An auditorium has a volume of 6 × 10³ m³. How many molecules of air are needed to fill the auditorium at one atmosphere and 0°C? A) 1.6 × 10²⁹ B) 1.6 × 10²⁷ C) 1.6 × 10²⁵ D) 1.6 × 10²³ E) 1.6 × 10²⁰

Question

Quizplus · Accepted Answer

The number of molecules of air needed to fill the auditorium can be calculated using the ideal gas law:PV = nRTwhere P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.At one atmosphere and 0°C, the number of moles of air needed to fill the auditorium is:n = PV/RT = (1 atm)(6 × 10³ m³)/(0.0821 Latm/(molK))(273 K) = 2.7 × 10⁴ molThe number of molecules of air needed to fill the auditorium is:N = nN_A = (2.7 × 10⁴ mol)(6.022 × 10²³ molecules/mol) = 1.6 × 10²⁷ moleculesTherefore, the correct answer is B) 1.6 × 10²⁷.

An Auditorium Has a Volume of 6 × 103 M3

An Auditorium Has a Volume of 6 × 10³ M³