Let's walk through the calculation step by step: ### Given Data - **n** (moles of Kr) = 0.9115 mol - **V** (volume) = 1.166 L - **T** (temperature) = 265.1 K - **\( P_{ideal} \)** (ideal pressure) = 17.01 atm ### Constants for Krypton (Kr) From standard tables: - **a** = 2.318 L²·atm·mol⁻² - **b** = 0.0398 L·mol⁻¹ - **R** = 0.08206 L·atm·mol⁻¹·K⁻¹ --- ## 1. **Calculate Pressure with the van der Waals Equation** The van der Waals equation is: \[ \left( P + a \left( \frac{n}{V} \right)^2 \right)(V - n b) = n R T \] Solve for \( P \): \[ P = \frac{nRT}{V - nb} - a \left(\frac{n}{V}\right)^2 \] #### **Calculate each term:** 1. \( nb = 0.9115 \times 0.0398 = 0.03629 \) L 2. \( V - nb = 1.166 - 0.03629 = 1.12971 \) L 3. \( nRT = 0.9115 \times 0.08206 \times 265.1 = 19.849 \) 4. \( \frac{nRT}{V - nb} = \frac{19.849}{1.12971} = 17.57 \) atm Now, \( \left( \frac{n}{V} \right)^2 = \left( \frac{0.9115}{1.166} \right)^2 = (0.7817)^2 = 0.6111 \) So, \[ a \left(\frac{n}{V}\right)^2 = 2.318 \times 0.6111 = 1.417 \text{ atm} \] #### **Plug these into the equation:** \[ P_{vdW} = 17.57 - 1.417 = 16.15 \text{ atm} \] --- ## 2. **Percent Difference** \[ \text{Percent Difference} = \frac{|P_{ideal} - P_{vdW}|}{P_{ideal}} \times 100\% \] \[ = \frac{|17.01 - 16.15|}{17.01} \times 100\% \] \[ = \frac{0.86}{17.01} \times 100\% \] \[ = 5.06\% \] --- ## **Final Answer** **The percent difference between the van der Waals pressure and the ideal pressure is:** \[ \boxed{5.06\%} \] **(rounded to three significant figures)** --- **Summary Table** | Method | Pressure (atm) | |------------------------- |---------------| | Ideal Gas Law | 17.01 | | van der Waals Equation | 16.15 | | Percent Difference | 5.06% |