What volume would 8.24 x 10²⁴ molecules of CO₂ occupy?
To calculate the volume occupied by 8.24 x 10^24 molecules of CO2, we first need to determine the volume occupied by a single molecule of CO2 and then multiply it by the total number of molecules.
The volume occupied by a single molecule of CO2 can be approximated using the ideal gas law:
V = (nRT)/P
Where:
V = volume of gas
n = number of moles of gas
R = gas constant (0.0821 L∙atm/(K∙mol))
T = temperature in Kelvin
P = pressure of gas in atmospheres
We can assume standard conditions for this calculation:
n = (8.24 x 10^24 molecules) / Avogadro's number
T = 273 K
P = 1 atm
Now, let's calculate the volume of a single molecule of CO2:
n = (8.24 x 10^24) / 6.022 x 10^23 = 13.67 moles
V = (13.67 x 0.0821 x 273) / 1 = 299.22 L/mol
Therefore, the volume occupied by 8.24 x 10^24 molecules of CO2 would be:
V_total = V_single molecule x 8.24 x 10^24 molecules
V_total = 299.22 L/mol x 8.24 x 10^24 = 2.47 x 10^27 Liters
So, 8.24 x 10^24 molecules of CO2 would occupy a volume of 2.47 x 10^27 liters.