What volume (mL) of the solute ethanol should be combines with 2.44L of the solvent H2O to prepare a solution that is 8.03m ethanol?
Assuming H2O has a density of 1.00 g/mL, then m = moles solute/kg solvent
8.03 m = moles solute/2.44 kg solvent
Solve for moles solute. Look up the density to calculate the volume needed to obtain the mass ethanol needed.
To determine the volume of ethanol required, we need to use the equation:
C1V1 = C2V2
where C1 and V1 represent the concentration and volume of the initial solution (ethanol), and C2 and V2 represent the concentration and volume of the final solution.
Given:
C1 = unknown
V1 = unknown
C2 = 8.03 mol/L (since the concentration is given in molarity)
V2 = 2.44 L
First, we need to convert the concentration of ethanol from molarity (mol/L) to the mass/volume percent, which can be calculated using the density and molar mass of ethanol.
1. Convert molarity to moles per liter.
Concentration of ethanol (mol/L) = C2 = 8.03 mol/L
2. Calculate the mass of ethanol in one liter of solution.
Using the molar mass of ethanol (C2H5OH), which is approximately 46.07 g/mol:
Mass of ethanol in one liter of solution = C2 * Molar mass of ethanol = 8.03 mol/L * 46.07 g/mol = 370.2421 g
3. Convert the mass of ethanol to milliliters.
Ethanol has a density of approximately 0.789 g/mL at room temperature.
Volume of ethanol in one liter of solution = Mass of ethanol / Density of ethanol = 370.2421 g / 0.789 g/mL = 469.04 mL
Now, we can use the equation C1V1 = C2V2 to solve for the unknown volume of ethanol.
C1 * V1 = C2 * V2
C1 * V1 = 8.03 mol/L * 2.44 L
Since the volume of solvent (H2O) is 2.44 L, we subtract this value from the total volume to obtain the volume of the solute (ethanol):
V1 = (C2 * V2) - V2
V1 = (8.03 mol/L * 2.44 L) - 2.44 L
V1 = 19.5752 L - 2.44 L
V1 = 17.1352 L
Finally, convert the volume of ethanol from liters to milliliters:
Volume of ethanol required = V1 * 1000 mL/L
Volume of ethanol required = 17.1352 L * 1000 mL/L
Volume of ethanol required = 17,135.2 mL
Therefore, to prepare a solution that is 8.03 mol ethanol, you would need to combine approximately 17,135.2 mL of ethanol with 2.44 L of water.