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?
Ideal gas formula is pv=nrt,but the problem is asking me to find the mass?
Compute the number of moles n first. You can then say that:
n = n_{N2} + n_{O2}
You also know that:
n_{N2}/n = 0.79
and
n_{O2}/n = 0.79
This allows you to solve for n_{N2} and n_{O2}. Using the molar masses for N2 and O2 you can then obtain the mass.
Air is a mixture of nitrogen, oxygen, and other gases.
At STP, one mole of an ideal gas occupies 22.4 liters.
Assume air is 21% O2 and 79% N2 by volume
0.21 x 32 g/mol + 0.79 x 28 g/mole = 28.8 g / mol of "air"
28.8 g / 22,400 mL = 0.0013 g/mL
To find the mass of the air in the living room, we can use the ideal gas equation, PV = nRT. However, since we are given the volume, temperature, and pressure of the air, we need to rearrange the formula to solve for the number of moles of gas first.
The ideal gas equation can be rearranged as:
n = PV / RT
Here's what each variable represents:
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)
Let's calculate the number of moles of gas first:
P = (1.01 × 10^5 Pa) (given)
V = (2.5 m) × (4.8 m) × (5.9 m) = 71.76 m^3 (given)
R = 8.314 J/(mol·K) (constant)
T = (27°C + 273.15) K = 300.15 K (converted to Kelvin)
Now, substitute the values in the formula to find the number of moles:
n = (1.01 × 10^5 Pa) × (71.76 m^3) / (8.314 J/(mol·K) × 300.15 K)
Calculate the value of n.
Next, to find the mass of the air, we need to know the molar mass of air. Air is a mixture, but we can approximate its molar mass as the sum of the molar masses of nitrogen and oxygen.
The molar mass of nitrogen (N2) is 28.0134 g/mol, and the molar mass of oxygen (O2) is 31.9988 g/mol.
Since the air is composed of 79% nitrogen and 21% oxygen, we can calculate the average molar mass of air using the weighted average formula:
Average Molar Mass = (0.79 × Molar Mass of Nitrogen) + (0.21 × Molar Mass of Oxygen)
Calculate the average molar mass of air.
Now, to find the mass (in grams) of the air, we can multiply the number of moles by the molar mass of air.
Mass = Moles of Gas × Molar Mass of Air
Calculate the mass of the air in grams.
That's it! You have now calculated the mass of the air in the living room.