Dalton's Law: Partial Pressure (Simplified) - Online Tutor, Practice Problems & Exam Prep

Partial pressure refers to the pressure exerted by an individual gas in a mixture, contributing to the total pressure in a container, as described by the law of partial pressures. To find a gas's partial pressure, use the ideal gas law: $P^1=\frac{nRT}{V}$. Dalton's law relates partial pressure to fractional composition, allowing calculation of a gas's contribution to total pressure.

Dalton's Law: Partial Pressure (Simplified) Concept 1

Partial pressure is the pressure exerted by an individual gas within a mixture. So think of it as the gas's individual pressure. We're going to say in a container of unreacting gases, the total pressure of the container is the sum of the partial pressures of each gas. Now, this is known as the Law of Partial Pressures. So, basically, the total pressure inside of a container comes from adding up all the pressures of each individual gas. So total pressure would equal the pressure of gas 1, plus gas 2, plus gas 3, and so on, if there are additional gases. Just remember, the total pressure that a container is experiencing is contributed by each of the individual gases within it.

Dalton's Law: Partial Pressure (Simplified) Example 1

Here we're told that a sample of neon gas exerts a pressure of 1.85 atmospheres inside a cylinder. Some nitrogen gas is also present at a pressure of 500 Torr. What is the total pressure inside the cylinder? So remember, we just learned about the law of partial pressures, which tells us that the total pressure felt inside of a container, or in this case, a cylinder, comes from adding up the partial pressures of each gas present. So in the container, we have neon gas, and we also have nitrogen gas. The total pressure is when you add their partial pressures together.

Now the issue is we don't have the same units for these gases. Neon is in atmospheres, but nitrogen is in Torr. Since atmospheres is a standard unit we usually use for pressure, let's convert Torr into atmospheres. So we're going to have 500 Torr, and remember that for every 1 atmosphere that's 760 Torr. So when we do that, we're going to get our atmosphere value as 0.65789 atmospheres. Take that and plug it in, and when we do that, we're going to get a total pressure of 2.50789 atmospheres. Within our question, 1.85 has 3 significant figures, 500 only has 1 significant figure. Here, if we round to 1 significant figure, this would round up to 3, which is a pretty big jump in terms of our value. So it's just better to go with the 3 significant figures from this 1.85. Again the question isn't asking for the number of significant figures in your final answer, we're doing this as continuous practice in terms of determining significant figures. Again, better to go with 3 significant figures. I know it's not the least number of significant figures, but going from 2.5 to 3 atmospheres is such a big increase. Better just to go with 3 significant figures and then we have 2.51 atmospheres at the end. So now that we've seen this question, let's move on to the next video.

Dalton's Law: Partial Pressure (Simplified) Concept 2

So we know at this point that the total pressure felt within a container is a result of adding up all the partial pressures of the gases present. Now, if we can focus on one of these gases and we know its moles, its temperature, and its volume, we can also find its partial pressure. Now we're going to say here, if you assume that the gases behave ideally, then their partial pressures can be calculated from the ideal gas law. We're going to say here that the pressure of that gas that I'm focusing on, so let's call it gas 1, we can find its partial pressure if we know its moles, so moles 1, \( r \) is our gas constant, times the temperature of the container, divided by the volume of the container. So here we're using the ideal gas law to just focus in on one gas, and from it determine its partial pressure.

Dalton's Law: Partial Pressure (Simplified) Example 2

If 12 grams of helium and 20 grams of oxygen are placed inside a 5-liter cylinder at 30 degrees Celsius, what is the partial pressure of the helium gas? Alright. So they're giving us information on 2 gases. They're giving us information on helium and oxygen, but realize they're only asking for information in terms of partial pressure for the helium. With the helium, I have its grams, and from that, I can determine its moles. I have the volume of the container, and I have the temperature of the container. With this information, I can find the partial pressure of helium gas by utilizing the ideal gas law. So we're going to say here pressure of helium equals moles of helium times R times T divided by V. We don't even need to look at the grams of oxygen because the question again is only asking about the partial pressure of helium.

Alright. So let's take the 12 grams of helium, we look on the periodic table, you'll see that the atomic mass of helium is approximately 4.003 grams per mole of helium. Using this we find the moles of helium: 12 4.003 = 2.998 mol . Now, with 2.998 moles of helium, we can apply the ideal gas law equation: P = n ⁢ R ⁢ ( T + 273.15 ) V , where R = 0.08206 L atm K^-1 mol^-1 and T = 30 °C. Substituting the values, we calculate the partial pressure: P = 2.998 ⁢ 0.08206 ⁢ ( 303.15 ) 5 = 14.9149 atm . Taking into account significant figures from the initial values given, we should round to 3 significant figures. Thus, the appropriate answer is about 14.9 atmospheres.

Remember, significant figures play a role in a lot of our calculations. Here, rounding to 10 atmospheres would greatly deviate from our more precise calculation. Therefore, we'll stick close to our derived value, presenting 14.9 atmospheres as the partial pressure of the helium gas by using the ideal gas law formula.

Dalton's Law: Partial Pressure (Simplified) Concept 3

Now when the percent composition of a gas is given, first determine its fractional composition. By fractional composition, we mean that it represents the percent composition of a gas divided by the total percent. So here we have our fractional composition formula. We're going to say fractional composition, which we're going to use m as a stand-in for the variable, equals the percentage of your particular gas you're looking at divided by the total percent, which is 100%. Then, we're going to say that we can calculate the partial pressure of a gas using its fractional composition and the total pressure. So that feeds into Dalton's law. And Dalton's law says that the partial pressure of a gas, let's say gas A, equals the fractional composition of gas A times the total pressure. Using fractional composition allows us to step into Dalton's law to help us figure out the partial pressure of gases within any given container.

m = % gas 100% P A = m ⁢ P total

Dalton's Law: Partial Pressure (Simplified) Example 3

A cylinder of a gas mixture used for calibration of blood gas analyzers in medical laboratories contains 5% carbon dioxide, 12% oxygen, and the remainder nitrogen at a total pressure of 146 atmospheres. What is the partial pressure of each component of the gas?

Alright. So we're going to say we have 5% CO₂, we have 12% oxygen, and if we do 100% minus the 5% and 12%, that will give us the percentage of our nitrogen gas. So that will come out to 83% nitrogen gas. Now that we know each of their percentages, we can figure out their fractional compositions and by extension their partial pressures.

So for CO₂, the pressure of CO₂ equals its fractional composition which is 5% divided by 100% times the total pressure of 146 atmospheres. This tells me that the partial pressure of CO₂ is about 7.3 atmospheres.

For O₂, that'd be 12%, so the pressure of O₂ equals 12% divided by 100%, times the total pressure. So that will come out to 17.5 atmospheres.

And then finally we have nitrogen gas, so that would be the pressure of nitrogen gas equals 83 percent divided by 100% times 146 atmospheres. So this comes out to approximately 121.2 atmospheres.

So these will be the partial pressures of each gas component within the gas mixture of this cylinder.

A gas mixture contains 72.8% chlorine and 27.2% neon by mass. What is the partial pressure of neon in the mixture if the total pressure is recorded as 809 mmHg?

• A. 220 mmHg
• B. 242 mmHg
• C. 588 mmHg
• D. 183 mmHg

The partial pressure of N₂ in the air is 593 mmHg at 1 atm. What is the partial pressure of N₂ in a bubble of air a scuba diver breathes when he is 66 ft below the surface of the water where the pressure is 3.00 atm?

• A. 2.34 mmHg
• B. 1779 mmHg
• C. 593 mmHg
• D. 2.28×10³ mmHg
• E. 7.02 mmHg

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What is Dalton's Law of Partial Pressures?

Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reacting gases in a container is equal to the sum of the partial pressures of each individual gas. Mathematically, it can be expressed as:

$P_{\mathrm{total}}=P_1+P_2+P_3+...$

Here, $P_{\mathrm{total}}$ is the total pressure, and $P_1$, $P_2$, $P_3$ are the partial pressures of the individual gases.

How do you calculate the partial pressure of a gas using the ideal gas law?

To calculate the partial pressure of a gas using the ideal gas law, you need to know the number of moles of the gas (n), the gas constant (R), the temperature (T), and the volume (V) of the container. The ideal gas law is given by:

$P=\frac{nRT}{V}$

Here, $P$ is the partial pressure of the gas, $n$ is the number of moles, $R$ is the gas constant, $T$ is the temperature in Kelvin, and $V$ is the volume of the container.

What is fractional composition and how is it used in Dalton's Law?

Fractional composition represents the ratio of the partial pressure of a gas to the total pressure in a mixture. It is calculated by dividing the percentage composition of a gas by 100%. The formula for fractional composition (m) is:

$m=\frac{\mathrm{percentage}}{100}$

Using Dalton's Law, the partial pressure of a gas (P_a) can be found by multiplying its fractional composition (m_a) by the total pressure (P_total):

$P_a=m_a\times P_{\mathrm{total}}$

How does Dalton's Law apply to real-life scenarios?

Dalton's Law of Partial Pressures is widely applicable in real-life scenarios, such as in respiratory physiology, where it helps in understanding how gases like oxygen and carbon dioxide are exchanged in the lungs. It is also used in scuba diving to calculate the partial pressures of gases in a diver's tank, ensuring safe breathing mixtures. Additionally, it is crucial in industrial processes involving gas mixtures, such as chemical manufacturing and environmental monitoring, to determine the contributions of individual gases to the total pressure.

What assumptions are made when using Dalton's Law?

When using Dalton's Law, several assumptions are made: (1) The gases in the mixture do not react with each other. (2) Each gas behaves ideally, meaning it follows the ideal gas law. (3) The volume of the container is constant. (4) The temperature is uniform throughout the container. These assumptions simplify the calculations but may not always hold true in real-world conditions, especially at high pressures or low temperatures where gases deviate from ideal behavior.