Question

Large amounts of Nitrogen gas (N₂) are used in the manufacture of ammonia, principally for use in fertilizers. Suppose 120 kg of N₂ gas is stored in a 1100.0 L metal cylinder at 280 degrees C.

a) Calculate the pressure of the gas, assuming ideal gas behavior.

Answer 1

The pressure of nitrogen gas stored in a 1100.0 L cylinder at 280 °C is calculated using the ideal gas law PV=nRT, resulting in a pressure of 194.69 atm.

Step-by-step explanation:

To calculate the pressure of nitrogen gas (N₂) in the cylinder, assumed to be an ideal gas, we can use the ideal gas law:

PV = nRT,

where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature in Kelvin.

First, we convert the given mass of nitrogen to moles. The molar mass of N₂ is 28.0 g/mol, so 120 kg (120,000 g) of N₂ is:

n = mass / molar mass = 120,000 g / 28.0 g/mol = 4285.71 moles.

Next, we convert the temperature to Kelvin:

T = 280 °C + 273.15 = 553.15 K.

The volume is given as 1100.0 L, which we will use directly in our calculation. The ideal gas constant, R, is 0.0821 L·atm/mol·K.

Now, we can solve for pressure, P:

P = nRT / V = (4285.71 mol) × (0.0821 L·atm/mol·K) × (553.15 K) / 1100.0 L = 194.69 atm.

The pressure of the nitrogen gas under the given conditions is 194.69 atm.