Glycerin, C3H8O3, is a nonvolatile liquid. What is the vapor pressure of a solution made by adding 159 g glycerin to 338 mL H2O at 39.8oC? The vapor pressure of pure water at 39.8oC is 54.74 torr and its density is 0.992 g/cm3.
To determine the vapor pressure of the solution, we need to use Raoult's Law, which states that the vapor pressure of a solution is equal to the vapor pressure of the pure solvent multiplied by the mole fraction of the solvent.
First, we need to calculate the mole fraction of water in the solution. Given that the solution is made by adding 159 g of glycerin to 338 mL of water, we need to convert the mass of glycerin to moles and find the number of moles of water in 338 mL.
1. Calculate the moles of glycerin:
Given mass of glycerin = 159 g
Molar mass of glycerin (C3H8O3) = 3(12.01 g/mol) + 8(1.01 g/mol) + 3(16.00 g/mol) = 92.09 g/mol
Number of moles of glycerin = mass of glycerin / molar mass of glycerin
Number of moles of glycerin = 159 g / 92.09 g/mol
2. Calculate the volume of water in liters:
Given volume of water = 338 mL
Volume of water in liters = 338 mL / 1000 mL/L
3. Calculate the moles of water:
Given density of water = 0.992 g/cm^3
Volume of water in cm^3 = volume of water in liters * (1000 cm^3 / 1 L)
Mass of water = volume of water in cm^3 * density of water
Number of moles of water = mass of water / molar mass of water
Molar mass of water (H2O) = 2(1.01 g/mol) + 16.00 g/mol = 18.02 g/mol
4. Calculate the mole fraction of water:
Mole fraction of water = moles of water / (moles of glycerin + moles of water)
5. Calculate the vapor pressure of the solution:
Vapor pressure of the solution = vapor pressure of pure water * mole fraction of water
Given vapor pressure of pure water = 54.74 torr
Substitute the values and calculate the vapor pressure of the solution.
Note: Remember to convert the volume of water to liters and the mass of water to grams before performing calculations.
Once you have completed the steps above, you should be able to calculate the vapor pressure of the solution.
To find the vapor pressure of a solution made by adding glycerin to water, we need to use Raoult's Law. According to Raoult's Law, the vapor pressure of a liquid in a solution is equal to the mole fraction of the liquid multiplied by its vapor pressure in its pure state.
First, we need to calculate the mole fraction of glycerin in the solution.
1. Calculate the moles of glycerin:
Mass of glycerin = 159 g
Molar mass of glycerin = 92.094 g/mol
Moles of glycerin = mass / molar mass
= 159 g / 92.094 g/mol
2. Calculate the moles of water:
Volume of water = 338 mL = 0.338 L (since 1 mL = 0.001 L)
Density of water = 0.992 g/cm3
Density of water = mass / volume
Mass of water = density × volume
= 0.992 g/cm3 × 0.338 L
= 0.335 g
Molar mass of water = 18.015 g/mol
Moles of water = mass / molar mass
= 0.335 g / 18.015 g/mol
3. Calculate the mole fraction of glycerin:
Mole fraction of glycerin = Moles of glycerin / (Moles of glycerin + Moles of water)
Next, we can calculate the vapor pressure of the solution using Raoult's Law equation:
Vapor pressure of the solution = Mole fraction of glycerin × Vapor pressure of pure water
Finally, substitute the given values to find the solution's vapor pressure:
Vapor pressure of pure water = 54.74 torr (given)
NOTE: Remember to convert the Celsius temperature to Kelvin when necessary.
I hope that helps! Let me know if you have any further questions.