Physics · Kinetic Theory · NEET
P is the pressure of the gas (in pascals, Pa = N per m squared). V is the volume the gas fills (in cubic metres, m cubed). n is the number of moles, found from n = given mass / molar mass. R is the universal gas constant = 8.314 J per mol per K (same for every gas). T is the absolute temperature in kelvin. The equation says these are not free: fix any three and the fourth is decided.
Always kelvin. T = temperature in Celsius + 273 (use 273 for NEET, or 273.15 if told). Using Celsius is the single most common mistake. For example 27 C is 300 K, and 0 C is 273 K. The gas laws come from absolute temperature, so a value like 0 C would wrongly make PV = 0 if you forgot to convert.
They are the same law written two ways. PV = nRT uses moles n and the universal gas constant R (macroscopic, for weighing-scale amounts). PV = N kB T uses the actual number of molecules N and the Boltzmann constant kB = 1.38 x 10^-23 J per K (microscopic, for counting molecules). They connect through N = n x NA and R = NA x kB, where NA is Avogadro number. Use the mole form for lab problems and the molecule form when the question gives molecular mass or number density.
If you use R = 8.314 J per mol per K, then P must be in pascals (Pa), V in cubic metres (m cubed), and T in kelvin. A common trap is volume in litres or cm cubed: convert 1 L = 10^-3 m cubed and 1 cm cubed = 10^-6 m cubed first. If pressure is in bar and volume in litres, it is easier to use R = 0.083 bar L per mol per K instead.
A gas behaves ideally at low pressure and high temperature, when the molecules are far apart. Then the molecules' own volume is tiny compared to the container and the forces between them are negligible. Real gases deviate at high pressure and low temperature (near liquefaction). For NEET numericals, unless told otherwise, treat the gas as ideal and apply PV = nRT.
For moles: n = PV / (RT). For density: write n = m / M (mass over molar mass), so PV = (m/M) RT, which rearranges to density rho = m/V = PM / (RT). In the molecule form, number density N/V = P / (kB T), and mass density = (P/kB T) x m, where m is the mass of one molecule. This is exactly the NEET 2016 density question.
The volume occupied by 1.8 g of water vapour at 374 C and 1 bar pressure will be: (Use R = 0.083 bar L per K per mol)
A container of volume 200 cm cubed contains 0.2 mole of hydrogen gas and 0.3 mole of argon gas. The pressure of the system at temperature 200 K (R = 8.3 J per K per mol) will be:
A sample of an ideal gas occupies volume V at pressure P and absolute temperature T. The mass of each molecule is m. The density of the gas is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
PV = nRT: pressure times volume equals number of moles times the universal gas constant times absolute temperature (in kelvin).
R = 8.314 J per mol per K in SI units. It also equals 0.0821 L atm per mol per K, or 0.083 bar L per mol per K, depending on the units of P and V you use.
Yes. When n is fixed, PV = nRT gives PV / T = constant, which is the combined gas law. Setting one variable constant recovers Boyle's law (PV = constant), Charles's law (V/T = constant) and Gay-Lussac's law (P/T = constant).
Yes. Use the total number of moles n = n1 + n2 + ... for the whole mixture. This matches Dalton's law of partial pressures, since each gas contributes pressure in proportion to its moles.
The law comes from absolute temperature, where 0 K means zero average kinetic energy. Celsius has an arbitrary zero (freezing point of water), so it would give wrong ratios and even negative values in the equation.
Kinetic theory derives P = (1/3)(N/V) m v-squared, and combining it with the average kinetic energy = (3/2) kB T gives PV = N kB T = nRT. So the ideal gas law is a direct result of molecular motion.
