An apartment has a living room whose dimensions are 2.5 m 4.8 m 5.9 m. Assume that the air in the room is composed of 79% nitrogen (N2) and 21% oxygen (O2). At a temperature of 27°C and a pressure of 1.01 105 Pa, what is the mass (in grams) of the air?
PV = nRT
volume = 2.5 x 4 x 5 = 50
temperature = 22+273.15 = 295.15 k
pressure = 1.01x 10^5 pa
79% of N2 = 0.79
21% of O2 = 0.21
pv = nrt
1.01 x 10^5 x 50 = n x 8.31 x 295.15
n= 2059
n = mass / mass over mole
mass= 2059 x (0.79 x 14*2+0.21 *32)
mass = 5.9*10^4
oh just change the temperature and the pressure in my equation. I got the wrong question but overall method is the same. Good luck!
To calculate the mass of air in the room, we need to know the volume of the room and the density of air at the given conditions.
Step 1: Calculate the volume of the room
The volume of the room can be calculated by multiplying the length, width, and height of the room. In this case, the dimensions of the living room are given as 2.5 m x 4.8 m x 5.9 m.
Volume = 2.5 m * 4.8 m * 5.9 m = 69.84 m^3
Step 2: Calculate the density of air at the given conditions
To calculate the density of air, we can use the ideal gas law. The ideal gas law is expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, convert the given temperature from degrees Celsius to Kelvin by adding 273.15.
Temperature in Kelvin = 27°C + 273.15 = 300.15 K
Next, we can rearrange the ideal gas law to solve for the number of moles (n) of air:
n = PV / RT
Given:
Pressure (P) = 1.01 x 10^5 Pa
Volume (V) = 69.84 m^3
R = 8.314 J/(mol·K) (the ideal gas constant)
Substituting the values into the equation:
n = (1.01 x 10^5 Pa) * (69.84 m^3) / (8.314 J/(mol·K) * 300.15 K)
Step 3: Calculate the mass of air
The mass of air can be calculated using the molar mass of air. Air primarily consists of nitrogen (N2) and oxygen (O2) gases. The molar masses of nitrogen and oxygen are approximately 28 g/mol and 32 g/mol, respectively.
Since the air is composed of 79% nitrogen and 21% oxygen, we can calculate the mass of air using the formula:
Mass of air = (n * 0.79 * molar mass of nitrogen) + (n * 0.21 * molar mass of oxygen)
Substituting the values:
Mass of air = (n * 0.79 * 28 g/mol) + (n * 0.21 * 32 g/mol)
Finally, we can calculate the mass of air by substituting the value of n from Step 2 into the above equation.