How to Calculate the Pressure of Ethane at a Specific Density and Temperature
How can we determine the pressure of ethane at a density of 37.2 g/L and a temperature of 50.4 °C?
Given the density of ethane at 37.2 g/L and the temperature of 50.4 °C, what is the formula and method to calculate the pressure of ethane?
Calculation of Ethane Pressure at Specific Density and Temperature
To determine the pressure at which ethane (C2H6) has a density of 37.2 g/L at 50.4 °C, we can utilize the ideal gas law and density formula.
The ideal gas law equation, PV = nRT, relates pressure, volume, number of moles, ideal gas constant, and temperature.
Firstly, we need to convert the given ethane density from g/L to kg/m3:
Density = mass / volume
37.2 g/L = (37.2 g) / (1 L) = 37200 kg/m3
Next, we convert the Celsius temperature to Kelvin:
T = 50.4 °C + 273.15 = 323.55 K
The molar mass of ethane (C2H6) is calculated as:
Molar mass = (2 * atomic mass of carbon) + (6 * atomic mass of hydrogen)
= (2 * 12.01 g/mol) + (6 * 1.01 g/mol)
= 30.07 g/mol
Now, we calculate the number of moles (n) using the given density and molar mass:
n = density / molar mass
= 37200 kg/m3 / (30.07 g/mol * 0.001 kg/g)
≈ 1233.89 mol/m3
We rearrange the ideal gas law equation to solve for pressure (P):
P = nRT / V
Substitute the values:
P = (1233.89 mol/m3) * (8.314 J/(mol·K)) * (323.55 K) / (1 m3)
≈ 332965 Pa