressure equation for the given problem gases. To illustrate this calculation, suppose we have a 2-liter bottle containing three gases: nitrogen (N ₂ ), oxygen (O ₂ ), and carbon dioxide (CO ₂ ). . Each gas has 10g, and the temperature of each gas in the bottle is 37 degrees Celsius. We need to find the partial pressure of each gas and the total pressure of the gas mixture acting on the bottle.

The partial pressure equation is written as P _total = P _nitrogen + P _oxygen + P _{carbon dioxide} .
Since we are finding the pressure of each gas, given the volume and temperature, and can find the mp of each gas based on their mass, the equation can be rewritten as: P _sum =(nRT/ V) _nitrogen + (nRT/V) _oxygen + (nRT/V) _{carbon dioxide}

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Convert the temperature to degrees Kelvin. The temperature of the gases is 37 degrees Celsius so we add 37 by 273 to get 310 degrees K.

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Find the mp number of each gas present in the bottle. The number of mp of gas is the mass of that gas divided by its mp mass, ^{[12] X Research source} where the mass mp is the total mass of each atom that makes up the substance.

For the first gas, nitrogen has the molecular formula ( _N2 ), each atom has a mass of 14. Since the nitrogen molecule has two atoms, we have to multiply 14 by 2 to get the mass. molecular weight of nitrogen is 28. Then divide the gram mass of 10g by 28 to get mp, rounding the result to approximately 0.4 mp of nitrogen gas.
For the second gas, oxygen has the molecular formula (O ₂ ), each atom has a mass of 16. The oxygen molecule also has two atoms, we have to multiply 16 by 2 to get the mass. The molecular weight of oxygen is 32. Dividing 10g by 32 gives approximately 0.3 mp of oxygen in the bottle.
The third gas is carbon dioxide with the formula (CO ₂ ), which has 3 atoms: one carbon atom with mass 12, two oxygen atoms with mass 16 each. We add the mass of three atoms: 12 + 16 + 16 = 44 is the molecular mass. Dividing 10g by 44 gives approximately 0.2 mp of carbon dioxide.

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Substitute the values of mp, volume and temperature into the equation. Now the equation will look like this: P _sum =(0.4 * R * 310/2) _nitrogen + (0.3 *R * 310/2) _oxygen + (0.2 * R *310/2) _{carbon dioxide} .

For simplicity we omit the unit of measure following the values. These units will be canceled out after you solve the equation, leaving only the measurement unit of the result, which is pressure.

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Substitute the value of the constant R. We will calculate the partial pressure and the total pressure in atmospheres, so we will use the R value of 0.0821 L atm/K mp. Substituting this value into the equation gives P _sum =(0.4 * 0.0821 * 310/2) _nitrogen + (0.3 *0.0821 * 310/2) _oxygen + (0.2 * 0 ,0821 * 310/2) _{carbon dioxide} .

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Calculate the partial pressure of each gas. Now that we have put the values into the equation, the next thing is to solve it.

For the partial pressure of nitrogen, you multiply 0.4 mp by the constant 0.0821 and the temperature of 310 degrees K, then divide by 2 liters: 0.4 * 0.0821 * 310/2 = 5 .09 atm (approx.).
For the partial pressure of oxygen, you multiply 0.3 mp by the constant 0.0821 and the temperature of 310 degrees K, then divide by 2 liters: 0.3 * 0.0821 * 310/2 = 3 .82 atm (approx.).
For the partial pressure of carbon dioxide, you multiply 0.2 mp by the constant 0.0821 and the temperature of 310 degrees K, then divide by 2 liters: 0.2 * 0.0821 * 310/ 2 = 2.54 atm (approx.).
Now you add these pressures to find the total pressure: P _sum = 5.09 + 3.82 + 2.54 = 11.45 atm (approximately).

Calculate the total pressure, then calculate the partial pressure

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Determine the partial pressure equation as above. Again, suppose we have a 2 liter bottle containing 3 gases: nitrogen (N ₂ ), oxygen (O ₂ ), and carbon dioxide (CO ₂ ). Each gas has 10g, and the temperature of each gas in the bottle is 37 degrees Celsius.

The Kelvin temperature is still 310 degrees, and as above, we have approximately 0.4 mp of nitrogen, 0.3 mp of oxygen and 0.2 mp of carbon dioxide.
Similarly, we will calculate the resulting pressure in atmospheres so we will use an R value of 0.0821 L atm/K mp.
So far the partial pressure equation is still: P _total =(0.4 * 0.0821 * 310/2) _nitrogen + (0.3 *0.0821 * 310/2) _oxygen + (0.2) * 0.0821 * 310/2) _{carbon dioxide} .

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Add the mp of each gas in the bottle to find the total mp of the gas mixture. Since the volumes and temperatures of the gases in the bottle are the same, and the molecular mass of each gas is multiplied by the same constant, we can use the distributive property of mathematics to rewrite the equation. The equation is P _sum = (0.4 + 0.3 + 0.2) * 0.0821 * 310/2.

Add 0.4 + 0.3 + 0.2 = 0.9 mp of gas mixture. The equation is further reduced to P _sum = 0.9 * 0.0821 * 310/2.

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Find the total pressure of the gas mixture. Take 0.9 * 0.0821 * 310/2 = 11.45 mp (approx.).

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Find the proportions of each gas that make up the mixture. You divide the mp per gas by the total mp of the gas mixture.

We have 0.4 mp of nitrogen so 0.4/0.9 = 0.44 (44%) in the gas mixture (approximately).
We have 0.3 mp of oxygen so 0.3/0.9 = 0.33 (33%) in the gas mixture (approximately).
We have 0.2 mp of carbon dioxide so take 0.2/0.9 = 0.22 (22%) in the gas mixture (approximately).
Although the approximate percentage values above add up to only 0.99, in reality the decimals repeat themselves, with the sum being a series of 9s followed by a comma. By definition, this is equivalent to 1 or 100 percent.

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Multiply the mass ratio of each gas by the total pressure to find the partial pressure.

Take 0.44 * 11.45 = 5.04 atm (approx.).
Take 0.33 * 11.45 = 3.78 atm (approx.).
Take 0.22 * 11.45 = 2.52 atm (approximately).

Advice

You will find there is a slight difference between calculating the partial pressure first and then calculating the total pressure and calculating the total pressure first and then calculating the partial pressure. Remember that the calculated values are only approximations as we round to 1 or 2 decimal places to make them simpler. If we use the calculator to do the calculations without rounding, the difference between the two methods is even smaller, even without bias.

Warning

For divers, knowledge of the partial pressure of a gas is especially important as it concerns their lives. A partial pressure of oxygen that is too low can cause unconsciousness or death, while a partial pressure of nitrogen or oxygen that is too high can cause poisoning. ^{[13] X Research Source}^{[14] X Research Source}

Things you need

Laptop
Atomic mass/mp mass reference book

Steps