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Chapter 5: Problem 95

A mixture of cyclopropane and oxygen is sometimes used as a general anesthetic. Consider a balloon with an anesthetic mixture of cyclopropane and oxygen at 170. torr and 570. torr, respectively. Calculate the mole fraction of cyclopropane in the mixture.

Short Answer

Expert verified
The mole fraction of cyclopropane in the mixture is approximately 22.97%. To calculate this, we used the given partial pressures of cyclopropane (170 torr) and oxygen (570 torr), and found the total pressure (740 torr). The mole fraction was then found by dividing the partial pressure of cyclopropane by the total pressure: \(X_{CYC} \approx \frac{170 \, torr}{740 \, torr} = 0.2297\), which was then converted to a percentage (22.97%).

Step by step solution

01

Identify the given values

We are given the partial pressures of both gases in the mixture: Partial pressure of cyclopropane (P_CYC) = 170 torr Partial pressure of oxygen (P_O2) = 570 torr
02

Calculate the total pressure

To find the total pressure of the mixture, we add the partial pressures of both gases: Total pressure (P_total) = P_CYC + P_O2 = 170 torr + 570 torr = 740 torr
03

Calculate the mole fraction of cyclopropane

Now we can use the formula for mole fraction, which is the ratio of the partial pressure of the gas in question (cyclopropane) to the total pressure: Mole fraction of cyclopropane (X_CYC) = P_CYC / P_total Plugging in the values, we get: X_CYC = 170 torr / 740 torr
04

Simplify the fraction

Now, we can simplify the fraction to get the mole fraction of cyclopropane: X_CYC ≈ 0.2297
05

Express the mole fraction as a percentage

To express the mole fraction as a percentage, multiply the decimal value by 100: Mole fraction of cyclopropane = 0.2297 * 100% ≈ 22.97% So, the mole fraction of cyclopropane in the mixture is approximately 22.97%.

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