A room has the dimensions 3.0 m by 4.0 m by 4.0 m . The air in the room is 79% N2( MW= 28) and 21% O2 (MW = 32). At a temperature of 20 degrees Celsius and pressure of 115 kPa , what is the mass of the air in the room in kilograms?

To calculate the mass of air in the room, we need to know the volume of the room and the density of the air.

First, let's calculate the volume of the room by multiplying the length, width, and height:

Volume = Length x Width x Height
= 3.0 m x 4.0 m x 4.0 m
= 48 cubic meters

Next, we can calculate the density of the air using the ideal gas law equation:

PV = nRT

Where:
P = pressure (in pascals)
V = volume (in cubic meters)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in kelvin)

We need to convert the given pressure from kilopascals to pascals, so:

P = 115 kPa x 1000 = 115,000 pascals

We also need to convert the given temperature from degrees Celsius to Kelvin:

T = 20 degrees Celsius + 273.15 = 293.15 K

Now we can rearrange the ideal gas law equation to solve for the number of moles (n):

n = PV / RT

n = (115,000 pascals) x (48 cubic meters) / [(8.314 J/(mol·K)) x (293.15 K)]

Simplifying, we have:

n = 661.21 moles

Finally, we can calculate the mass of air in the room by multiplying the number of moles by the molecular weight of air, considering the given percentages of N2 and O2:

Mass of N2 = 79% x 661.21 moles x 28 g/mol
Mass of O2 = 21% x 661.21 moles x 32 g/mol

Total mass of air = Mass of N2 + Mass of O2

Remember to convert grams to kilograms (divide by 1000) to get the mass in kilograms.