Answer:
The difference in pressure = 21.59 atm
Explanation:
Step 1: Data given
Moles of gas = 14.0 moles
Volume = 3.00 L
Temperature = 23.3 °C
The van der Waals constants for methane are a=2.300L²*atm/mol² and b=0.0430 L/mol
Step 2: Calculate pressure
p*V = n*R*T
⇒ p = the pressure = TO BE DETERMINED
⇒ V = the volume of the tank = 3.00 L
⇒ R = the gas constant = 0.08206 L*atm/mol*K
⇒ T = the temperature = 23.3 °C = 296.45 K
⇒ n = the number of moles gas = 14.0 moles
p = (n*R*T)/V
p = (14.0 *0.08206 * 296.45)/3.00
p = 113.52 atm
Step 3: Calculate the pressure via the van der waals equation
The Van der waals equation is (p + n²a/V²)*(V-nb) = nRT
⇒p = To be determined
⇒ n =the number of moles = 14.0 moles
⇒a=2.300 L²*atm/mol²
⇒b=0.0430 L/mol
(p + 14.0²*2.300 / 3.00²) * (3.00 - 14.0*0.0430) = 14.0*0.08206*296.45
(p + 14.0²*2.300 / 3.00²) * (3.00 - 14.0*0.0430) = 340.57
(p + 14.0²*2.300 / 3.00²) * 2.398 = 340.57
(p + 14.0²*2.300 / 3.00²) = 142.02
(p + 50.09) = 142.02
p = 91.93 atm
The difference in pressure = 113.52 atm - 91.93 atm = 21.59 atm
