at a temperature of 5 celsius, 21.5 mg of a non electrolyte is dissolved in enough water to make a 150.0 ml solution. the osmotic pressure of the solution is 0.200 atm. what is the molar mass of the substance dissolved
pi = MRT
Substitute and solve for M.
Then M = mols/L. You know M and L, solve for mols.
Then mols = grams/molar mass. You know mols and grams, solve for molar mass.
To find the molar mass of the substance dissolved, we can use the equation for osmotic pressure:
π = MRT
Where:
π = osmotic pressure
M = molarity of the solution (in moles per liter)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T = 5°C + 273.15 = 278.15 K
Now, let's calculate the molarity of the solution:
Molarity (M) = moles of solute / liters of solution
We are given that 21.5 mg of the non-electrolyte is dissolved in enough water to make a 150.0 ml solution.
First, we need to convert the mass from milligrams to grams:
mass = 21.5 mg = 0.0215 g
Then, we can calculate the moles of the substance dissolved:
moles = mass / molar mass
Now, we can determine the molarity of the solution:
M = moles / liters of solution
Since the solution volume is given in milliliters, we need to convert it to liters:
liters of solution = 150.0 ml = 0.150 L
Finally, we can substitute the values into the osmotic pressure equation and solve for the molar mass (M):
π = MRT
Rearranging the equation:
M = π / (RT)
Substituting the known values:
M = 0.200 atm / (0.0821 L·atm/(mol·K) * 278.15 K)
Calculating this expression will give you the molar mass of the substance dissolved in grams per mole.