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A mixture of helium and neon gases is collected over water at \(28.0^{\circ} \mathrm{C}\) and \(745 \mathrm{mmHg}\). If the partial pressure of helium is \(368 \mathrm{mmHg}\), what is the partial pressure of neon? (Vapor pressure of water at \(28^{\circ} \mathrm{C}=\) \(28.3 \mathrm{mmHg} .)\)

Short Answer

Expert verified
The partial pressure of neon is 348.7 mmHg.

Step by step solution

01

Identify the items given

The total pressure collected over water is given as 745 mmHg. The partial pressure of helium is given as 368 mmHg. The vapor pressure of water at \(28^{\circ} \mathrm{C}\) is given as 28.3 mmHg.
02

Apply Dalton’s Law of Partial Pressures

According to Dalton’s Law of partial pressures, the total pressure is the sum of the partial pressures of each gas and the vapor pressure. So, the equation based on Dalton’s Law would be: Total pressure = Partial pressure of helium + Partial pressure of neon + Vapor pressure of water. Plug the given values into this equation and isolate the unknown (the partial pressure of neon).
03

Solve the equation

Substitute the given values into the equation to solve for the partial pressure of neon: 745 mmHg (total pressure) = 368 mmHg (helium) + Neon + 28.3 mmHg (water vapor). Solving for Neon, we find Neon= 745 mmHg - 368 mmHg - 28.3 mmHg = 348.7 mmHg.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Dalton's Law of Partial Pressures
Understanding Dalton's Law of Partial Pressures is crucial when dealing with gas mixtures. This law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the individual gases' partial pressures.
When a gas is collected over water, like in the exercise provided, we need to consider the vapor pressure of water as part of the total pressure. In our case, a student may mistake the pressure exerted by the gas mixture as belonging entirely to the gases of interest (helium and neon), but Dalton's Law helps us account for the vapor pressure of water as well.
Improving on the textbook solution, it's beneficial to emphasize the word 'non-reacting' for the gases. This means the gases don't chemically interact with each other, which is an important condition for Dalton's Law to be applicable. The takeaway for students is to always confirm if the gases are ideal and non-reacting when using this law.
Vapor Pressure of Water
Vapor pressure is another key term in this exercise. It is the pressure exerted by a vapor that is in equilibrium with its liquid or solid form. At any given temperature, this pressure is constant for a pure substance.
In our scenario, the vapor pressure of water at the specified temperature is given, which is critical data needed to solve the problem correctly. It's important to understand that this represents the part of the total pressure that comes from water vapor present in the collection container. This concept underscores the importance of considering all components within a mixture when calculating total pressure.
An essential piece of advice for students is that the vapor pressure of water varies with temperature, and using the wrong value for the given temperature could result in an incorrect calculation. Therefore, students should always ensure they are using the correct vapor pressure for the current temperature.
Gas Mixture Pressure Calculation
Solving problems involving gas mixtures often involves calculations to find unknown pressures. To do this successfully, one must understand how to manipulate equations and isolate the desired variable.
In our provided exercise, the gas mixture pressure calculation is performed by applying Dalton's Law. The equation initially contains the sum of the partial pressures of helium and neon, plus the vapor pressure of water. With two known pressures and the total pressure, we rearrange to solve for the unknown—neon in this case.
A student aiming to improve their problem-solving skills should practice rearranging equations and isolating variables. It's a fundamental skill in chemistry (and physics) that allows for the successful calculation of unknown quantities in a variety of contexts.
Helium and Neon Partial Pressures
The partial pressure of each gas in a mixture is the pressure that gas would exert if it alone occupied the entire volume at the same temperature. In our exercise, the partial pressure of helium is provided, and the student is asked to calculate the partial pressure of neon.
Understanding that the respective partial pressure of each gas contributes to the total pressure allows for an insightful connection to Dalton's Law. When the pressures of individual gases are provided, it makes for a straightforward calculation after considering the vapor pressure of water.
For conceptual clarity, it's helpful to inform students that it does not matter whether we are working with helium, neon, or any other gas; the partial pressure concept applies universally to all components of a gas mixture that follow the ideal gas behavior.

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Most popular questions from this chapter

The apparatus shown in the diagram can be used to measure atomic and molecular speed. Suppose that a beam of metal atoms is directed at a rotating cylinder in a vacuum. A small opening in the cylinder allows the atoms to strike a target area. Because the cylinder is rotating, atoms traveling at different speeds will strike the target at different positions. In time, a layer of the metal will deposit on the target area, and the variation in its thickness is found to correspond to Maxwell's speed distribution. In one experiment it is found that at \(850^{\circ} \mathrm{C}\) some bismuth (Bi) atoms struck the target at a point \(2.80 \mathrm{~cm}\) from the spot directly opposite the slit. The diameter of the cylinder is \(15.0 \mathrm{~cm}\) and it is rotating at 130 revolutions per second. (a) Calculate the speed \((\mathrm{m} / \mathrm{s})\) at which the target is moving. (Hint: The circumference of a circle is given by \(2 \pi r\), in which \(r\) is the radius.) (b) Calculate the time (in seconds) it takes for the target to travel \(2.80 \mathrm{~cm} .\) (c) Determine the speed of the Bi atoms. Compare your result in (c) with the \(u_{\mathrm{rms}}\) of Bi at \(850^{\circ} \mathrm{C}\). Comment on the difference.

Apply your knowledge of the kinetic theory of gases to these situations. (a) Does a single molecule have a temperature? (b) Two flasks of volumes \(V_{1}\) and \(V_{2}\left(V_{2}>V_{1}\right)\) contain the same number of helium atoms at the same temperature. (i) Compare the root- mean-square (rms) speeds and average kinetic energies of the helium (He) atoms in the flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers (c) Equal numbers of He atoms are placed in two flasks of the same volume at temperatures \(T_{1}\) and \(T_{2}\left(T_{2}>T_{1}\right)\) (i) Compare the rms speeds of the atoms in the two flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (d) Equal numbers of He and neon (Ne) atoms are placed in two flasks of the same volume and the temperature of both gases is \(74^{\circ} \mathrm{C}\). Comment on the validity of these statements: (i) The rms speed of He is equal to that of Ne. (ii) The average kinetic energies of the two gases are equal. (iii) The rms speed of each He atom is \(1.47 \times 10^{3} \mathrm{~m} / \mathrm{s}\).

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