The vapor pressure is the pressure of the vapor phase of a substance when it is in equilibrium with the solid or liquid phase of the substance. The relative humidity is the partial pressure of water vapor in the air divided by the vapor pressure of water at that same temperature, expressed as a percentage. The air is saturated when the humidity is $100 percent sign$ . The vapor pressure of water at $20.0$ °C is $2.34 times 10 cubed$ Pa. If the air temperature is $20.0$ °C and the relative humidity is $60 percent sign$ , what is the partial pressure of water vapor in the atmosphere (that is, the pressure due to water vapor alone)?

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Understand the concept of relative humidity: It is the ratio of the partial pressure of water vapor in the air to the vapor pressure of water at the same temperature, expressed as a percentage.

Identify the given values: The vapor pressure of water at 20.0°C is 2.34 × 10^3 Pa, and the relative humidity is 60%.

Use the formula for relative humidity: $ \text{Relative Humidity} = \frac{\text{Partial Pressure of Water Vapor}}{\text{Vapor Pressure of Water}} \times 100 \% $.

Rearrange the formula to solve for the partial pressure of water vapor: $ \text{Partial Pressure of Water Vapor} = \frac{\text{Relative Humidity} \times \text{Vapor Pressure of Water}}{100 \%} $.

Substitute the known values into the equation: $ \text{Partial Pressure of Water Vapor} = \frac{60 \% \times 2.34 \times 10^3 \text{ Pa}}{100 \%} $.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It represents the tendency of particles to escape from the liquid or solid phase into the vapor phase. At 20.0°C, the vapor pressure of water is 2.34 * 10^3 Pa, indicating the pressure exerted by water vapor when in equilibrium with liquid water at this temperature.

Relative Humidity

Relative humidity is a measure of the amount of water vapor present in the air compared to the maximum amount the air can hold at a given temperature, expressed as a percentage. It is calculated by dividing the partial pressure of water vapor by the vapor pressure of water at the same temperature. A relative humidity of 60% means the air contains 60% of the maximum water vapor it can hold at 20.0°C.

Partial Pressure

Partial pressure refers to the pressure exerted by a single component of a mixture of gases. In the context of the question, it is the pressure due to water vapor alone in the atmosphere. To find the partial pressure of water vapor at 60% relative humidity and 20.0°C, multiply the vapor pressure of water (2.34 * 10^3 Pa) by 0.60, resulting in the pressure exerted by water vapor in the air.