Question

If the concentration of water vapour in the air is \(1 \%\) and the total atmospheric pressure equals 1 atm, then the partial pressure of water vapour is (a) \(0.1\) atm (b) \(1 \mathrm{~mm} \mathrm{Hg}\) (c) \(7.6 \mathrm{~mm} \mathrm{Hg}\) (d) \(100 \mathrm{~atm}\)

Short answer

The partial pressure of water vapour is 0.01 atm, which corresponds to choice (a) 0.1 atm.

Step-by-step solution

Understanding the Concept of Partial Pressure

Partial pressure is the pressure that a single component of a mixture of gases would exert if it occupied the entire volume of the mixture at the same temperature. The partial pressure of a gas in a mixture can be calculated by multiplying the total pressure by the mole fraction (or by percent fraction in this case) of the gas in the mixture.

Calculating the Partial Pressure of Water Vapour

Since the concentration of water vapour is given as 1%, we can calculate its partial pressure by taking 1% of the total atmospheric pressure, which is 1 atm. To do this, convert the percentage to decimal by dividing by 100 and then multiply by the total pressure.

Converting Percent to Decimal

To convert the water vapour concentration from percent to decimal, divide 1% by 100, which gives 0.01.

Applying the Partial Pressure Formula

Now, multiply the decimal fraction of water vapour (0.01) by the total pressure (1 atm) to find the partial pressure of the water vapour in atm.

Key concepts

Partial Pressure Calculation

Partial pressure captures the notion that in a blend of different gases, each gas contributes to the overall pressure proportionate to its presence. The practical application of this concept allows us to pinpoint the pressure exerted by a single gas in a mix.

For instance, consider a room filled with various gases - nitrogen, oxygen, carbon dioxide, and others. Although they all share the space, each gas behaves as if it's alone, exerting a pressure that would be different if it filled the room by itself. This concept radically simplifies our understanding of gaseous behavior in mixed environments.

When diving into calculations, it becomes straightforward when the mole fraction is known. The formula used is: \( P_{\text{gas}} = X_{\text{gas}} \times P_{\text{total}} \) where \( P_{\text{gas}} \) represents the partial pressure of the gas you're interested in, \( X_{\text{gas}} \) is the mole fraction of that gas in the mixture, and \( P_{\text{total}} \) is the total pressure exerted by the entire mixture.

Mole Fraction

Diving into the essentials of mole fraction, it's necessary to understand that this concept is a way of expressing the concentration of a component in a mixture. The mole fraction is the ratio of the number of moles of a particular component to the total number of moles of all components present in the mixture.

The calculation of mole fraction is simple and is represented by the formula: \( X_{i} = \frac{n_{i}}{n_{\text{total}}} \) where \( X_{i} \) is the mole fraction of component \( i \) in the mixture, \( n_{i} \) is the number of moles of \( i \) and \( n_{\text{total}} \) is the total number of moles of all the constituents combined.

Understanding mole fraction is crucial because it factors directly into calculations of partial pressures. In atmospheric studies, the mole fraction is particularly useful as atmospheric constituents are often dealt with in terms of their mole fractions.

Atmospheric Pressure

Atmospheric pressure is fundamental to understanding gas-related phenomena. It's the total pressure exerted by the air above a particular point on Earth. The standard atmospheric pressure at sea level is set as 1 atmosphere (atm).

In more scientific terms, atmospheric pressure is the force per unit area exerted on a surface by the weight of the air above that surface in the Earth's atmosphere. It's an important variable in meteorology, aviation, and in computations concerning the behavior of gases via the ideal gas law: \( P \times V = n \times R \times T \) where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is the temperature.

Atmospheric pressure decreases with higher altitude, which is why mountaineers and pilots require specialized equipment to cope with the diminishing pressure and subsequent decrease in oxygen levels.

Water Vapour Concentration

Water vapour concentration has a significant role in meteorology, climatology, and our day-to-day weather experience. It's the amount of water in the gaseous state present in the air, usually expressed as a percentage of the air's volume or as a partial pressure.

In the context of the exercise, when we talk about a '1% water vapour concentration,' this is referring to water vapour occupying 1% of the total volume of air. The measure has direct effects on humidity, precipitation patterns, and even on the greenhouse effect due to water vapour being a potent greenhouse gas.

Understanding water vapour concentration is also pivotal in calculating dew point, which is the temperature to which air must be cooled to become saturated with water vapour and for dew to form. As water vapour concentration increases, the dew point rises, and air that holds more water vapour feels more humid.