Liquid nitrogen is obtained by condensing gaseous nitrogen found in air and boils at 77.36 K. At the boiling point, the density of the liquid is 809 g/L and that of the gas 4.566 g/L. How many liters of liquid nitrogen are produced when 500.0 L of nitrogen gas are liquefied at this temperature

To solve this problem, we need to first calculate the mass of the nitrogen gas using its density, and then use the molar mass of N2 to convert the mass into moles. Finally, we can use the molar volume of a gas at standard conditions to determine the volume of the liquid nitrogen. Here are the steps to calculate the volume of liquid nitrogen produced:

Step 1: Calculate the mass of nitrogen gas
Given: Density of gas = 4.566 g/L
Volume of gas = 500.0 L

Mass of gas = Density × Volume of gas
Mass of gas = 4.566 g/L × 500.0 L

Step 2: Convert the mass of gas into moles
To convert the mass into moles, we need to know the molar mass of nitrogen (N2).

The molar mass of nitrogen (N2) is approximately 28.014 g/mol.

Moles of gas = Mass of gas / Molar mass of nitrogen
Moles of gas = (4.566 g/L × 500.0 L) / 28.014 g/mol

Step 3: Calculate the volume of liquid nitrogen
Given: Density of liquid = 809 g/L
Boiling point = 77.36 K

Since both the gas and liquid are at the same temperature, the relationship between the volumes can be expressed using the molar volumes of gases at standard conditions. At standard conditions (273.15 K and 1 atm), the molar volume of any ideal gas is 22.414 L/mol.

Volume of liquid = Moles of gas × Molar volume of gas at standard conditions
Volume of liquid = (Mass of gas / Molar mass of nitrogen) × 22.414 L/mol

Finally, you can substitute the values to calculate the volume of liquid nitrogen produced.