Dalton’s Law, or the Law of Partial Pressures, states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the gases in the mixture. Based on the kinetic theory of gases, a gas will diffuse in a container to fill up the space it is in and does not
have any forces of attraction between the molecules. In other words, the different molecules in a mixture of gases are so far apart that they act independently; they do not react with each other. The pressure of an ideal gas is determined by its collisions with the container, not collisions with molecules of other substances since there are no other collisions. A gas will expand to fill the container it is in without affecting the pressure of another gas. So it can be concluded that the
pressure of a certain gas is based on the number of moles of that gas and the volume and temperature of the system. Since the gases in a mixture of gases are in one container, the Volume (V) and Temperature (T) for the different gases are the same as well. Each gas exerts its own pressure on the system, which can be added up to find the total pressure of the mixture of gases in a container. This is shown by the equation \[P_{total} = P_A + P_B + ... \tag{1}\] We have, from the
Ideal Gas Law \[PV = nRT \tag{2}\] If we know the molar composition of the gas, we can write \[n_{total} = n_a + n_b + ... \tag{3}\] Again, based on the kinetic theory of gases and the ideal gas law, Dalton’s law can also be applied to the number of moles so that the total number of moles equals the sum of the number of moles of the individual gases. Here, the pressure, temperature and volume are held constant in the system. The total volume of a gas can be found the same way, although this is not used as much. This yields the equation, \[P_{total} V=n_{total} RT \tag{4}\] We can rearrange this equation to find the total number of moles. Sometimes masses of each sample of gas are given and students are asked to find the total pressure. This can be done by converting grams to moles and using Dalton's law to find the pressure. Mole RatioFrom the partial pressure of a certain gas and the total pressure of a certain mixture, the mole ratio, called Xi, of a gas can be found. The mole ratio describes what fraction of the mixture is a specific gas. For example, if oxygen exerts 4 atm of pressure in a mixture and the total pressure of the system is 10 atm, the mole ratio would be 4/10 or 0.4. The mole ratio applies to pressure, volume, and moles as seen by the equation below. This also means that 0.4 moles of the mixture is made up of gas i. \[X_i=\dfrac{P_i}{P_{tot}}=\dfrac{n_i}{n_{tot}}=\dfrac{V_i}{V_{tot}} \tag{5}\] The mole ratio, (\(X_i\)) is often used to determine the composition of gases in a mixture. The sum of the mole ratios of each gas in a mixture should always equal one since they represent the proportion of each gas in the mixture. Collection of a Gas Over WaterThe Law of Partial Pressures is commonly applied in looking at the pressure of a closed container of gas and water. The total pressure of this system is the pressure that the gas exerts on the liquid. The gas is made up of whatever sample of gas there is plus the evaporated water. The pressure of the gas on the liquid consists of the pressure of the evaporated water and the pressure of the gas collected. Based on Dalton’s law, the pressure of the gas collected can be calculated by subtracting the pressure of the water vapor from the total pressure. Real GasesReal gases are gases that do not behave ideally. That is, they violate one or more of the rules of the kinetic theory of gases. Real gases behave ideally when the gases are at low pressure and high temperature. Therefore at high pressures and low temperatures, Dalton’s law is not applicable since the gases are more likely to react and change the pressure of the system. For example, if there are forces of attraction between the molecules, the molecules would get closer together and the pressure would be adjusted because the molecules are interacting with each other. Problems
Solutions1:
2. The law of partial pressures also applies to the total number of moles if the other values are constant, so 4 mol Hydrogen+8 mol Oxygen+12 mol Helium+6 mol Nitrogen=30 moles total 3.
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References
What is Dalton's Law of partial pressure PDF?According to Dalton's law of partial pressures, the total pressure by a mixture of gases is equal to the sum of the partial pressures of each of the constituent gases. The partial pressure is defined as the pressure each gas would exert if it alone occupied the volume of the mixture at the same temperature.
What is Dalton's Law of partial pressure write its equation?Dalton's law of partial pressures
Dalton's law of partial pressures states that the total pressure of a mixture of gases is the sum of the partial pressures of its components: P Total = P gas 1 + P gas 2 + P gas 3 .
What is the application of Dalton law of partial pressure?Application of Dalton's Law of Partial pressure of gas-
The total pressure of a mixture of gas and water will be equal to atmospheric pressure if the water level inside and outside the vessel are equal. The gas present over water exerts combined pressure due to its vapor pressure and due to the pull of gravity.
What is Dalton's law simple definition?Dalton's law, the statement that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual component gases.
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