Using van der Waals’ equation, calculate the constant ‘a...
**Van der Waals Equation**
The Van der Waals equation is used to account for the non-ideal behavior of gases. It is given by:
\[ \left(P + \frac{an^2}{V^2} \right) \left(\frac{V}{n} - b \right) = RT \]
Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of the gas
- T is the temperature in Kelvin
- R is the ideal gas constant
- a and b are the Van der Waals constants
**Given Data**
- P = 11.0 atm
- V = 4 L
- n = 2 mol
- T = 300 K
- b = 0.05 L mol^(-1)
We are asked to calculate the value of constant a.
**Solving for a**
We can rearrange the Van der Waals equation to solve for constant a:
\[ \frac{a}{V^2} = \frac{P}{n^2} - \frac{RT}{V} + \frac{b}{V} \]
Substituting the given values:
\[ \frac{a}{(4 \, \text{L})^2} = \frac{(11.0 \, \text{atm})}{(2 \, \text{mol})^2} - \frac{(0.0821 \, \text{L atm mol}^{-1} \, \text{K}^{-1})(300 \, \text{K})}{4 \, \text{L}} + \frac{(0.05 \, \text{L mol}^{-1})}{4 \, \text{L}} \]
Simplifying:
\[ \frac{a}{16 \, \text{L}^2} = \frac{11.0 \, \text{atm}}{4 \, \text{mol}^2} - \frac{0.0821 \, \text{L atm mol}^{-1} \, \text{K}^{-1} \times 300 \, \text{K}}{4 \, \text{L}} + \frac{0.05 \, \text{L mol}^{-1}}{4 \, \text{L}} \]
\[ a = 16 \, \text{L}^2 \left( \frac{11.0 \, \text{atm}}{4 \, \text{mol}^2} - \frac{0.0821 \, \text{L atm mol}^{-1} \, \text{K}^{-1} \times 300 \, \text{K}}{4 \, \text{L}} + \frac{0.05 \, \text{L mol}^{-1}}{4 \, \text{L}} \right) \]
Evaluating the expression:
\[ a = 16 \, \text{L}^2 \left( \frac{11.0 \, \text{atm}}{16 \, \text{mol}^2} - \frac{0.0821 \, \text{L atm mol}^{-1} \, \text