p+a |(V-nb)=nRT The van der Waals equation of state. R stands for the gas constant and n for moles of gas. The parameters a and b must be determined for each gas from experimental data. Use the van der Waals equation to answer the questions in the table below. What are the units of a? 믐 What are the units of b? ? For argon the numerical value of a is 1.337 and the numerical value of b is 0.0320. atm Use the van der Waals equation to calculate the pressure of a sample of argon at -90.0 °C with a molar volume of 0.192 L/mol . Round your answer to 3 significant digits. Use the Ideal Gas Law to calculate the pressure of the same sample under the same conditions. Round this answer to 3 significant digits also. atm

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**The van der Waals Equation of State**

The van der Waals equation is given by:

\[
\left( p + a \frac{n^2}{V^2} \right) (V - nb) = nRT
\]

**R** stands for the gas constant and **n** for moles of gas.

The parameters **a** and **b** must be determined for each gas from experimental data.

Use the van der Waals equation to answer the questions in the table below.

---

### Questions:

1. **What are the units of \( a \)?**
   - Answer: \([Pressure] \cdot [Volume]^2\)

2. **What are the units of \( b \)?**
   - Answer: \([Volume] / [mole]\)

3. **Problem for Argon:**

   For argon, the numerical value of \( a \) is 1.337 and the numerical value of \( b \) is 0.0320.

   Use the van der Waals equation to calculate the pressure of a sample of argon at \(-90.0 \, ^\circ C\) with a molar volume of 0.192 \( L/mol \). Round your answer to 3 significant digits.

   - Answer: \( \boxed{?} \, \text{atm} \)

4. **Use the Ideal Gas Law** to calculate the pressure of the same sample under the same conditions. Round this answer to 3 significant digits also.

   - Answer: \( \boxed{?} \, \text{atm} \)

---

### Diagram Explanation:

There is a visual representation showing a square root symbol for calculations and settings to reset, undo, and offer help within a typical digital interface. This could be part of a software or digital textbook interface used to help students interact with the problem or run simulations/calculations based on the van der Waals equation.
Transcribed Image Text:**The van der Waals Equation of State** The van der Waals equation is given by: \[ \left( p + a \frac{n^2}{V^2} \right) (V - nb) = nRT \] **R** stands for the gas constant and **n** for moles of gas. The parameters **a** and **b** must be determined for each gas from experimental data. Use the van der Waals equation to answer the questions in the table below. --- ### Questions: 1. **What are the units of \( a \)?** - Answer: \([Pressure] \cdot [Volume]^2\) 2. **What are the units of \( b \)?** - Answer: \([Volume] / [mole]\) 3. **Problem for Argon:** For argon, the numerical value of \( a \) is 1.337 and the numerical value of \( b \) is 0.0320. Use the van der Waals equation to calculate the pressure of a sample of argon at \(-90.0 \, ^\circ C\) with a molar volume of 0.192 \( L/mol \). Round your answer to 3 significant digits. - Answer: \( \boxed{?} \, \text{atm} \) 4. **Use the Ideal Gas Law** to calculate the pressure of the same sample under the same conditions. Round this answer to 3 significant digits also. - Answer: \( \boxed{?} \, \text{atm} \) --- ### Diagram Explanation: There is a visual representation showing a square root symbol for calculations and settings to reset, undo, and offer help within a typical digital interface. This could be part of a software or digital textbook interface used to help students interact with the problem or run simulations/calculations based on the van der Waals equation.
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