Answer: To calculate the number of moles of water in 12 dm³ of water vapor at STP (Standard Temperature and Pressure), we need to use the ideal gas law. The ideal gas law is given by:
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)
At STP, the conditions are defined as follows:
Pressure (P) = 1 atmosphere = 101,325 Pa
Temperature (T) = 273.15 K (0°C)
Now, we need to convert the volume from dm³ to cubic meters:
1 dm³ = 0.001 m³
So, 12 dm³ = 12 * 0.001 m³ = 0.012 m³
Now we can plug the values into the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
n = (101325 Pa) * (0.012 m³) / (8.314 J/(mol·K) * 273.15 K)
n ≈ 0.0049 moles
Therefore, there are approximately 0.0049 moles of water in 12 dm³ of water vapor at STP.