When 3.15 g of a nonelectrolyte solute is dissolved in water to make 135 mL of solution at 21 °C, the solution exerts an osmotic pressure of 869 torr.

What is the molar mass of the solute?
What is the molar concentration of the solution?
How many moles of solute are in the solution?

*insert middle finger*

To find the molar mass of the solute, we can use the formula for osmotic pressure:

π = (n/V)RT

Where:
π = osmotic pressure
n = number of moles of solute
V = volume of solution in liters
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin

First, let's convert the given values to the appropriate units:

3.15 g to kg: 3.15 g / 1000 = 0.00315 kg
135 mL to L: 135 mL / 1000 = 0.135 L
21 °C to K: 21 °C + 273.15 = 294.15 K

Now we can rearrange the osmotic pressure formula to solve for the number of moles of solute (n):

n = (πV) / (RT)

Substituting the given values:

n = (869 torr * 0.135 L) / (0.0821 L.atm/mol.K * 294.15 K)

n = 0.1164 mol

The number of moles of solute is 0.1164 mol.

Next, to find the molar concentration of the solution, we divide the number of moles of solute by the volume of the solution:

Molar concentration (M) = (n/V)

M = 0.1164 mol / 0.135 L

M = 0.862 M

The molar concentration of the solution is 0.862 M.

Finally, to calculate the molar mass of the solute, we divide the mass of the solute by the number of moles:

Molar mass = mass / moles

Molar mass = 0.00315 kg / 0.1164 mol

Molar mass = 27.08 g/mol

The molar mass of the solute is 27.08 g/mol.

To find the molar mass of the solute, the molar concentration of the solution, and the number of moles of solute in the solution, we can use the ideal gas law equation, which relates osmotic pressure (π) to molar concentration (C) and temperature (T):

π = C * R * T

Where:
π = osmotic pressure
C = molar concentration
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (21 °C + 273.15 = 294.15 K)

Step 1: Calculate the molar concentration (C).
First, convert the volume from mL to liters:
135 mL = 0.135 L

Rearrange the equation to solve for C:
C = π / (R * T)

Substitute the given values:
C = 869 torr / (0.0821 L·atm/(mol·K) * 294.15 K)

Calculate C:
C ≈ 32.422 M

Step 2: Calculate the molar mass of the solute.
The molar concentration (C) is equal to moles of solute divided by liters of solution. Rearrange this equation to solve for the moles of solute (n) using the given volume (V) and molar concentration (C):

n = C * V

Substitute the values:
n = 32.422 M * 0.135 L

Calculate n:
n ≈ 4.38 moles

To find the molar mass (M), divide the grams of solute (m) by the moles of solute (n):

M = m / n

Substitute the given value:
M = 3.15 g / 4.38 moles

Calculate M:
M ≈ 0.719 g/mol

Therefore:
- The molar mass of the solute is approximately 0.719 g/mol.
- The molar concentration of the solution is approximately 32.422 M.
- There are approximately 4.38 moles of solute in the solution.

pi = MRT

pi = 869/760 = ?
M solve for this
R = 0.08205 L*atm/mol*k
T = 273 + 21 = ?
M gives you part b.
Then M = mols/L solution, you know L solution and M, solve for mols and that is part c.
Part a is mol = grams/molar mass. You know grams and mols, solve for molar mass.