A solution of acetic acid, CH3COOH, has a concentration of 0.201 M and a density of 1.00 g mL-1. What is the molality of this solution?
The molar mass of acetic acid is 24+4+32=60
Then,
There is 0.201 mol acetic acid per litre or 0.201*60=12.06g of acetic acid
The density is 1g/ml to change to g/l it becomes 1000g/l then the solution is 1000g
to know the mass of the water substract mass of the acetic acid from the mass of the solution
And then,1000g-12.06g=987.94g
change this to kg =0.98794kg
At the last molality=0.201mol/0.98794kg=0.2035
To find the molality of the solution, you need to first understand the difference between molarity and molality. Molarity (M) is the number of moles of solute per liter of solution, while molality (m) is the number of moles of solute per kilogram of solvent.
In this case, the acetic acid, CH3COOH, is the solute, and the solution has a concentration of 0.201 M. Molarity is calculated by dividing the number of moles of solute by the volume of the solution in liters. However, since we want to find the molality, we need to convert the concentration in terms of moles of solute per kilogram of solvent.
To calculate the molality, we need to determine the number of moles of solute in a known mass of solution.
Step 1: Calculate the mass of the solution
Since the density of the solution is given as 1.00 g mL-1, and the volume is not specified, we will assume that we have 1 liter of the solution. Thus, the mass of the solution would be equal to its volume multiplied by its density: 1 L x 1.00 g mL-1 = 1000 g.
Step 2: Calculate the moles of solute
To find the moles of solute, we use the molarity of the solution. The molarity is given as 0.201 M, which means there are 0.201 moles of acetic acid per liter of solution.
0.201 moles/L x 1 L = 0.201 moles of acetic acid
Step 3: Calculate the molality
Now that we have the mass of the solution (1000 g) and the moles of solute (0.201 moles), we can calculate the molality.
Molality (m) is calculated by dividing the moles of solute by the mass of the solvent in kilograms. The solvent in this case is the acetic acid itself.
Mass of solvent = Mass of solution
Mass of solvent = 1000 g
To convert grams to kilograms, we divide by 1000: 1000 g / 1000 = 1 kg
Molality (m) = moles of solute / mass of solvent in kilograms
Molality (m) = 0.201 moles / 1 kg
Molality (m) = 0.201 m
Therefore, the molality of the acetic acid solution is 0.201 m.