what pressure is required to cause n2 to have a density of 1.00 g/L at 45 C?
To determine the pressure required to cause nitrogen gas (N2) to have a density of 1.00 g/L at 45°C, we can use the ideal gas law equation.
The ideal gas law equation is represented as:
PV = nRT
Where:
P = Pressure (in units of Pascal, Pa)
V = Volume (in units of cubic meters, m3)
n = Number of moles of gas
R = Ideal gas constant (8.314 J/(mol·K))
T = Temperature (in units of Kelvin, K)
First, let's convert the given density of 1.00 g/L to units of kg/m3. Since 1 L = 0.001 m3, we can calculate:
Density = (mass of gas) / (volume of gas)
1.00 g/L = (m) / (0.001 m3)
Now, let's convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature:
T = 45°C + 273.15 = 318.15 K
To calculate the molar mass of nitrogen gas (N2), we add the atomic masses of two nitrogen atoms:
Molar mass of N2 = (2 × atomic mass of nitrogen)
= (2 × 14.01 g/mol)
= 28.02 g/mol
Next, we need to convert the given density from g/L to kg/m3:
1.00 g/L = 1000.00 kg/m3 (since 1 g = 0.001 kg)
To calculate the number of moles (n), we use the equation:
n = (mass of gas) / (molar mass)
= (1000.00 kg/m3) / (28.02 g/mol)
= (1000.00 kg/m3) / (0.02802 kg/mol)
= 35,680.94 mol/m3
Now, rearrange the ideal gas law equation to solve for pressure (P):
P = (nRT) / V
Since the volume (V) is not given, we can use the molar volume of an ideal gas at standard temperature and pressure (STP) conditions, which is approximately 22.4 L/mol.
V = 22.4 L/mol = 0.0224 m3/mol
Now substitute the known values in the equation:
P = (35,680.94 mol/m3) × (8.314 J/(mol·K)) × (318.15 K) / (0.0224 m3/mol)
Calculating the pressure (P):
P ≈ 38,421,432.69 Pa ≈ 38.4 MPa (rounded to one decimal place)
Therefore, it would require approximately 38.4 megapascals of pressure (MPa) to cause nitrogen gas (N2) to have a density of 1.00 g/L at 45°C.