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Chapter 5: Problem 96

A 1;1 mixture by moles of nitrous oxide and oxygen is often used as a sedative in dentistry. If the total pressure of this mixture in a cylinder is 2.50 atm, what is the partial pressure of each gas?

Short Answer

Expert verified
The partial pressure of nitrous oxide (N2O) and oxygen (O2) in the cylinder is 1.25 atm for each gas.

Step by step solution

01

Understand Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures states that the total pressure of a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases. Mathematically, this is represented as: \[P_{total} = P_{1} + P_{2} + \cdots + P_{n}\] where \(P_{total}\) is the total pressure, and \(P_{1}, P_{2}, \cdots, P_{n}\) are the partial pressures of the individual gases.
02

Identify the given information

We are given the following information: - The mole ratio of nitrous oxide to oxygen is 1:1. - The total pressure in the cylinder is 2.50 atm.
03

Apply Dalton's Law to the given information

As we have a 1:1 ratio of gases, we can assume that both gases contribute equally to the total pressure. Therefore, the partial pressure of each gas will be half of the total pressure in the cylinder. We can express this as: \[P_{N2O} = P_{O2}\] Using the given total pressure of 2.50 atm, we can rewrite Dalton's Law as follows: \[2.50 atm = P_{N2O} + P_{O2}\]
04

Calculate the partial pressures of each gas

Since \(P_{N2O} = P_{O2}\), we can substitute one of these partial pressures into the equation, and solve for the partial pressure. \[2.50 atm = P_{N2O} + P_{N2O}\] Combine the like terms: \[2.50 atm = 2 P_{N2O}\] Now, divide by 2 to find the partial pressure of nitrous oxide: \[P_{N2O} = \frac{2.50 atm}{2} = 1.25 atm\] Since \(P_{N2O} = P_{O2}\), the partial pressure of oxygen is also 1.25 atm.
05

State the final answer

The partial pressure of nitrous oxide (N2O) and oxygen (O2) in the cylinder is 1.25 atm for each gas.

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Most popular questions from this chapter

A tank contains a mixture of 52.5 g oxygen gas and 65.1 \(\mathrm{g}\) carbon dioxide gas at \(27^{\circ} \mathrm{C}\) . The total pressure in the tank is 9.21 atm. Calculate the partial pressures of each gas in the container.

Consider separate \(1.0-\mathrm{L}\) samples of \(\mathrm{He}(g)\) and \(\mathrm{UF}_{6}(g),\) both at 1.00 atm and containing the same number of moles. What ratio of temperatures for the two samples would produce the same root mean square velocity?

Do all the molecules in a 1 -mole sample of \(\mathrm{CH}_{4}(g)\) have the same kinetic energy at 273 \(\mathrm{K}\)? Do all molecules in a 1 -mole sample of \(\mathrm{N}_{2}(g)\) have the same velocity at 546 \(\mathrm{K}\) ? Explain.

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