A student wants to find the volume of 1.0 mol of gas at 27°C and 1.0 atm. She plugs in T = 27 into PV = nRT and gets V = (1.0)(0.08206)(27)/(1.0) = 2.22 L. A classmate uses T = 300 K and gets V = 24.6 L. Who is correct, and why?
AThe first student — Celsius is more precise and the gas constant was measured in Celsius
BThe classmate — temperature must be in Kelvin because the proportionalities in the gas laws require an absolute scale
CBoth are valid approximations depending on the context; at room temperature the difference is negligible
DNeither — the calculation requires converting to Fahrenheit first when using the R = 0.08206 constant
Temperature must always be in Kelvin when using the ideal gas law. Charles's law says V ∝ T — this proportionality only holds when T is on an absolute scale starting at absolute zero (0 K = −273°C). If T = 0°C were substituted, V = 0 would be predicted, which is nonsensical. The Celsius scale's zero is arbitrary, not physically meaningful. 27°C = 300 K is the correct conversion, giving V ≈ 24.6 L, close to the 22.4 L/mol benchmark at 0°C (273 K).
Question 2 Multiple Choice
Under which conditions does the ideal gas law become least accurate, and what physical properties of real gases cause the deviations?
AAt high temperature and low pressure — molecules move too fast for the model to apply
BAt low temperature and high pressure — molecules are close enough that their own volume matters and intermolecular attractions become significant
CAt high temperature and high pressure — the gas constant R changes at extreme conditions
DThe ideal gas law is equally accurate at all conditions for monatomic gases like helium
The ideal gas law assumes two things: molecules occupy negligible volume compared to the container, and there are no intermolecular forces. Both assumptions break down at high pressure (molecules are squeezed together, so their own volume is no longer negligible) and low temperature (molecules move slowly enough that attractive forces significantly influence behavior). Real gases deviate most from ideality under these conditions, which is why van der Waals corrections add terms for molecular volume (b) and intermolecular attraction (a).
Question 3 True / False
A gas at high temperature and low pressure behaves more like a real gas (deviates from ideal behavior) than the same gas at low temperature and high pressure.
TTrue
FFalse
Answer: False
It's the opposite: high temperature and low pressure is where ideal gas behavior is most accurate. At high temperature, molecules have enough kinetic energy to overcome intermolecular attractions (making attractions negligible). At low pressure, molecules are far apart, so their own volume is negligible compared to container volume. Low temperature and high pressure bring molecules close together, where both their finite volume and mutual attractions become significant deviations from the ideal assumptions.
Question 4 True / False
Boyle's law (P ∝ 1/V), Charles's law (V ∝ T), and Avogadro's law (V ∝ n) are all special cases of PV = nRT obtained by holding different variables constant.
TTrue
FFalse
Answer: True
The ideal gas law unifies all three: hold n and T constant and you get PV = constant (Boyle's law); hold n and P constant and you get V/T = constant (Charles's law); hold P and T constant and you get V/n = constant (Avogadro's law). They are not separate empirical laws — they are mathematical consequences of the same equation under different constrained conditions. This is why they all fail under the same conditions: when the ideal gas assumptions break down, all three fail simultaneously.
Question 5 Short Answer
Why must temperature be expressed in Kelvin — not Celsius or Fahrenheit — when using the ideal gas law? What goes wrong mathematically and physically if you use Celsius?
Think about your answer, then reveal below.
Model answer: The gas laws express direct proportionalities: V ∝ T (Charles's law) and PV ∝ T (ideal gas law). These proportionalities only hold on an absolute scale where zero means zero molecular kinetic energy. Kelvin is that scale: 0 K corresponds to no thermal motion. If you substitute T = 0°C into PV = nRT, you get V = 0 (gas disappears) — physically nonsensical. If you double the Celsius temperature from 10°C to 20°C, the ideal gas law predicts volume increases by a factor of 293/283 ≈ 1.035, not 2 — because you must double the Kelvin temperature (286 K to 572 K) to double the volume. Using Celsius gives the wrong proportionality and a numerically wrong answer.
This is the most common calculation error with gas laws. The Celsius scale's zero is arbitrary (the freezing point of water), not physically meaningful. Kelvin zero is physically grounded. Any time you see T in a thermodynamics formula expressing proportionality or ratio, it means Kelvin.