a) Calculate the pressure exerted by 0.5160 mol N2 in a 1.0000 L container at 24.6°C using the ideal gas law.
atm
(b) Calculate the pressure exerted by 0.5160 mol N2 in a 1.0000 L container at 24.6°C using the van der Waals equation.
atm
(c) Compare the results. (Write the percentage difference between the results, based on the higher value result.)
%
Surely you know how to do these. Perhaps you just want to know what answer I get but I don't have the time to work these things unless I have a reason. If you truly don't understand them, explain what kind of problem you are having.
so i plugged int he information that i have from the question... i am using an electronic based hmwk. it says that the answers that i have gotten are wrong... here is what i have come up with....
with using PV=nRT
i got a pressure of 12.6012 atm...
with using the van der w.
i got apressure of 12.2816 rounded
am i even close?
I have 12.61 atm. Is the T given as 24.6 or 24.60? If 24.6 then you are allowed 3 sifnificant figures and the answer would be 12.6 atm. If 24.60, then 12.61 atm would be the answer.
For the van der Waals question I have 12.75 but I think only three s.f. are allowed so that would round to 12.7. Check my arithmetic.
or 12.8 if we round to the nearest whole even number.
To calculate the pressure exerted by N2 in a container at a specific temperature and volume, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K for atm units)
T = temperature in Kelvin
Let's start by converting the given temperature from Celsius to Kelvin:
T = 24.6°C + 273.15 = 297.75 K
(a) Using the ideal gas law:
Given:
n = 0.5160 mol
V = 1.0000 L
T = 297.75 K
First, we need to convert temperature from Celsius to Kelvin (24.6°C + 273.15 = 297.75 K).
Now we can substitute the values into the ideal gas law equation:
P * V = n * R * T
P = (n * R * T) / V
Now we can calculate the pressure:
P = (0.5160 mol * 0.0821 L·atm/mol·K * 297.75 K) / 1.0000 L
P ≈ 12.647 atm
Therefore, the pressure exerted by 0.5160 mol N2 in a 1.0000 L container at 24.6°C using the ideal gas law is approximately 12.647 atm.
(b) To calculate the pressure using the van der Waals equation:
P = (nRT / V - nb) / (V - na)
Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K for atm units)
T = temperature in Kelvin
a and b are constants specific to the gas (0.141 atm·L^2/mol^2 and 0.0391 L/mol for N2 respectively)
Given:
n = 0.5160 mol
V = 1.0000 L
T = 297.75 K (same as before)
a = 0.141 atm·L^2/mol^2
b = 0.0391 L/mol
Substituting the values into the van der Waals equation:
P = (nRT / V - nb) / (V - na)
P = (0.5160 mol * 0.0821 L·atm/mol·K * 297.75 K) / (1.0000 L - (0.0391 L/mol * 0.5160 mol)) / (1.0000 L - 0.141 atm·L^2/mol^2 * 0.5160 mol^2)
P ≈ 11.793 atm
Therefore, the pressure exerted by 0.5160 mol N2 in a 1.0000 L container at 24.6°C using the van der Waals equation is approximately 11.793 atm.
(c) To find the percentage difference between the two results, we can use the formula:
% Difference = [(Value 1 - Value 2) / ((Value 1 + Value 2) / 2)] * 100
% Difference = [(12.647 - 11.793) / ((12.647 + 11.793) / 2)] * 100
% Difference = (0.854 / 12.220) * 100
% Difference ≈ 7%
Therefore, the percentage difference between the two results is approximately 7%.