A solution of ethanol has a concentration of 4.613 mol/L at 20ºC. The density of the solution is 0.9667 g m/L.. Calculate the molality of the solution..please show the solution..thanks a lot
To calculate the molality of a solution, you need to know the moles of solute and the mass of the solvent. In this case, ethanol is the solute and the solution's density can be used to determine the necessary information.
Step 1: Calculate the mass of the solution.
To determine the mass of the solution, you can use the formula:
Mass of solution (g) = Density of solution (g/mL) * Volume of solution (mL)
In this case, the density of the solution is given as 0.9667 g/mL, but we need to convert it to g/L since the solution concentration is given in mol/L. Therefore:
Density of solution (g/mL) = Density of solution (g/L) / 1000
Density of solution (g/mL) = 0.9667 g/L / 1000
Density of solution (g/mL) = 0.0009667 g/mL
Next, we can calculate the mass of the solution using the following information:
Volume of the solution = 1 L
Mass of solution (g) = 0.0009667 g/mL * 1 L
Mass of solution (g) = 0.0009667 g
Step 2: Calculate the moles of ethanol.
The concentration of ethanol is given as 4.613 mol/L. This means that for every liter of solution, there are 4.613 moles of ethanol.
Step 3: Calculate the molality.
Molality (m) is defined as moles of solute per kilogram of solvent:
Molality (m) = Moles of solute / Mass of solvent (kg)
In this case, the mass of the solvent (water) is equal to the mass of the solution since ethanol is dissolved in water.
Mass of solvent (kg) = Mass of solution (g) / 1000
Mass of solvent (kg) = 0.0009667 g / 1000
Mass of solvent (kg) = 0.00000097 kg (approximately)
Finally, we can calculate the molality:
Molality (m) = 4.613 mol / 0.00000097 kg
Molality (m) ≈ 4.74 * 10^9 mol/kg
Therefore, the molality of the solution is approximately 4.74 * 10^9 mol/kg.