Final answer:
The relative humidity of the air in the closed room is calculated as the ratio of the current water vapor in the air to the total water vapor the air can hold before saturation. With 47.7 g present and adding 13.6 g leading to saturation, the relative humidity is 77.8%.
Step-by-step explanation:
Understanding Relative Humidity
To calculate the relative humidity of the air in the closed room, we first understand that relative humidity is defined as the ratio of the actual vapor density to the saturation vapor density. Given that the air currently contains 47.7 g of water vapor and can hold a maximum of 47.7 g + 13.6 g = 61.3 g before becoming saturated, the relative humidity of the room can be calculated as:
Percent Relative Humidity = (Vapor Density / Saturation Vapor Density) × 100%
Therefore:
Percent Relative Humidity = (47.7 g / 61.3 g) × 100% = 77.8%
This means that the current humidity level is 77.8% of what is required for the air in the room to reach saturation, where 100% relative humidity means the air cannot hold any more water vapor at the current temperature.