Calculate the percent deviation from ideal behavior for 0.85 mol of CO2 gas in a 1.20 L container at 45.0°C, which exerts a pressure of 19.2 atm.
Use the ideal gas law and solve for P.
Use the van der Waals equation and solve for P. Compare the two.
%deviation = [(delta P)/(Pvan der waals]*(100 = ?
To calculate the percent deviation from ideal behavior, we need to compare the observed behavior of the gas to the behavior predicted by the ideal gas law. The ideal gas law equation is given as:
PV = nRT
Where:
P = pressure
V = volume
n = moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
Step 1: Convert the temperature from Celsius to Kelvin.
To convert from Celsius to Kelvin, use the formula: K = °C + 273.15.
Given temperature, T = 45.0°C
Converting to Kelvin:
T = 45.0 + 273.15
T = 318.15 K
Step 2: Convert the pressure from atm to Pa.
The SI unit of pressure is Pascal (Pa), and 1 atm is equal to 101325 Pa.
Given pressure, P = 19.2 atm
Converting to Pa:
P = 19.2 atm x 101325 Pa/atm
P = 1,946,560 Pa
Step 3: Calculate the expected pressure using the ideal gas law.
Using the ideal gas law equation, PV = nRT, we can solve for the expected pressure.
P = nRT/V
Given:
n = 0.85 mol
R = 0.0821 L·atm/mol·K
V = 1.20 L
T = 318.15 K
Substituting the values into the formula:
P = (0.85 mol)(0.0821 L·atm/mol·K)(318.15 K) / 1.20 L
P ≈ 18.3525 atm
Step 4: Calculate the percent deviation from ideal behavior.
The percent deviation from ideal behavior can be calculated using the formula:
% Deviation = (Observed pressure - Expected pressure) / Expected pressure x 100
Given:
Observed pressure = 19.2 atm
Expected pressure = 18.3525 atm
Substituting the values into the formula:
% Deviation = (19.2 atm - 18.3525 atm) / 18.3525 atm x 100
% Deviation ≈ 4.61%
Therefore, the percent deviation from ideal behavior for 0.85 mol of CO2 gas in a 1.20 L container at 45.0°C and a pressure of 19.2 atm is approximately 4.61%.
To calculate the percent deviation from ideal behavior, we need to compare the actual pressure of the gas to the pressure that would be predicted by the ideal gas law.
The ideal gas law is represented by the equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
First, let's calculate the predicted pressure using the ideal gas law.
Given:
n = 0.85 mol
V = 1.20 L
T = 45.0°C = 318.15 K (Temperature must be in Kelvin)
R = 0.0821 L·atm/(mol·K) (Ideal gas constant for pressure in atm)
We can rearrange the ideal gas law formula to solve for P:
P = (nRT) / V
Let's plug in the values:
P = (0.85 mol * 0.0821 L·atm/(mol·K) * 318.15 K) / 1.20 L
Calculating this, we get:
P ≈ 18.5325 atm
The predicted pressure (P) for the given conditions is approximately 18.5325 atm.
Now, let's calculate the percent deviation from ideal behavior (PD):
PD = ((Actual Pressure - Predicted Pressure) / Predicted Pressure) * 100
Given:
Actual Pressure = 19.2 atm
Predicted Pressure = 18.5325 atm
Calculating this, we get:
PD = ((19.2 atm - 18.5325 atm) / 18.5325 atm) * 100
PD ≈ 3.6%
Therefore, the percent deviation from ideal behavior for 0.85 mol of CO2 gas in a 1.20 L container at 45.0°C with a pressure of 19.2 atm is approximately 3.6%.