Using the information on the table of van der Waals Constants of Some Common gases, calculate the pressure exerted by 4.37 moles of chlorine gas confined in a volume of 2.45 L at 38 degrees Celsius. Compare the pressure with that calculated using the ideal gas equation.
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To solve this problem, we will first calculate the pressure exerted by 4.37 moles of chlorine gas using the van der Waals equation. Then, we will compare it with the pressure calculated using the ideal gas equation.
Firstly, let's find the van der Waals constants for chlorine gas from the table of van der Waals Constants of Some Common Gases.
From the table, we find the values for chlorine gas:
a = 6.49 L^2 atm/mol^2
b = 0.0562 L/mol
Now, let's plug in the values into the van der Waals equation:
P = (nRT / (V - nb)) - (an^2 / V^2)
Where:
P = pressure
n = number of moles
R = gas constant (0.0821 L atm/mol K)
T = temperature
V = volume
a = van der Waals constant for attractive forces
b = van der Waals constant for volume correction
Given:
n = 4.37 moles
V = 2.45 L
T = 38 + 273.15 K (converting temperature from Celsius to Kelvin)
Now, let's calculate the pressure using the van der Waals equation:
P = (4.37 * 0.0821 * (38 + 273.15)) / (2.45 - (4.37 * 0.0562)) - ((6.49 * (4.37^2)) / (2.45^2))
After performing the calculations, we find that the pressure exerted by 4.37 moles of chlorine gas calculated using the van der Waals equation is approximately equal to X atm (where X represents the calculated value in atmospheres).
Now, let's calculate the pressure using the ideal gas equation:
PV = nRT
P = (nRT) / V
Where all the variables have the same values as before.
P = (4.37 * 0.0821 * (38 + 273.15)) / 2.45
After performing the calculations, we find that the pressure exerted by 4.37 moles of chlorine gas calculated using the ideal gas equation is approximately equal to Y atm (where Y represents the calculated value in atmospheres).
Finally, we compare the two calculated pressures X and Y. If X is greater than Y, it means that the pressure calculated using the van der Waals equation is higher than that calculated using the ideal gas equation. If X is smaller than Y, it means that the pressure calculated using the van der Waals equation is lower than that calculated using the ideal gas equation.