vander waal b for oxygen is 32 cm3/mol compute the diameter of o2 molecule.
To compute the diameter of an O2 molecule using the van der Waals constant (b), we can use the equation:
b = (V/n) - (4/3)πr^3
Where:
b = van der Waals constant (32 cm^3/mol in this case)
V = molar volume of the gas (unknown for O2)
n = number of moles of the gas (1 mol for O2)
r = radius of the O2 molecule (unknown)
First, let's convert the given van der Waals constant from cm^3/mol to m^3/mol:
32 cm^3/mol = (32/1000000) m^3/mol = 0.000032 m^3/mol
Substituting the given values and rearranging the equation, we have:
0.000032 = (V/1) - (4/3)πr^3
Now, we need to find the molar volume (V) to determine the diameter of the O2 molecule. The molar volume can be calculated using the ideal gas law equation:
V = (n × R × T) / P
Where:
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
P = pressure (in Pascal)
Assuming standard conditions (STP) of 273.15 K and 101325 Pa, we get:
V = (1 × 8.314 × 273.15) / 101325 = 0.022414 m^3/mol
Substituting this value of V into our previous equation, we now have:
0.000032 = (0.022414/1) - (4/3)πr^3
Now, rearrange the equation to isolate the radius (r):
(4/3)πr^3 = (0.022414 - 0.000032)
r^3 = [(0.022414 - 0.000032) / ((4/3)π)]
r = [(0.022414 - 0.000032) / ((4/3)π)]^(1/3)
Calculating this using a calculator, we find that the radius (r) of the O2 molecule is approximately 0.0001278 meters (m).
Since the diameter (d) of a molecule is twice the radius, we can calculate the diameter as:
d = 2 * r = 2 * 0.0001278 ≈ 0.0002556 meters (m)
So, the diameter of an O2 molecule is approximately 0.0002556 meters or 0.2556 nanometers.