The density of dinitrogen monoxide gas at exactly 30°C and exactly 1 atm is approximately 1.743 g/L.
How to calculate the density of dinitrogen monoxide
To calculate the density of dinitrogen monoxide (N2O) gas at 30°C and 1 atm, use the ideal gas law and the molar mass of N2O.
The ideal gas law is given by:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/K·mol)
T = Temperature (in Kelvin)
First, convert the given temperature of 30°C to Kelvin:
T = 30°C + 273.15 = 303.15 K
At STP (Standard Temperature and Pressure), the pressure is 1 atm and the temperature is 273.15 K. Since the temperature and pressure given are different from STP, adjust the ideal gas law equation to account for these conditions.
The adjusted equation is:
(P * V) / (n * T) = (P' * V') / (n' * T')
Where the primed variables represent the conditions at STP.
We can rearrange the equation to solve for the density (d = mass/volume):
d = (molar mass * P) / (R * T)
The molar mass of N2O is approximately 44.013 g/mol.
Using the given values:
P = 1 atm
R = 0.0821 L·atm/K·mol
T = 303.15 K
Molar mass of N2O = 44.013 g/mol
Substituting these values into the equation, we get:
d = (44.013 g/mol * 1 atm) / (0.0821 L·atm/K·mol * 303.15 K)
d ≈ 1.743 g/L
Therefore, the density of dinitrogen monoxide gas at exactly 30°C and exactly 1 atm is approximately 1.743 g/L.