One litre flask containing vapours of methyl alcohol (Mol mass 32 ) at...
Given Information:
- Volume of the flask = 1 liter = 1000 cm³
- Pressure of the vapors = 1 atm
- Temperature of the vapors = 25°C = 298 K
- Final pressure after evacuation = 10^(-3) mm
Conversion of Pressure:
To solve this problem, we need to convert the final pressure from millimeters (mm) to atmospheres (atm).
1 mm = 0.00133 atm
So, the final pressure is 10^(-3) mm = 10^(-3) * 0.00133 atm = 1.33 * 10^(-6) atm.
Calculating the Number of Molecules:
To calculate the number of molecules, we can use the ideal gas equation: PV = nRT.
- P = Pressure in atm (1 atm initially and 1.33 * 10^(-6) atm finally)
- V = Volume in liters (1 liter initially)
- n = Number of molecules in moles
- R = Gas constant = 0.0821 L·atm/(mol·K)
- T = Temperature in Kelvin (298 K)
We can rewrite the equation as:
n₁ = (P₁ * V₁) / (R * T) (initial number of molecules)
n₂ = (P₂ * V₁) / (R * T) (final number of molecules)
Substituting the values:
n₁ = (1 atm * 1 liter) / (0.0821 L·atm/(mol·K) * 298 K)
n₂ = (1.33 * 10^(-6) atm * 1 liter) / (0.0821 L·atm/(mol·K) * 298 K)
Simplifying the equations:
n₁ = 0.0406 moles
n₂ = 5.36 * 10^(-11) moles
Converting Moles to Molecules:
To convert moles to molecules, we use Avogadro's number, which is 6.022 x 10^23 molecules per mole.
Number of molecules = Number of moles * Avogadro's number
Substituting the values:
Number of molecules initially = 0.0406 moles * 6.022 x 10^23 molecules/mole
Number of molecules finally = 5.36 * 10^(-11) moles * 6.022 x 10^23 molecules/mole
Simplifying the equations:
Number of molecules initially = 2.45 x 10^22 molecules
Number of molecules finally = 3.24 x 10^16 molecules
Conclusion:
Therefore, the number of molecules of methyl alcohol left in the flask after evacuation is approximately 3.24 x 10^16 molecules.