Final answer:
The number of particles per cubic meter for an ideal gas at SATP can be calculated using the ideal gas law. To find the number of atoms in one cubic centimeter, the volume is converted to cubic centimeters and the number of particles per cubic meter formula is used again.
Step-by-step explanation:
The number of particles per cubic meter for an ideal gas at SATP can be calculated using the ideal gas law PV = nRT. At standard ambient temperature and pressure (SATP), T = 25°C and P = 100 kPa. Rearranging the formula and substituting the given values, we can solve for n (the number of moles of the gas). Then, using Avogadro's number (6.022 x 10^23 particles/mol), we can calculate the number of particles per cubic meter.
1. Convert the temperature from Celsius to Kelvin: T(K) = 25° C + 273.15 = 298.15 K
2. Convert pressure from kPa to atm: P(atm) = 100 kPa / 101.325 kPa/atm = 0.987 atm
3. Rearrange the ideal gas law equation: n = PV / RT
4. Substitute the given values into the equation: n = (0.987 atm) * V / (0.08206 (L.atm)/(K.mol) * 298.15 K)
5. Rearrange the equation again to solve for V: V = nRT / P
6. Convert the volume from liters to cubic meters: V(m^3) = (22.4 L * V) / 1000
7. Calculate the number of particles per cubic meter: particles/m^3 = n * NA / V(m^3)
Using these steps, we can find the number of particles per cubic meter for an ideal gas at SATP.
To find the number of atoms of an ideal gas at SATP in one cubic centimeter, we can use the same steps but convert the volume from cubic meters to cubic centimeters: V(cm^3) = (100 cm^3 * V(m^3)) / 1.