What is the process to calculate the real pressure in atmospheres of 3.991 kg of neon gas in a 32.21 L gas cylinder at 19.73 C using the Van der Waals equation?

To calculate the real pressure of neon gas in atmospheres using the Van der Waals equation, we need to follow these steps:

## Calculate Number of Moles of Neon Gas:

To calculate the number of moles of neon gas, we first need to convert the given mass of neon from kg to g and then determine the number of moles using the molar mass of neon.
Given:
Mass of neon gas = 3.991 kg
Molar mass of neon (Ne) = 20.18 g/mol = 0.02018 kg/mol
Number of moles (n) = mass / molar mass
n = 3.991 kg / 0.02018 kg/mol
## Convert Temperature to Kelvin:

To use the Van der Waals equation, the temperature must be in Kelvin. We can convert the given temperature from Celsius to Kelvin using the formula: K = °C + 273.15
Given temperature = 19.73 °C
T = 19.73 + 273.15
## Substitute Values into Van der Waals Equation:

Now, we can substitute the known values into the Van der Waals equation:
(P + (0.211 * (n²/V²)))(V - 0.0171n) = nRT
Solving the equation step by step will help us determine the real pressure of neon gas in atmospheres based on the provided data.
Follow the calculations carefully to ensure accurate results.