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Chapter 5: Problem 116

A mixture of cyclopropane and oxygen is sometimes used as a general anesthetic. Consider a balloon filled with an anesthetic mixture of cyclopropane and oxygen at \(170 .\) torr and 570 . torr. respectively. Calculate the ratio of the moles \(\mathrm{O}_{2}\) to moles cyclopropane in this mixture.

Short Answer

Expert verified
The ratio of moles of oxygen to cyclopropane in the mixture is 3.35:1.

Step by step solution

01

Understand 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 is equal to the sum of the partial pressures of the individual gases. Mathematically, this can be represented as: \(P_{total} = P_{1} + P_{2} + P_{3} + ...\), where P is the pressure and subscript numbers represent different gases.
02

Use given partial pressures to find total pressure

In our case, we are given the partial pressures of cyclopropane (\(P_{Cyclo}\)) and oxygen (\(P_{O_2}\)). We can find the total pressure using Dalton's law: \(P_{total} = P_{Cyclo} + P_{O_2}\) \(P_{total} = 170 \, \mathrm{torr} + 570 \, \mathrm{torr}\) \(P_{total} = 740 \, \mathrm{torr}\)
03

Find the mole fraction of each gas in the mixture

The mole fraction is the ratio of the partial pressure of a gas to the total pressure of the mixture. We will find the mole fractions of oxygen (\(X_{O_2}\)) and cyclopropane (\(X_{Cyclo}\)): \(X_{O_2} = \frac{P_{O_2}}{P_{total}}\) \(X_{Cyclo} = \frac{P_{Cyclo}}{P_{total}}\) Plug in the known values to calculate the mole fractions: \(X_{O_2} = \frac{570 \, \mathrm{torr}}{740 \, \mathrm{torr}}\) \(X_{Cyclo} = \frac{170 \, \mathrm{torr}}{740 \, \mathrm{torr}}\)
04

Calculate the ratio of moles for oxygen to cyclopropane

To calculate the molar ratio of oxygen to cyclopropane in the mixture, we will simply divide the mole fraction of oxygen by the mole fraction of cyclopropane: Molar Ratio (\(O_2:Cyclo\)) = \(\frac{X_{O_2}}{X_{Cyclo}}\) Substitute the values of mole fractions: Molar Ratio (\(O_2:Cyclo\)) = \(\frac{\frac{570}{740}}{\frac{170}{740}}\) Simplify: Molar Ratio (\(O_2:Cyclo\)) = \(\frac{570}{170}\) Molar Ratio (\(O_2:Cyclo\)) = 3.35 The ratio of moles of oxygen to cyclopropane in the mixture is 3.35:1.

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