Question

Using the van der Waals equation, calculate the pressure for a 3.88 L container with 8.44 moles of carbon tetrachloride at 284°C. Note that a = 20.4 L^2 atm/mol^2 and b = 0.1383 L/mol. (Provide the calculated pressure in atm.)

Answer 1

To calculate the pressure using the van der Waals equation, we need to follow the formula: P = (nRT)/(V - nb) - (an²)/V². Given the values for volume, number of moles, temperature, and the van der Waals constants, we can plug them into the equation and calculate the pressure. The pressure is approximately 4.71 atm.

Step-by-step explanation:

To calculate the pressure using the van der Waals equation, we need to follow the formula:

P = (nRT)/(V - nb) - (an²)/V²

Where:

• P is the pressure
• n is the number of moles
• R is the ideal gas constant, which is 0.0821 L·atm/(mol·K)
• T is the temperature in Kelvin
• V is the volume
• a and b are the van der Waals constants

First, let's convert the volume from liters to cubic meters:

V = 3.88 L = 0.00388 m³

Next, let's convert the temperature from Celsius to Kelvin:

T = 284°C + 273.15 = 557.15 K

Now we can substitute the values into the van der Waals equation:

P = (8.44 mol)(0.0821 L·atm/(mol·K))(557.15 K) / (0.00388 m³ - (8.44 mol)(0.1383 L/mol)) - (20.4 L² atm/mol²)(8.44 mol)² / (0.00388 m³)²

After calculating the equation, we find that the pressure is approximately 4.71 atm.

Answer 2

To calculate the pressure using the van der Waals equation, convert the temperature to Kelvin, use the equation
`P = (RT / (V - b)) - (a / (V^2))`, and substitute the given values.

Step-by-step explanation:

To calculate the pressure of a 3.88 L container with 8.44 moles of carbon tetrachloride at 284°C using the van der Waals equation, follow these steps:

1. Convert the temperature from Celsius to Kelvin by adding 273.15: 284°C + 273.15 = 557.15 K.
2. Plug the values into the van der Waals equation:
   `P = (RT / (V - b)) - (a / (V^2))`,.
3. R is the ideal gas constant (0.08206 L atm/mol K) and T is the temperature in Kelvin.
4. V is the volume of the container.
5. a is the van der Waals constant for carbon tetrachloride (
   `20.4 L^2 atm/mol^2`)
6. b is the van der Waals constant for carbon tetrachloride (0.1383 L/mol).
7. To substitute the values into the given expression, let's first calculate the numerical values:
8. Now substitute these values into the expression:
9. 
   `\[ P = \frac{{R \cdot T}}{{V - b}} - \frac{{a}}{{V^2}} \]`
10. 
    `\[ P = \frac{{0.08206 \, \text{{L atm/(mol K)}} \cdot 557.15 \, \text{{K}}}}{{3.88 \, \text{{L}} - 0.1383 \, \text{{L}}}} - \frac{{20.4 \, \text{{L}}^2 \, \text{{atm/mol}}^2}}{{(3.88 \, \text{{L}})^2}} \]`
11. Now, let's calculate the numerical result. Please note that you need to be careful with units to ensure they cancel out correctly:
12. 
    `\[ P = \frac{{0.08206 \cdot 557.15}}{{3.88 - 0.1383}} - \frac{{20.4}}{{(3.88)^2}} \]\\`
13. 
    `\[ P \approx \frac{{45.6464}}{{3.7417}} - \frac{{20.4}}{{15.0544}} \]\\`
14. 
    `\[ P \approx 12.228 - 1.354 \]`
15. 
    `\[ P \approx 10.874 \, \text{{atm}} \]`
16. So, the value of \( P \) is approximately 10.874 atm.