what is molarity and molality of 47% ethyl alcohol having density 0.92 gm per cubic centimetre
To find the molarity and molality of the 47% ethyl alcohol, we need to understand the definitions of these two terms:
1. Molarity (M): Molarity is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution (mol/L or M).
2. Molality (m): Molality is another measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per kilogram of solvent (mol/kg).
To calculate Molarity:
Step 1: Determine the molecular weight of ethyl alcohol (C2H5OH).
- The atomic weights for carbon (C), hydrogen (H), and oxygen (O) are 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol, respectively.
- Calculate it as follows:
Molecular weight of C2H5OH = (2 * C) + (6 * H) + (1 * O)
= (2 * 12.01) + (6 * 1.01) + (1 * 16.00)
= 46.07 g/mol
Step 2: Calculate the mass of ethyl alcohol in the solution:
- Take the 47% concentration as a percentage by volume.
- Assume you have 100 grams of the solution, which means you have 47 grams of ethyl alcohol (47% of 100 grams).
Step 3: Calculate the volume of the solution:
- Use the density information provided (0.92 g/cm3) to convert the mass into volume.
- Divide the mass of the solution by its density to get the volume in cm3.
- In this case, you have 100 grams of the solution, so the volume will be 100 g / 0.92 g/cm3 = 108.70 cm3.
Step 4: Convert the volume to liters:
- There are 1000 cm3 in a liter, so divide the volume by 1000:
- 108.70 cm3 / 1000 = 0.1087 L
Step 5: Calculate the molarity using the formula:
Molarity (M) = moles of solute / volume of solution (in liters)
- Calculate moles of ethyl alcohol using the formula:
Moles = mass of Ethyl alcohol / molar mass of Ethyl alcohol
- Calculate the moles as follows:
Moles of C2H5OH = Mass of C2H5OH / Molecular weight of C2H5OH
= 47 g / 46.07 g/mol
= 1.02 mol
- Now calculate the Molarity:
Molarity (M) = 1.02 mol / 0.1087 L
Molarity (M) = 9.39 M (rounded to two decimal places)
To calculate Molality:
Step 6: Calculate the mass of the solvent:
- The mass of the solvent is the difference between the mass of the solution and the mass of the solute.
- In this case, there are 100 grams of the solution, and we already found that there are 47 grams of ethyl alcohol.
- So, the mass of the solvent is 100 g - 47 g = 53 g.
Step 7: Convert the mass of the solvent to kilograms:
- Divide the mass of the solvent by 1000 to convert it to kilograms:
- 53 g / 1000 = 0.053 kg
Step 8: Calculate the molality using the formula:
Molality (m) = moles of solute / mass of solvent (in kilograms)
- Calculate molality as follows:
Molality (m) = 1.02 mol / 0.053 kg
Molality (m) = 19.25 m (rounded to two decimal places)
So, the molarity of the 47% ethyl alcohol solution is approximately 9.39 M, and the molality is approximately 19.25 m.