Final answer:
Using the ideal gas law, we can calculate that there are approximately 32.5 moles of air molecules within a 300.0 liter kiln operating at 845 °C and a pressure of 0.9500 atm.
Step-by-step explanation:
To determine how many moles of air molecules are within the confines of the kiln, we can use the ideal gas law, which is PV = nRT. Here, P stands for pressure, V for volume, n for the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Given that the volume (V) is 300.0 Liters (or 300.0 L), the pressure (P) is 0.9500 atm, and the temperature (T) is 845 °C, we first need to convert the temperature from Celsius to Kelvin by adding 273.15, resulting in a temperature of 1118.15 K.
The ideal gas constant (R) we'll use is 0.0821 L·atm/K·mol since we have volume in liters and pressure in atmospheres. Plugging in the values,
P = 0.9500 atm,
V = 300.0 L,
R = 0.0821 L·atm/K·mol,
T = 1118.15 K.
We can now solve for n (moles of air) using the formula:
n = “ P·V /(R·T) ”
n = (0.9500 atm × 300.0 L ) / (0.0821 L·atm/K·mol × 1118.15 K)
n ≈ 32.5 mol
Thus, there are approximately 32.5 moles of air molecules within the kiln.