What mass of the ionic substance KBr would result in the same osmotic pressure as 34.2 g of nonionic sucrose (C12H22O11)?
A little step by step walk through would help me. Thanks
Use P = MRT to calculate the osmotic pressure of 34.2 g sucrose. You will need to assume a volume.
Then P = iMRT for KBr.
OR you can do it the easy way and realize that there is one particle in sucrose, two in KBr. Determine mols sucrose, then calculate g KBr required for half the mols sucrose. I suspect this is the way the prof/book/notes/ whatever intended for the problem to be worked since no volume was given. Check my thinking.
To determine the mass of KBr that would result in the same osmotic pressure as 34.2 g of sucrose (C12H22O11), we need to use the concept of osmotic pressure and the formula for calculating it.
Step 1: Understand the concept of osmotic pressure.
Osmotic pressure is the pressure required to prevent the osmotic flow of solvent into a solution through a semipermeable membrane. It depends on the concentration of solute particles in the solution.
Step 2: Know the formula for osmotic pressure.
The formula for osmotic pressure (π) is given by π = MRT, where M is the molar concentration of the solute, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
Step 3: Calculate the molar concentration of sucrose.
To calculate the molar concentration, we need to know the molar mass of sucrose (C12H22O11). The molar mass of carbon (C) is 12.01 g/mol, hydrogen (H) is 1.008 g/mol, and oxygen (O) is 16.00 g/mol. The molar mass of sucrose can be calculated as follows:
(12.01 g/mol × 12) + (1.008 g/mol × 22) + (16.00 g/mol × 11) = 342.34 g/mol
Now, we can calculate the molar concentration of sucrose by dividing the mass of sucrose (34.2 g) by its molar mass (342.34 g/mol):
Molar concentration (M) = mass (g) / molar mass (g/mol)
M = 34.2 g / 342.34 g/mol = 0.0999 mol/L
Step 4: Calculate osmotic pressure using sucrose concentration.
We now have the molar concentration of sucrose, so we can calculate the osmotic pressure using the formula:
Osmotic pressure (π) = MRT
Given that the temperature (T) is not provided, we'll assume it to be 298 K (room temperature). Substituting the values:
π = (0.0999 mol/L) × (0.0821 L·atm/mol·K) × (298 K)
π = 2.465 atm
Step 5: Calculate the mass of KBr.
Now, let's calculate the mass of KBr required to produce the same osmotic pressure. To do this, we need to convert the osmotic pressure of KBr (2.465 atm) to its molar concentration, then use the molar mass of KBr (119 g/mol) to convert back to mass.
Molar concentration (M) = Osmotic pressure (π) / (RT)
M = 2.465 atm / (0.0821 L·atm/mol·K × 298 K)
M = 0.1002 mol/L
Finally, we can calculate the mass of KBr using its molar mass (119 g/mol) and the molar concentration (0.1002 mol/L):
Mass = Molar concentration (mol/L) × Molar mass (g/mol)
Mass = 0.1002 mol/L × 119 g/mol
Mass = 11.9 g
Therefore, the mass of KBr that would result in the same osmotic pressure as 34.2 g of sucrose is approximately 11.9 g.