What is the density (in g/L) of hydrogen gas at 23.0 degrees Celsius and a pressure of 1670 psi?
Use PV = nRT to calculate n, number of moles H2 gas. Don't forget to change 1670 psi to atmospheres and temperature to Kelvin. Use 1 L for volume.
Convert n to mass (moles = grams/molar mass).
Then use mass = volume x density to determine density.
To calculate the density of a gas, we can use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperature from Celsius to Kelvin. The Kelvin temperature can be obtained by adding 273.15 to the Celsius temperature. In this case, 23.0 degrees Celsius + 273.15 = 296.15 Kelvin.
Next, we need to convert the pressure from pounds per square inch (psi) to Pascals (Pa) for use in the ideal gas law equation. There are 6894.76 Pascals in 1 psi. So, 1670 psi * 6894.76 Pa/psi = 11,473,287.2 Pa.
We also need to determine the molar mass of hydrogen gas (H2). The molar mass of hydrogen gas is 2.016 g/mol.
Now we can rearrange the ideal gas law equation to isolate density (mass/volume). The ideal gas law equation can be rearranged as follows:
PV = nRT
(PV)/(RT) = n
Since density (mass/volume) is equal to the number of moles (n) multiplied by the molar mass (M) divided by the volume (V), we can substitute these values into the equation:
density = (n * M) / V
density = ((P * V) / (R * T)) * M
Plugging in the values:
density = ((11,473,287.2 Pa) * V) / (8.314 J/(mol*K) * 296.15 K) * 2.016 g/mol
Now, we just need to convert the density from g/mol to g/L. Since 1 mol occupies 22.4 L at standard temperature and pressure (STP), we can multiply the density by (22.4 L/mol) to obtain the density in g/L.
Therefore, the density of hydrogen gas at 23.0 degrees Celsius and a pressure of 1670 psi is:
density = (((11,473,287.2 Pa) * V) / (8.314 J/(mol*K) * 296.15 K) * 2.016 g/mol) * (22.4 L/mol)