Skip to main content
Ch.10 - Gases
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970당신이 사용하는 게 아니라요?교과서 변경
10장, 문제 71

At an underwater depth of 250 ft, the pressure is 8.38 atm. What should the mole percent of oxygen be in the diving gas for the partial pressure of oxygen in the mixture to be 0.21 atm, the same as in air at 1 atm?

검증된 단계별 안내
1
Identify the given values: total pressure at depth is 8.38 atm, desired partial pressure of oxygen is 0.21 atm.
Use the formula for partial pressure: \( P_{\text{O}_2} = X_{\text{O}_2} \times P_{\text{total}} \), where \( P_{\text{O}_2} \) is the partial pressure of oxygen, \( X_{\text{O}_2} \) is the mole fraction of oxygen, and \( P_{\text{total}} \) is the total pressure.
Rearrange the formula to solve for the mole fraction of oxygen: \( X_{\text{O}_2} = \frac{P_{\text{O}_2}}{P_{\text{total}}} \).
Substitute the known values into the equation: \( X_{\text{O}_2} = \frac{0.21\, \text{atm}}{8.38\, \text{atm}} \).
Convert the mole fraction to mole percent by multiplying by 100: \( \text{Mole percent of oxygen} = X_{\text{O}_2} \times 100 \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
1m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Partial Pressure

Partial pressure refers to the pressure exerted by a single component of a gas mixture. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. In this context, understanding how to calculate the partial pressure of oxygen in a diving gas mixture is essential for determining the appropriate mole percent of oxygen.
추천 영상:
가이드 코스
00:48
Partial Pressure Calculation

Mole Fraction and Mole Percent

Mole fraction is the ratio of the number of moles of a specific component to the total number of moles in a mixture. Mole percent is simply the mole fraction expressed as a percentage. To find the mole percent of oxygen needed in the diving gas, one must relate the desired partial pressure of oxygen to the total pressure at the given depth, using the formula: mole fraction = partial pressure of oxygen / total pressure.
추천 영상:
가이드 코스
00:36
Mole Fraction Formula

Gas Laws

Gas laws describe the behavior of gases under various conditions of temperature and pressure. The ideal gas law (PV=nRT) is particularly relevant here, as it relates pressure, volume, and temperature to the number of moles of gas. Understanding these laws helps in calculating how gases behave in different environments, such as underwater, where pressure significantly affects gas mixtures.
추천 영상:
가이드 코스
01:43
Combined Gas Law