Calculate the vapor pressure of a solution containing 28.7g of glycerin (C3H8O3) in 136mL of water at 30.0 ∘C. The vapor pressure of pure water at this temperature is 31.8 torr. Assume that glycerin is not volatile and dissolves molecularly (i.e., it is not ionic) and use a density of 1.00 g/mL for the water.
mols glycerin = grams/molar mass = ?
mols H2O = grams/molar mass = ?
mols fraction glycerin = Xgly = mols glycerin/total mols.
Then pH2O = Xglycerin*PoH2O
To calculate the vapor pressure of a solution containing glycerin and water, we can use Raoult's Law, which states that the vapor pressure of the solution is the product of the mole fraction of the solvent (water) and the vapor pressure of the pure solvent at that temperature.
First, let's calculate the mole fraction of water (solvent) in the solution:
1. Calculate the moles of glycerin:
- Mass of glycerin = 28.7 g
- Molar mass of glycerin (C3H8O3) = (3*12.01) + (8*1.01) + (3*16.00) = 92.09 g/mol
- Moles of glycerin = 28.7 g / 92.09 g/mol
2. Calculate the volume of water in liters:
- Volume of water = 136 mL = 136 mL * (1 L / 1000 mL)
3. Calculate the density of water in the solution:
- Density of water = 1.00 g/mL
4. Calculate the mass of water:
- Mass of water = Density of water * Volume of water
5. Calculate the moles of water:
- Molar mass of water (H2O) = (2*1.01) + (16.00) = 18.02 g/mol
- Moles of water = Mass of water / Molar mass of water
Now that we have the moles of glycerin and water, we can calculate their mole fractions:
6. Calculate the mole fraction of water:
- Mole fraction of water = Moles of water / (Moles of water + Moles of glycerin)
Now, let's use Raoult's Law to calculate the vapor pressure of the solution:
7. Calculate the vapor pressure of the solution:
- Vapor pressure of solution = Mole fraction of water * Vapor pressure of pure water
Finally, substitute the given values into the equation to get the answer:
- Vapor pressure of pure water = 31.8 torr (given)
- Temperature = 30.0 °C (given)
Follow the steps above to obtain the answer by substituting the calculated values into the equation.
To calculate the vapor pressure of the solution, we can use Raoult's law, which states that the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent.
First, let's find the mole fraction of water in the solution:
Moles of water = (136 mL water) x (1.00 g/mL) / (18.015 g/mol) = 7.55 mol
Now, let's find the mole fraction of glycerin in the solution:
Moles of glycerin = 28.7 g / (92.094 g/mol) = 0.311 mol
Total moles of solution = moles of water + moles of glycerin = 7.55 mol + 0.311 mol = 7.861 mol
Mole fraction of water = moles of water / total moles = 7.55 mol / 7.861 mol ≈ 0.959
Now, let's calculate the vapor pressure of the solution using Raoult's law:
Vapor pressure of solution = mole fraction of water * vapor pressure of pure water
= 0.959 * 31.8 torr
= 30.54 torr
Therefore, the vapor pressure of the solution containing 28.7g of glycerin in 136mL of water at 30.0 ∘C is approximately 30.54 torr.