Final answer:
To find the pressure at which the density of air is 0.64 kg/m³ with constant temperature and number of molecules, use Boyle's Law. At half the original density of 1.28 kg/m³, the pressure is half the original pressure of 1 atm, which is 0.5 atm.
Step-by-step explanation:
The question pertains to the density of air at different pressures while keeping the temperature constant. According to the provided information, the density of air at standard conditions (1 atm and 20°C) is 1.28 kg/m³. The question asks at what pressure would the density of air be 0.64 kg/m³ assuming the temperature and the number of molecules are kept constant. Using the directly proportional relationship between pressure and density, known as Boyle's Law, if we halve the density, we must also halve the pressure as long as the temperature remains constant. Since the initial pressure is at 1 atm for a density of 1.28 kg/m³, halving this density to 0.64 kg/m³ would imply that the required pressure is 0.5 atm.