(L2bar/mol2) (L/mol)
Acetylene 4.448 0.05136
Calculate the difference in pressure (in atm) when 100.0g of acetylene acts as an ideal gas versus as a real gas in a 100L tank at a temperature of 1000K.
(L2bar/mol2) (L/mol)
Acetylene 4.448 0.05136
Calculate the difference in pressure (in atm) when 100.0g of acetylene acts as an ideal gas versus as a real gas in a 100L tank at a temperature of 1000K.
1) Change 100.0g C2H2 to moles (n)
2) Calculate the ideal pressure using the Ideal Gas Law:
PV = nRT, P = nRT/V
3) Calculate the real pressure using the Van der Waals Equation. You can find the equation here:
http://hyperphysics.phy-astr.gsu.edu/Hbase/Kinetic/waal.html
Constants "a" and "b" for acetylene can be found here:
http://en.wikipedia.org/wiki/Van_der_Waals_constants_(data_page)
The difference between P(ideal) and P(real) can be found by subtracting the smaller from the larger one.
[Be prepared to spend some time on this problem]
HERE IS MY HOMEWORK:
I have been trying the real gases homework for hours and am completely stuck. This is what I have been attempting to make work. First I found the moles then plugged in all the other variables.
100gC2H2/26.0373g/mol=3.84mol C2H2=n
P=nRT/(V-nb)-an^2/V^2
P= n R T /(V - n b) - a n^2 / V^2
319.49=3.84x8.3145x1000/(100-3.84x.05136)-4.39x3.84^2/100^2
319.49 is not the correct answer and I have only confused myself further and further trying to understand this. At this point I am just pushing buttons on my calculator hoping for a miracle. Please release me from my torture:)
To calculate the difference in pressure when acetylene acts as an ideal gas versus a real gas in a 100L tank at a temperature of 1000K, we need to consider the ideal gas equation and the van der Waals equation.
1. Ideal Gas Equation:
The ideal gas equation is given by:
PV = nRT
Where:
- P is the pressure of the gas (in atm)
- V is the volume of the gas (in L)
- n is the number of moles of the gas
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature of the gas (in Kelvin)
2. Van der Waals Equation:
The van der Waals equation corrects for the volume occupied by gas molecules and the intermolecular forces between them. It is given by:
(P + a(n/V)^2) (V - nb) = nRT
Where:
- P is the pressure of the gas (in atm)
- V is the volume of the gas (in L)
- n is the number of moles of the gas
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature of the gas (in Kelvin)
- a is a constant that incorporates the attractive forces between gas molecules
- b is a constant that accounts for the volume occupied by gas molecules
To calculate the difference in pressure, we need to follow these steps:
Step 1: Convert the given L2bar/mol2 value to L·atm/(mol2)
To convert the L2bar/mol2 value to L·atm/(mol2), divide it by 1000.
4.448 L2bar/mol2 = 4.448/1000 L·atm/(mol2) = 0.004448 L·atm/(mol2)
Step 2: Calculate the values of a and b for acetylene
The values of a and b for acetylene can be found using the following equations:
a = 27 * (L2bar/mol2) * (R^2)
b = 0.0644 L/mol
Substituting the given values:
a = 27 * 0.004448 * (0.0821^2) L·atm/(mol2) = 0.008060 L·atm/(mol2)
b = 0.0644 L/mol
Step 3: Calculate the number of moles of acetylene
To calculate the number of moles of acetylene, we need to use its molar mass. The molar mass of acetylene (C₂H₂) is:
2 * 12.01 g/mol (for carbon atoms) + 2 * 1.01 g/mol (for hydrogen atoms) = 26.04 g/mol
Given mass of acetylene = 100.0 g
Number of moles of acetylene = (100.0 g) / (26.04 g/mol) = 3.84 mol
Step 4: Calculate the pressure using the ideal gas equation
Using the ideal gas equation, we can calculate the pressure of acetylene as an ideal gas:
P_ideal = nRT/V
P_ideal = (3.84 mol)(0.0821 L·atm/(mol·K))(1000 K) / (100 L) = 31.2516 atm
Step 5: Calculate the pressure using the van der Waals equation
Using the van der Waals equation, we can calculate the pressure of acetylene as a real gas:
(P + a(n/V)^2) (V - nb) = nRT
Substituting the given values:
(P + 0.008060(3.84/100)^2) (100 - 0.0644 * 3.84) = 3.84 * 0.0821 * 1000
Now, you can solve this equation to find the value of P.