An oxygen sample has a volume of 5 L at 27�C
and 800 torr. How many oxygen molecules
does it contain?
How many mols O2 do you have? There are 6.02E23 molecules O2 in a mole of O2.
To determine the number of oxygen molecules in the sample, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 27°C + 273.15 = 300.15 K
Next, let's convert the given pressure from torr to atmospheres:
1 atm = 760 torr
P(atm) = P(torr) / 760
P(atm) = 800 torr / 760 = 1.053 atm
Now, we can substitute the given values into the ideal gas law equation and solve for the number of moles (n):
(1.053 atm) * (5 L) = n * (0.0821 L·atm/(mol·K)) * (300.15 K)
Simplifying the equation:
5.2655 = n * 24.736
Solving for n:
n = 5.2655 / 24.736
n ≈ 0.2127 moles
Finally, to calculate the number of oxygen molecules, we can use Avogadro's number. Avogadro's number states that there are approximately 6.022 × 10^23 molecules in one mole of any substance.
Number of molecules = n * Avogadro's number
Number of molecules = 0.2127 moles * (6.022 × 10^23 molecules/mole)
Calculating the final result:
Number of molecules ≈ 1.28 × 10^23 molecules
Therefore, the oxygen sample contains approximately 1.28 × 10^23 oxygen molecules.