A sample of liquid H2O of mass 18.0 g is injected into an evacuated 7....
Given information:
- Mass of liquid water injected = 18.0 g
- Volume of flask = 7.6 L
- Temperature of flask = 27.0°C
- Vapour pressure of water at 27°C = 24.63 mmHg
To find: Weight percentage of water vaporized at equilibrium
Assumptions:
- Water vapour behaves as an ideal gas
- Volume of liquid water is negligible compared to the volume of the container
Solution:
1. Calculate the number of moles of liquid water injected:
- The molar mass of water (H2O) = 18.02 g/mol
- Number of moles of water injected = mass of water injected / molar mass of water
= 18.0 g / 18.02 g/mol
= 0.999 mol
2. Calculate the pressure of water vapour at equilibrium:
- Since the flask is evacuated initially, the total pressure at equilibrium will be the vapour pressure of water (since no other gases are present)
- Convert the vapour pressure from mmHg to atm (using conversion factor 1 atm = 760 mmHg):
Vapour pressure of water at 27°C = 24.63 mmHg = 0.0324 atm
3. Use the ideal gas law to calculate the volume of water vapour at equilibrium:
- Ideal gas law: PV = nRT
- We know the pressure (P), temperature (T), and number of moles (n) of water vapour at equilibrium
- We need to find the volume (V) of water vapour at equilibrium
- Rearrange the ideal gas law to solve for V: V = nRT/P
- Substitute the values: V = (0.999 mol)(0.0821 L·atm/mol·K)(300.15 K)/(0.0324 atm)
- V = 23.6 L
4. Calculate the weight of water vapour at equilibrium:
- The density of water vapour at 27°C and 0.0324 atm is 0.000598 g/L (from water vapour density tables)
- Weight of water vapour at equilibrium = density of water vapour x volume of water vapour
= 0.000598 g/L x 23.6 L
= 0.0141 g
5. Calculate the weight percentage of water vaporized:
- Weight of water vaporized = initial weight of water injected - weight of water vapour at equilibrium
= 18.0 g - 0.0141 g
= 17.99 g
- Weight percentage of water vaporized = weight of water vaporized / initial weight of water injected x 100%
= 0.079% ≈ 1% (to one significant figure)
Therefore, the weight percentage of water vaporized when the system comes to equilibrium is approximately 1%.
A sample of liquid H2O of mass 18.0 g is injected into an evacuated 7....