How Does Dalton's Law Affect Real-World Gases?
Dalton’s law of partial pressure first published by John Dalton in the year 1802 states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by each individual gas present in the mixture. Eg: the total pressure exerted in a mixture of two gases is equal to the sum of the individual partial pressures exerted by each of the gas. In simple words, it can be stated that it is a mixture of two or more non-reacting gases, the total pressure is equal to the sum of the partial pressures of the non-reacting gases. In this topic, we have discussed what is dalton's law, let us state dalton's law of partial pressure with some examples. Let us suppose we have two mixture of gases A and B, so Dalton's gas law states that the total pressure exerted by a mixture of two gases A and B is equal to the sum of the individual partial pressures exerted by both gas A and gas B as shown below:
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Dalton's Law Formula
For a mixture containing n number of gases the total pressure can be given as:
p\[_{total}\] = \[\sum_{i=1}^{n}\] p\[_{i}\]
Or simply it can be written as:
p\[_{total}\] = p\[_{1}\] + p\[_{2}\] + p\[_{3}\] + p\[_{4}\] + p\[_{5}\] .... + p\[_{n}\]
Where Ptotal denotes total pressure exerted by the mixture of gases
and p1, p2,…, pn denotes the partial pressures of the gases 1, 2,…, ‘n’ in the mixture.
Expressing Partial Pressures in Terms of Mole Fraction
The mole fraction of a specific gas in a mixture of gases can be defined as the ratio of the partial pressure of that gas to the total pressure exerted by the gaseous mixture. This mole fraction is used to calculate the total number of moles of a constituent gas when the total number of moles in the mixture is known. Also, the volume occupied by a specific gas in a mixture can be calculated with the mole fraction formula with the help of the given equation.
X\[_{i}\] = P\[_{i}\] / P\[_{total}\] = V\[_{i}\] / V\[_{total}\] = n\[_{i}\] / n\[_{total}\]
Here X\[_{i}\] denotes the mole fraction of a gas ‘i’ in a mixture of ‘n’ gases, ‘n’ denotes the number of moles, ‘P’ denotes the pressure, and ‘V’ denotes the volume of the mixture.
Use of Dalton's law
Dalton's law can be used to calculate the mixtures of gases and the pressure and volume of each gas.
Presently many industries use sophisticated software for calculating these parameters. Still, Dalton’s and Avogadro’s laws are the basis of all these technologies.
Dalton's Law of Partial Pressure Explanation by an Example
If there is a mixture of nitrogen gas, helium gas, and argon gas we have to measure the pressure and it was assessed in 2 atm. Further, the specialist also confirmed that the pressure of nitrogen in the mixture is 0.8 atm and the pressure of helium is 0.5 atm. Calculate the pressure of argon gas in the given mixture?
Solution: In order to calculate the pressure we can use Dalton’s law formula given as:
p\[_{total}\] = p\[_{1}\] + p\[_{2}\] + p\[_{3}\] + p\[_{4}\] + p\[_{5}\] .... + p\[_{n}\]
Now we put all the given value in it and rearrange the formula:
p\[_{total}\] = p\[_{nitrogen}\] + p\[_{helium}\] + p\[_{argon}\]
p\[_{total}\] = p\[_{nitrogen}\] - p\[_{helium}\] = p\[_{argon}\]
p\[_{argon}\] = 2atm - 0.8atm - 0.5atm
p\[_{argon}\] = 0.7atm
Conclusion
In this article, we have discussed Dalton's law of partial pressure definition and the Uses of Dalton’s law, We have also learned how to express Partial pressure in terms of mole fraction along with an example. To understand this topic more clearly try to solve maximum numerical.
FAQs on Dalton's Law: Definition, Formula & Applications
1. What is Dalton's Law of Partial Pressures?
Dalton's Law of Partial Pressures states that in a mixture of non-reacting gases, the total pressure exerted by the mixture is equal to the sum of the partial pressures of the individual gases. The partial pressure is the pressure that each gas would exert if it were the only gas present in the entire volume of the container at the same temperature.
2. What is the formula for Dalton's Law?
The formula for Dalton's Law is expressed as:
Ptotal = P1 + P2 + P3 + ... + Pn
Where:
- Ptotal is the total pressure of the gas mixture.
- P1, P2, P3, ... Pn are the partial pressures of each individual gas (1, 2, 3, ... n) in the mixture.
3. What are some important real-world applications of Dalton's Law?
Dalton's Law is crucial in many scientific and real-world scenarios. Key applications include:
- Scuba Diving: It helps calculate the safe composition and pressure of breathing gas mixtures (like Nitrox) to avoid oxygen toxicity at different depths.
- Meteorology: Atmospheric pressure is the sum of the partial pressures of nitrogen, oxygen, argon, water vapour, and other trace gases. This law is fundamental to weather forecasting.
- Respiration: Gas exchange in our lungs depends on the differences in the partial pressures of oxygen and carbon dioxide between the air in the alveoli and the blood.
- Industrial Gas Production: It is used in processes that involve creating and storing gas mixtures for various industrial uses.
4. How is the partial pressure of a gas related to its mole fraction?
The partial pressure of a specific gas in a mixture is directly proportional to its mole fraction. The relationship can be expressed by the formula:
Pi = Xi × Ptotal
Where:
- Pi is the partial pressure of the individual gas 'i'.
- Xi is the mole fraction of that gas (moles of gas 'i' / total moles of all gases).
- Ptotal is the total pressure of the mixture.
5. How is Dalton's Law used to find the pressure of a gas collected over water?
When a gas is collected over water in a laboratory setting, the collected gas is not pure; it is saturated with water vapour. According to Dalton's Law, the total pressure inside the collection container (which equals the external atmospheric pressure) is the sum of the partial pressure of the collected gas and the partial pressure of the water vapour. This water vapour pressure is also known as aqueous tension. To find the pressure of the dry gas, you must subtract the aqueous tension from the total pressure:
Pdry gas = Ptotal - Pwater vapour
The value for Pwater vapour depends on the temperature and can be found in standard reference tables.
6. Under what conditions is Dalton's Law not accurate?
Dalton's Law provides an accurate description for ideal gases but has limitations under certain conditions. The law becomes less accurate:
- At Very High Pressures: When gases are highly compressed, the volume occupied by the gas molecules themselves becomes significant and intermolecular forces are no longer negligible. This behaviour deviates from the ideal gas model on which Dalton's law is based.
- When Gases React Chemically: The law is strictly valid only for mixtures of non-reacting gases. If the gases react, the number of moles of gas changes, which in turn alters the total pressure in a way not predicted by the simple sum of initial partial pressures.
7. Why is it crucial that gases do not react for Dalton's Law to apply?
It is crucial that the gases in a mixture do not react because the foundation of Dalton's Law is that each gas molecule behaves independently, contributing to the total pressure as if no other gases were present. If a chemical reaction occurs (e.g., 2H₂ + O₂ → 2H₂O), the constituent molecules are consumed and new molecules are formed. This changes the total number of gas moles in the container. Since pressure is directly proportional to the number of moles of gas (as per the Ideal Gas Law), a chemical reaction alters the total pressure in a way that cannot be calculated by simply summing the initial partial pressures.
