What is the total mass in grams of oxygen in a room measuring 4.0 m by 5.0 m by 2.5 m? Assume that the gas is at STP and that air contains 20.95% oxygen by volume.

Verified step by step guidance

1. Calculate the volume of the room by multiplying its dimensions: \( V = 4.0 \, \text{m} \times 5.0 \, \text{m} \times 2.5 \, \text{m} \).
2. Convert the volume from cubic meters to liters, knowing that 1 cubic meter equals 1000 liters.
3. Determine the volume of oxygen in the room by multiplying the total volume of the room by the percentage of oxygen in air (20.95%).
4. Use the ideal gas law at STP to find the number of moles of oxygen, where 1 mole of gas occupies 22.4 liters at STP.
5. Calculate the mass of oxygen by multiplying the number of moles by the molar mass of oxygen (32.00 g/mol).

Key Concepts

Standard Temperature and Pressure (STP)

STP is a reference point in chemistry defined as 0 degrees Celsius (273.15 K) and 1 atmosphere of pressure. At STP, one mole of an ideal gas occupies 22.4 liters. This concept is crucial for calculating the volume of gas in a given space and determining the number of moles present.

Volume of a Room

The volume of a room is calculated by multiplying its length, width, and height. In this case, the room's dimensions are 4.0 m, 5.0 m, and 2.5 m, resulting in a total volume of 50 cubic meters. This volume is essential for determining how much air, and consequently oxygen, is present in the room.

Composition of Air

Air is composed of various gases, with oxygen making up approximately 20.95% by volume. To find the total mass of oxygen in the room, one must first calculate the total mass of air and then apply the percentage of oxygen. This concept is vital for understanding how to derive the mass of a specific component from a mixture.