Assume that an exhaled breath of air consists of 74.8% N₂, 15.3% O₂, 3.7% CO₂, and 6.2% water vapor. (a) If the total pressure of the gases is 99.8 kPa, calculate the partial pressure of each component of the mixture.

검증된 단계별 안내

Step 1: Understand that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. This is known as Dalton's Law of Partial Pressures.

Step 2: Identify the percentage of water vapor in the mixture, which is 6.2%.

Step 3: Convert this percentage to a decimal by dividing by 100. So, 6.2% becomes 0.062.

Step 4: Multiply the total pressure of the gas mixture by the decimal equivalent of the percentage of water vapor. This will give you the partial pressure of the water vapor.

Step 5: The result from step 4 is the partial pressure of water vapor in the exhaled breath of air. Remember to keep the units consistent, so the partial pressure should be in kPa.

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주요 개념

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Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. Each gas in the mixture behaves independently, contributing to the total pressure based on its mole fraction. This principle is essential for calculating the partial pressure of a specific gas when the total pressure and the composition of the gas mixture are known.

Mole Fraction

The mole fraction of a component in a gas mixture is defined as the ratio of the number of moles of that component to the total number of moles of all components in the mixture. It is a dimensionless quantity that helps in determining the contribution of each gas to the total pressure. In this context, the mole fraction of water vapor can be calculated from its percentage in the mixture.

Calculating Partial Pressure

To find the partial pressure of a gas in a mixture, you can multiply the total pressure by the mole fraction of that gas. For example, if the mole fraction of water vapor is known, the partial pressure can be calculated using the formula: Partial Pressure = Total Pressure × Mole Fraction. This calculation allows for the determination of the specific pressure exerted by water vapor in the exhaled breath.

Assume that an exhaled breath of air consists of 74.8% N2, 15.3% O2, 3.7% CO2, and 6.2% water vapor. (a) If the total pressure of the gases is 99.8 kPa, calculate the partial pressure of each component of the mixture.