Final answer:
To calculate the number density of oxygen molecules, use the ideal gas law, rearrange it to n/V = P/(RT), and then substitute the known pressure and temperature values, considering that R is the ideal gas constant 8.31 J/mol K.
Step-by-step explanation:
To calculate the number density (n/V) of oxygen molecules at a given pressure and temperature, we use the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (8.31 J/mol K), and T is the temperature in Kelvin.
First, we need to rearrange the ideal gas law to solve for n:
n = PV/RT
We then substitute the known values into the equation:
n = (101,325 Pa × V) / (8.31 J/mol K × 190 K)
Since we don't have a specific volume value, we leave V in the equation. However, we can cancel them out since we're interested in number density n/V:
n/V = P/(RT)
n/V = 101,325 Pa / (8.31 J/mol K × 190 K)
After calculating, we find the number density:
n/V = 6.43 × 10²³ molecules/m³
Finally, we can use Avogadro's number to find the number of molecules.