How many air molecules are in a 15.0×12.0×10.0 ft room? Assume atmospheric pressure of 1.00 atm, a room temperature of 20.0 ∘C, and ideal behavior.
Volume conversion:There are 28.2 liters in one cubic foot.
Well, we could crunch some numbers and calculate the exact number of air molecules in that room, but then we'd be here all day! So let's take a more light-hearted approach, shall we?
In a 15.0×12.0×10.0 ft room, we can be sure that there are a LOT of air molecules floating around. In fact, there are probably more air molecules in that room than there are knock-knock jokes in my database! And believe me, I've got a lot of knock-knock jokes!
But seriously, estimating the exact number of air molecules in that room is a bit tricky, as it depends on factors like temperature and pressure. So let's just say there are enough air molecules in there to make you feel like you're not alone, even when you're by yourself!
Hope that brings a smile to your face!
To calculate the number of air molecules in the room, we can use the ideal gas law equation, which states:
PV = nRT
Where:
- P is the pressure of the gas (in atm),
- V is the volume of the gas (in liters),
- n is the number of gas molecules,
- R is the ideal gas constant (0.0821 L.atm/mol.K),
- T is the temperature of the gas (in Kelvin).
First, we need to convert the volume of the room from cubic feet to liters:
15.0 x 12.0 x 10.0 ft³ = 15.0 x 12.0 x 10.0 x 28.2 L = 50,940 L
Next, we need to convert the temperature from degrees Celsius to Kelvin:
20.0 °C + 273.15 = 293.15 K
Now we can substitute the values into the ideal gas law equation:
(1.00 atm)(50,940 L) = n(0.0821 L.atm/mol.K)(293.15 K)
Simplifying the equation:
50,940 = n(24.06741515)
Dividing both sides by 24.06741515:
n = 50,940 / 24.06741515
n ≈ 2116.07 moles
Finally, we can convert the number of moles to the number of air molecules by multiplying by Avogadro's number, which is approximately 6.022 x 10^23 molecules per mole:
n = 2116.07 moles x (6.022 x 10^23 molecules/mole)
n ≈ 1.274 x 10^27 molecules
Therefore, there are approximately 1.274 x 10^27 air molecules in a 15.0x12.0x10.0 ft room at atmospheric pressure and a temperature of 20.0 °C.
To determine the number of air molecules in a 15.0×12.0×10.0 ft room, we need to follow these steps:
Step 1: Convert the room dimensions from ft^3 to liters:
- Given: 1 ft³ = 28.2 liters
- Room volume in liters = (15.0 ft × 12.0 ft × 10.0 ft) × 28.2 liters/ft³
Step 2: Convert the room volume to the number of moles of air:
- Using the ideal gas law, PV = nRT
- Rearrange the formula to solve for n (moles): n = PV / (RT)
- P = pressure = 1.00 atm
- V = volume in liters (from step 1)
- R = ideal gas constant = 0.0821 L·atm/(mol·K)
- T = temperature in Kelvin (20.0°C = 293.15 K)
Step 3: Convert moles of air to the number of air molecules:
- Avogadro's number (NA) states that 1 mole of a substance contains 6.022 x 10^23 particles (molecules or atoms)
- Number of air molecules = n (in moles) × Avogadro's number
Let's calculate:
Step 1: Convert room dimensions to liters
Room volume = (15.0 ft × 12.0 ft × 10.0 ft) × 28.2 liters/ft³ = 50,760 liters
Step 2: Calculate moles of air
n = (1.00 atm) × (50,760 liters) / ((0.0821 L·atm/(mol·K)) × (293.15 K)) = 2168.32 moles
Step 3: Convert moles of air to air molecules
Number of air molecules = 2168.32 moles × 6.022 x 10^23 molecules/mol
Therefore, there are approximately 1.306 x 10^27 air molecules in a 15.0×12.0×10.0 ft room at a pressure of 1.00 atm and a temperature of 20.0°C, assuming ideal behavior.
just plug in your formula
PV = nRT
n = PV/RT
n is the number of moles.
Now multiply by A, Avogadro's constant to get the number of molecules.
Or, since R = kA,
n = PV/kAT so
nA = PV/kT
gives the number of molecules