A 35.0g sample of ethylene glycol is dissolved in 500.0g of water. The vapor pressure of water at 32C is equal to 35.7mm Hg. What is the vapor pressure of the water-ethylene glycol solution at 32C?
To calculate the vapor pressure of the water-ethylene glycol solution, we will use Raoult's Law. According to Raoult's Law, the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent in the solution.
To start the calculation, we need to determine the mole fraction of the solvent, which in this case is water. Let's assume the moles of ethylene glycol are nEG and the moles of water are nW. We can calculate the mole fraction of water (XW) using the following formula:
XW = nW / (nEG + nW)
Since we know the mass of each component, we can calculate the number of moles of water and ethylene glycol using their molar masses. The molar mass of water (MW) is 18.015 g/mol, and the molar mass of ethylene glycol (MEG) is 62.07 g/mol.
First, let's calculate the number of moles of water:
moles of water (nW) = mass of water / molar mass of water
= 500.0 g / 18.015 g/mol
Next, let's calculate the number of moles of ethylene glycol:
moles of ethylene glycol (nEG) = mass of ethylene glycol / molar mass of ethylene glycol
= 35.0 g / 62.07 g/mol
Now we can calculate the mole fraction of water:
XW = nW / (nEG + nW)
Substituting the values, we get:
XW = (moles of water) / (moles of water + moles of ethylene glycol)
Finally, we can use Raoult's Law to calculate the vapor pressure (P) of the water-ethylene glycol solution at 32°C:
P = XW * P°W
where P°W is the vapor pressure of pure water at 32°C, which is given as 35.7 mm Hg.
Substituting the values, we can calculate the vapor pressure of the solution.
To find the vapor pressure of the water-ethylene glycol solution, we need to first calculate the mole fraction of water and ethylene glycol in the solution.
1. Calculate the number of moles of water and ethylene glycol:
- Moles of water = mass of water / molar mass of water
- Moles of ethylene glycol = mass of ethylene glycol / molar mass of ethylene glycol
2. Calculate the mole fraction of water and ethylene glycol:
- Mole fraction of water = moles of water / (moles of water + moles of ethylene glycol)
- Mole fraction of ethylene glycol = moles of ethylene glycol / (moles of water + moles of ethylene glycol)
3. Use the mole fractions to calculate the vapor pressure of the solution using Raoult's law:
- Vapor pressure of the solution = mole fraction of water * vapor pressure of pure water
Let's go through the calculations step by step:
1. Calculate the number of moles:
- Molar mass of water = 18.015 g/mol
- Molar mass of ethylene glycol = 62.07 g/mol
Moles of water = 500.0g / 18.015 g/mol
Moles of ethylene glycol = 35.0g / 62.07 g/mol
2. Calculate the mole fractions:
Mole fraction of water = Moles of water / (Moles of water + Moles of ethylene glycol)
Mole fraction of ethylene glycol = Moles of ethylene glycol / (Moles of water + Moles of ethylene glycol)
3. Use Raoult's law:
Vapor pressure of the solution = Mole fraction of water * Vapor pressure of pure water
Plug in the values and calculate the result.
mol ethylene glycol = 35.00/molar mass = ?
mol H2O = grams/molar mass
Xethylene glycol = n eth/total mols
psoln = Xethyl gly*PoH2O