--- title: "A chemical engineer studies a sample of \\(1.00\\text{ mol}\\) of \\(\\text{N}_2\\text{(g)}\\) at \\(200\\text{ K}\\), a temperature at which no phase transition occurs. To isolate the effect of finite molecular volume, the engineer compares the following models. \\[ P_{\\text{ideal}}=\\dfrac{nRT}{V} \\] \\[ P_{\\text{vol}}=\\dfrac{nRT}{V-nb} \\] In the second model, \\(b\\) is a positive constant that accounts for the volume occupied by the gas molecules. As the sample is compressed to progressively smaller container volumes, which statement correctly compares the pressures predicted by the two models and explains the comparison?" description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]" url: "https://nerd-notes.com/ubq/119422/" date_modified: "2026-08-19T12:40:15+00:00" --- # A chemical engineer studies a sample of \(1.00\text{ mol}\) of \(\text{N}_2\text{(g)}\) at \(200\text{ K}\), a temperature at which no phase transition occurs. To isolate the effect of finite molecular volume, the engineer compares the following models. \[ P_{\text{ideal}}=\dfrac{nRT}{V} \] \[ P_{\text{vol}}=\dfrac{nRT}{V-nb} \] In the second model, \(b\) is a positive constant that accounts for the volume occupied by the gas molecules. As the sample is compressed to progressively smaller container volumes, which statement correctly compares the pressures predicted by the two models and explains the comparison? A chemical engineer studies a sample of \(1.00\text{ mol}\) of \(\text{N}_2\text{(g)}\) at \(200\text{ K}\), a temperature at which no phase transition occurs. To isolate the effect of finite molecular volume, the engineer compares the following models. \[ P_{\text{ideal}}=\dfrac{nRT}{V} \] \[ P_{\text{vol}}=\dfrac{nRT}{V-nb} \] In the second model, \(b\) is a positive constant that accounts for the volume occupied by the gas molecules. As the sample is compressed to progressively smaller container volumes, which statement correctly compares the pressures predicted by the two models and explains the comparison? - **A.** The finite-volume model predicts a lower pressure, with an increasing discrepancy, because subtracting \(nb\) makes the denominator smaller and therefore makes the calculated pressure smaller. - **B.** The finite-volume model predicts a lower pressure, with an increasing discrepancy, because intermolecular attractions become more important at low temperatures and reduce collisions with the container walls. - **C.** The finite-volume model predicts a higher pressure, with an increasing discrepancy, because the value of \(b\) increases as the molecules are compressed closer together. - **D.** The finite-volume model predicts a higher pressure, with an increasing discrepancy, because \(V-nb