Final answer:
Using the Ideal Gas Law, the number density of air at atmospheric pressure and a temperature of 25°C can be calculated by rearranging the equation to solve for n/V, and then performing the necessary unit conversions to find the density in particles per meter cubed.
Step-by-step explanation:
To calculate the number density of air at atmospheric pressure and 25°C, we must first use the ideal gas law, which is PV = nRT, where 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 in Kelvin. The number density is the number of particles per unit volume; hence, it's equivalent to n/V. At standard atmospheric pressure and 25°C, which is 298.15 K, the number density can be calculated using the equation P = (n/V)RT, where the pressure P is 1 atm, R is 0.0821 L·atm/(K·mol), and temperature T is 298.15 K. To solve for n/V, rearrange the equation to get n/V = P/(RT). Therefore, the number density is 1 atm/(0.0821 L·atm/(K·mol) × 298.15 K), which can be simplified to calculate the number density in moles per liter, and further converted to particles per meter cubed using Avogadro's number.