The number of molecules in 1.0 L of air at 0°C and 1.0 atm pressure is A)between 10²⁰ and 10²¹. B)between 10²³ and 6 × 10²³. C)between 10²² and 10²³. D)less than 10²⁰. E)between 10²¹ and 10²².

Question

Quizplus · Accepted Answer

The number of molecules in a gas can be calculated using the ideal gas equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature in Kelvin. At 0°C, the temperature in Kelvin is 273 K. Plug in the values of P, V, R, and T and solve for n.

n = PV/RT = (1.0 atm)(1.0 L)/(0.0821 L*atm/mol*K)(273 K) = 0.0409 mol

Then use Avogadro's number, 6.022 x 10^23 molecules/mol, to convert from moles to molecules:

Number of molecules = (0.0409 mol)(6.022 x 10^23 molecules/mol) = 2.46 x 10^22 molecules

The answer closest to this value is C, between 10^22 and 10^23 molecules.

The Number of Molecules in 1