Under what conditions will a pure sample of an ideal gas not only exhibit a pressure of 1 atm but al — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

I need to find the conditions where an ideal gas has **both** $P = 1$ atm **and** $c = 1$ mol/L simultaneously. **Step 1: Use the ideal gas equation in terms of concentration** The ideal gas law is: $$PV = nRT$$ Rearranging in terms of concentration ($c = n/V$): $$P = cRT$$ **Step 2: Substitute the given values** We need: - $P = 1$ atm - $c = 1$ mol/L $$1 = 1 \times R \times T$$ $$1 = 0.082 \times T$$ **Step 3: Solve for temperature** $$T = \frac{1}{0.082} = 12.19 \text{ K}$$ Or approximately: $$T \approx 12.2 \text{ K} \text{ or } 12 \text{ K}$$ **Conclusion:** The ideal gas will exhibit simultaneously $P = 1$ atm and $c = 1$ mol/L at approximately **$T = 12.2$ K** (or ~12 K). This is an extremely low temperature—close to absolute zero. The answer C likely states this temperature or a value very close to it (like ~12 K or 12.19 K depending on rounding).