A 2.28 m solution of the solute formic acid dissolved in the solvent H2O is available. Calculate the mass ( kg ) of the solution that must be taken to obtain 12.40 mol of formic acid.
Correct Answer = 6.01
Molar Mass (g/mol):
HCO2H 46.03
H2O 18.015
Density ( g/mL ):
HCO2H 1.220
H2O 0.9982
Can someone please explain to me how to come to the answer above.
m = moles solute/kg solvent
2.28 = 12.40/kg solvent.
Solve for kg solvent, then add the equivalent of 12.40 moles HCOOH (at 46.03 g/mole) and add to kg solvent to obtain total mass of solution. I get 6.009 which rounds to 6.01 kg.
To calculate the mass of the solution needed to obtain a certain number of moles of formic acid, we need to use the given information, such as the molar mass and density of the substances involved.
Here's how you can solve the problem step by step:
1. Determine the molar mass of formic acid (HCO2H) which is given as 46.03 g/mol.
2. Calculate the amount of formic acid in grams that is needed to obtain 12.40 mol. It can be calculated using the formula:
Mass of formic acid = number of moles × molar mass
= 12.40 mol × 46.03 g/mol
= 570.972 g
3. Next, we need to determine the volume of the solution required to obtain 570.972 g of formic acid. To do this, we can use the density of the solution.
The molarity of the solution tells us the number of moles of solute (formic acid) per liter of solution. Given that the solution has a concentration of 2.28 m, it means that there are 2.28 moles of formic acid per liter of solution.
We can use the molarity to calculate the volume of the solution needed to obtain 570.972 g of formic acid:
Volume of solution = Mass of formic acid / (Molarity × molar mass)
= 570.972 g / (2.28 mol/L × 46.03 g/mol)
≈ 6.010 L
4. Finally, we need to convert the volume of the solution from liters to kilograms. We can use the density of water (H2O) to make the conversion.
Density = Mass / Volume
Rearranging the equation, we get:
Mass = Density × Volume
Now, we substitute the given density of water (0.9982 g/mL) and the volume of the solution (6.010 L) into the equation:
Mass = 0.9982 g/mL × 6.010 L
≈ 5.995 kg (rounded to two decimal places)
Therefore, the mass of the solution that must be taken to obtain 12.40 mol of formic acid is approximately 5.995 kg.