Standard Temperature and Pressure (STP) is defined as a temperature of 0.00oC and a pressure of 100kPa. If the molar mass M of nitrogen is 14.0 g/mol, find the density (kg/m3) of nitrogen gas (N2) at STP. Nitrous Oxide or laughing gas is composed of the molecule N2O. If the molar mass of oxygen is 16.0g/mol, what is the density of N2O at STP?
To find the density of nitrogen gas (N2) at STP, we need to use the ideal gas law. The ideal gas law is given as:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature in Kelvin
At STP, the temperature is 0.00°C, which needs to be converted to Kelvin. To convert Celsius to Kelvin, you simply add 273.15 to the temperature.
So, T = 0.00°C + 273.15 = 273.15 K
The molar mass of nitrogen gas (N2) is given as 14.0 g/mol. To convert this mass to moles, we use the equation:
moles = mass/molar mass
moles = 1 g / 14.0 g/mol = 0.0714 mol (rounded to four significant figures)
At STP, the pressure is given as 100 kPa.
Now we can substitute our values into the ideal gas law:
PV = nRT
(100 kPa)(V) = (0.0714 mol)(8.31 J/mol·K)(273.15 K)
To convert kPa to Pa, we multiply by 1000:
(100000 Pa)(V) = (0.0714 mol)(8.31 J/mol·K)(273.15 K)
Now, we can solve for V:
V = [(0.0714 mol)(8.31 J/mol·K)(273.15 K)] / (100000 Pa)
V ≈ 1.9959 m^3
To find density, we need to know the mass of the gas. Since the molar mass of nitrogen (N2) is given as 14.0 g/mol, we can calculate the mass of 0.0714 mol of nitrogen gas:
mass = (0.0714 mol) × (14.0 g/mol) ≈ 1 g
Finally, we can calculate the density:
density = mass / volume
density = 1 g / 1.9959 m^3 ≈ 0.501 kg/m^3
So, the density of nitrogen gas (N2) at STP is approximately 0.501 kg/m^3.
To find the density of nitrous oxide (N2O) at STP, we would follow the same steps as above, but use the molar mass of oxygen (O2) instead. The molar mass of oxygen (O2) is given as 16.0 g/mol. So, you would calculate the mass of 0.0714 mol of oxygen, and then use that in the density calculation.