How many grams of ethylene glycol, HOCH2CH2OH, are present in 2.6 gallons of a 4.61 m solution with a density of 1.88 g/mL?
i think that this is a dimensional analysis type of question. 1 gal ~ 3485.41 ml.
i just need help with the set up, i think...
I typed in 2.6 gallons to liters in google and it returned 9.842 liters and that is 9842 mL. That will have a mass of 9842 mL x 1.88 g/mL = 18503 grams
If we take 1 kg of solution that will contain 4.61 moles ethylene glycol and that is 4.61 x 62.07 g/mol = about 286 grams which makes the solution have a mass of 1000 g + 286 g = 1286 grams. (I'm rounding here and there and estimating so you need to redo all of the calculations and keep in mind the number of significant figures.)
So how many grams ethylene glycol will we need in the 18503 g soln? That will be
286 g x (18503/1286) = about 4100 g.
I like to check these things to see if 4100 g will give 4.61 m in 18503g soln. If may not be exact because I've rounded here and there.
moles solute = 4100/62 = 66 moles.
Grams soln = 18503 - 4100 g solute = 14,400 g solvent which is 14.4 kg solvent. Then 66 moles/14.4 kg solvent = 4.58 which is very close considering the approximations made.
To solve this problem using dimensional analysis, we need to convert the given information into consistent units and then set up the appropriate calculation. Here's the step-by-step approach:
1. Convert the volume from gallons to milliliters:
- 1 gallon is approximately equal to 3,785.41 milliliters (ml). Given: 2.6 gallons
- Calculation: 2.6 gallons * 3,785.41 ml/gallon = 9,829.5666 ml
2. Determine the mass of the solution using the density:
- Given: Density = 1.88 g/ml
- Calculation: Mass = Density * Volume
Mass = 1.88 g/ml * 9,829.5666 ml ≈ 18,477.31 g
3. Calculate the number of moles of ethylene glycol:
- Given: Molarity = 4.61 mol/L (which is equivalent to 4.61 mol/L * 1000 ml/L)
- Calculation: Moles = Molarity * Volume
Moles = 4.61 mol/L * (9,829.5666 ml/1000 ml/L) ≈ 45.26 moles
4. Convert moles into grams using the molar mass of ethylene glycol:
- The molar mass of ethylene glycol (HOCH2CH2OH) is:
1 Hydrogen (H) atom = 1.01 g/mol
4 Carbon (C) atoms = 4 * 12.01 g/mol
6 Hydrogen (H) atoms = 6 * 1.01 g/mol
2 Oxygen (O) atoms = 2 * 16.00 g/mol
Total molar mass = 62.07 g/mol
- Calculation: Grams = Moles * Molar mass
Grams = 45.26 moles * 62.07 g/mol ≈ 2,810.8 grams
Therefore, there are approximately 2,810.8 grams of ethylene glycol present in 2.6 gallons of a 4.61 m solution with a density of 1.88 g/mL.