an aqueous solution contains 1.00g/L of a derivative of detergent lauryl alcohol.the osmotic pressure of this solution at 25 °c is 2.0 x 10³ Nm-², what is the molar mass of the detergent.
2000 N/m^2 = 2000 pascals.
Convert to atmospheres 2000/101325 = approx 0.02 but that's an estimate.
Then pi = MRT
You know pi, R, T, solve for M = molarity.
Then M = mols/L. You know M and L, solve for mols.
Then mol = grams/molar mass. You know mols and grams, solve for molar mass.
Post your work if you get stuck.
To find the molar mass of the detergent, we need to first understand the relationship between osmotic pressure (π) and molar concentration (C).
According to the ideal gas law, the osmotic pressure (π) of a solution can be calculated using the formula:
π = MRT
Where:
π = osmotic pressure in units of pascals (Pa)
M = molar concentration in moles per cubic meter (mol/m³)
R = ideal gas constant = 8.314 J/(mol·K)
T = temperature in Kelvin (K)
In this case, we are given the osmotic pressure (π) and temperature (25 °C). However, the concentration of the solution (C) is not directly provided.
To find the concentration (C), we can use the molarity equation:
Molarity (M) = moles of solute / volume of solution in liters
Since the molar mass (Mm) of the detergent is unknown, we can assume it to be "x" g/mol. Therefore, 1.00 g/L of the detergent corresponds to x moles per liter (mol/L).
Now, let's calculate the concentration (C) using the given information:
C = x mol/L
Now, we need to convert the concentration (C) from moles per liter to moles per cubic meter to match the units required in the osmotic pressure equation:
1 L = 10⁻³ m³
Therefore, the concentration (C) becomes:
C = x mol/L = x mol/(10⁻³ m³)
Now, substituting the values into the osmotic pressure equation:
π = MRT
2.0 x 10³ N/m² = C x (8.314 J/(mol·K)) x (25 + 273) K
Solving for C:
C = (2.0 x 10³ N/m²) / [(8.314 J/(mol·K)) x 298 K]
Now, convert Newtons (N) to Joules (J):
1 N = 1 J/m
C = (2.0 x 10³ J/m²) / [(8.314 J/(mol·K)) x 298 K]
Simplifying:
C = 0.982 mol/m³
Now, we have determined the molar concentration (C) of the solution. Next, we can find the molar mass (Mm) of the detergent using the molarity equation:
Molarity (M) = moles of solute / volume of solution in liters
Rearranging the equation to solve for the moles of solute:
moles of solute = Molarity (M) x volume of solution in liters
In this case, the volume of solution is 1.00 L.
moles of solute = 0.982 mol/m³ x 1.00 L (convert liter to cubic meter: 1 L = 10⁻³ m³)
moles of solute = 0.982 mol/m³ x 10⁻³ m³
moles of solute = 9.82 x 10⁻⁴ mol
Finally, we can calculate the molar mass (Mm) using the formula:
Molar mass (Mm) = mass of solute / moles of solute
In this case, the mass of solute is 1.00 g.
Molar mass (Mm) = 1.00 g / 9.82 x 10⁻⁴ mol
Molar mass (Mm) = 1.00 g / 9.82 x 10⁻⁴ mol
Molar mass (Mm) ≈ 1019 g/mol
Therefore, the molar mass of the detergent is approximately 1019 g/mol.