When 3.54 g of a nonelectrolyte solute is dissolved in 675 mL of water at 24 °C, the resulting solution exerts an osmotic pressure of 913 torr.
Do you have a question?
What is molar concentration of solution?
how many moles of solute are in solution?
What is the molar mass of solute?
pi = MRT
pi is osmotic pressure in atm.
M is molarity
R = 0.99206
T = 24 C converted to kelvin.
Then M = mol/L. You know L and M, solve for mols.
Then mols = grams/molar mass
You know mols and grams, solve for molar mass.
To calculate the molar mass of the nonelectrolyte solute, we can use the formula:
Molar mass = (mass of solute) / (moles of solute)
First, we need to calculate the moles of solute using the ideal gas law equation:
PV = nRT
where:
P = osmotic pressure (in atm)
V = volume of the solution (in liters)
n = moles of solute
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
Let's convert the given osmotic pressure from torr to atm:
1 atm = 760 torr
Osmotic pressure (P) = 913 torr / 760 torr/atm = 1.2 atm
We are given the volume of the solution in mL, so we need to convert it to liters:
Volume (V) = 675 mL / 1000 mL/L = 0.675 L
The temperature is given in Celsius, but we need to convert it to Kelvin:
Temperature (T) = 24 °C + 273.15 = 297.15 K
Now we can rearrange the ideal gas law equation to solve for moles of solute (n):
n = PV / RT
n = (1.2 atm) * (0.675 L) / (0.0821 L·atm/mol·K) * (297.15 K)
Calculate the value of n.
Once we have the moles of solute, we can use the formula:
Molar mass = (mass of solute) / (moles of solute)
Rearrange the formula to solve for the molar mass:
Molar mass = (mass of solute) / (moles of solute)
Plug in the given values:
Molar mass = 3.54 g / (moles of solute)
Calculate the molar mass of the nonelectrolyte solute.