Question

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

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

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

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

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

Simplify the fraction

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

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%.

Key concepts

Partial Pressure

Partial pressure refers to the pressure exerted by a particular gas in a mixture of gases. Each gas in a mixture behaves as if it exists alone, contributing to the overall pressure with its partial pressure.
The concept is based on Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. This is mathematically expressed as:

• \( P_{ ext{total}} = P_1 + P_2 + ext{...} + P_n \)

where \( P_1, P_2, \ldots P_n \) are the partial pressures of each gas component. Knowing how to calculate partial pressures is crucial in many scientific fields, such as chemistry and medicine, especially when dealing with gas mixtures like those used in anesthesia.

Gas Mixtures

Gas mixtures are combinations of two or more gases that are blended together without reacting chemically. In gas mixtures, each individual gas retains its own properties, and the laws applying to gases in general also apply to the mixture. They can be described by their partial pressures, as each gas contributes to the total pressure based on its proportion in the mix.
For practical calculations, it’s important to understand the individual behavior (described by their partial pressures) and the total behavior of the mixture. Gas mixtures are utilized in various applications such as breathing gases for scuba diving, and more critically, for anesthetic purposes in medical settings. In these scenarios, precise calculations of individual gas concentrations are vital to ensure safety and efficacy.

Anesthetics in Chemistry

Anesthetics are substances that cause loss of sensation or consciousness, used primarily during surgeries and medical procedures. In the field of chemistry, anesthetics often involve mixtures of gases. Their purpose is to safely induce anesthesia when inhaled by patients.
One common mixture is made of oxygen and cyclopropane. The role of chemistry in anesthesia includes determining the correct composition and concentration of gas mixtures to maintain the desired effect without causing harm. Calculating mole fractions of each gas component is essential to achieve an accurate dosage, ensuring that the mixture is both effective and safe.
Understanding the chemical properties and interactions of each gas component allows medical professionals to devise appropriate anesthetic protocols, taking into account factors like patient size, duration of the procedure, and expected reactions to the anesthetic.