When 4.73 g of a nonelectrolyte solute is dissolved in 965 mL of water at 28 °C, the resulting solution exerts an osmotic pressure of 945 torr. What is the molar concentration of the solution? How many moles of solute are in the solution? What is the molar mass of the solute?
pi = MRT.
Substitute pi in atm, R is 0.08206 and T in kelvin. Solve for M = molarity.
b. moles = M x L
c. mols = grams/molar mass. You know moles and grams, solve for molar mass.
To calculate the molar concentration, number of moles of solute, and the molar mass of the solute, we can use the following equations:
1. Molar concentration (mol/L) = Π / (RT)
2. Number of moles of solute (mol) = Molar concentration (mol/L) * Volume of solution (L)
3. Molar mass of solute (g/mol) = Mass of solute (g) / Number of moles of solute (mol)
Given data:
- Mass of solute (m) = 4.73 g
- Volume of solution (V) = 965 mL = 0.965 L
- Osmotic pressure (Π) = 945 torr
- Temperature (T) = 28 °C = 28 + 273 = 301 K
- R (gas constant) = 0.0821 L·atm/(mol·K)
Using equation 1, we can find the molar concentration (C):
C = Π / (RT)
C = 945 torr / (0.0821 L·atm/(mol·K) * 301 K)
C = 945 torr / 24.7081 L·mol/(atm·K)
C = 38.24 mol/L
So, the molar concentration of the solution is 38.24 mol/L.
Using equation 2, we can find the number of moles of solute (n):
n = C * V
n = 38.24 mol/L * 0.965 L
n = 36.91 mol
So, there are 36.91 moles of solute in the solution.
Using equation 3, we can find the molar mass of the solute (M):
M = m / n
M = 4.73 g / 36.91 mol
M = 0.128 g/mol
So, the molar mass of the solute is approximately 0.128 g/mol.