A 23.6 molar solution of formic acid (methanoic acid) has a density of 1.16 g/ml. The molar mass of H, C, and O are 1g/mol, 12g/mol and 16 g/mol, respectively. What is the molality of this solution?
A molality is the number of moles of solute dissolved in one kilogram of solvent.
molar mass for HCOOH = 2*1+12+2*16=46
(more accurate value = 46.03)
A litre of the solution contains 23.6 moles, or 1085.6 g of the pure acid, and has a total mass of 1000*1.16=1160 g.
The mass of solvent (water) is therefore 1160-1085.6=74.4.
The molality is 23.6*(1000/74.4) = 317 m
Note: Formic acid is a liquid at room temperature, and is miscible with water.
That is really right
To find the molality of the solution, we need to first calculate the moles of formic acid present in the solution.
The molar mass of formic acid (methanoic acid, HCOOH) can be calculated by adding the atomic masses of the elements it contains: H (1 g/mol) + C (12 g/mol) + 2O (2 * 16 g/mol) = 46 g/mol.
Given that the density of the solution is 1.16 g/ml, we can use this information to find the mass of the solution. The density is defined as mass per unit volume, so the mass of the solution can be calculated as the product of density and volume.
As we know the molarity of the formic acid solution (23.6 M), the volume of the solution required to obtain one mole of the solute (formic acid) can be determined using the formula:
Volume = Moles / Molarity.
Let's perform the calculations step by step:
1. Calculate the molar mass of formic acid:
Molar mass of HCOOH = 1 g/mol + 12 g/mol + 16 g/mol + 16 g/mol = 46 g/mol.
2. Determine the mass of the solution:
Density = Mass / Volume.
Mass = Density * Volume.
Assuming we have 1 liter (1000 ml) of the solution, we can find the mass as:
Mass = 1.16 g/ml * 1000 ml = 1160 g.
3. Convert mass of the solution to moles of formic acid:
Moles of formic acid = Mass of the solution / Molar mass of formic acid.
Moles of formic acid = 1160 g / 46 g/mol = 25.217 mol.
4. Calculate the molality of the solution:
Molality = Moles of formic acid / Mass of the solvent (in kg).
Assuming the solvent is water and the mass of 1 liter (1000 ml) is approximately 1000 g or 1 kg, we have:
Molality = 25.217 mol / 1 kg = 25.217 mol/kg.
Therefore, the molality of the 23.6 molar solution of formic acid is approximately 25.217 mol/kg.
To find the molality of the solution, we need to determine the moles of solute (formic acid) and the mass of the solvent (water) in the solution.
First, let's calculate the moles of formic acid. The molar mass of formic acid (HCOOH) is:
(1 atom of H * 1 g/mol) + (1 atom of C * 12 g/mol) + (2 atoms of O * 16 g/mol) + (1 atom of H * 1 g/mol) = 46 g/mol
Given that the solution is 23.6 molar, it means that 23.6 moles of formic acid are present in 1 liter (1000 ml) of the solution.
To find the mass of formic acid in the solution, we can use the equation:
Mass = Moles * Molar Mass
Mass of formic acid = 23.6 moles * 46 g/mol = 1085.6 g
Next, let's calculate the mass of the solvent (water) in the solution. We can use the density of the solution to find the volume of the solution, and then subtract the mass of formic acid.
Density = Mass / Volume
Given that the density of the solution is 1.16 g/ml, we can rearrange the equation to solve for the volume:
Volume = Mass / Density
Volume of solution = 1085.6 g / 1.16 g/ml = 936.9 ml ≈ 0.9369 L
Now, to calculate the molality, we need to convert the mass of solvent (water) into kilograms:
Mass of solvent = Volume of solution (in liters) * Density
Mass of solvent = 0.9369 L * 1.16 g/mL = 1.0867 kg
Finally, we can calculate the molality using the formula:
Molality = Moles of solute / Mass of solvent (in kg)
Molality = 23.6 mol / 1.0867 kg = 21.7 mol/kg
Therefore, the molality of the solution is approximately 21.7 mol/kg.