the vapour pressure of 2.1%solution of non electrolyte in water at 100 degree celsius is 755 mm Hg.calculate the molar mass of the solute

To calculate the molar mass of the solute, you need to use Raoult's law and the Ideal Gas Law. Here's how you can approach it step by step:

Step 1: Understand Raoult's law:
According to Raoult's law, the vapor pressure of a solution is directly proportional to the mole fraction of the solvent present in the solution. The equation can be expressed as follows:

P_total = X_solvent * P_solvent

Where:
P_total is the total vapor pressure of the solution
X_solvent is the mole fraction of the solvent in the solution
P_solvent is the vapor pressure of the pure solvent

Step 2: Calculate the mole fraction of the solvent:
In this case, water is the solvent, and the solution is 2.1% solute. The mole fraction of the solvent (X_solvent) can be calculated by dividing the mass of the solvent by the total mass of the solution.

Given that the solution is 2.1% solute, it means that 97.9% is water (solvent). So X_solvent = 0.979.

Step 3: Obtain the vapor pressure of water:
At 100 degrees Celsius, the vapor pressure of pure water is 760 mm Hg. So P_solvent = 760 mm Hg.

Step 4: Apply Raoult's law to calculate the total vapor pressure of the solution:
From Raoult's law, we have:
P_total = X_solvent * P_solvent

Substituting the known values:
755 mm Hg = 0.979 * 760 mm Hg

Step 5: Calculate the molar mass of the solute:
To calculate the molar mass of the solute, we can use the equation derived from the ideal gas law:

PV = nRT

Where:
P is the pressure of the gas (in atm or Pa)
V is the volume of the gas (in liters)
n is the number of moles of the gas
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature in Kelvin

In this case, we can rearrange the equation to solve for n (number of moles):

n = (P * V) / (R * T)

Since we know the vapor pressure and temperature, and we can assume a fixed volume, we can rewrite the formula as:

n = P / (R * T)

Substituting the known values:
n = (755 mm Hg) / (0.0821 L·atm/(mol·K) * 373 K)
= 24.55 mol

Finally, the molar mass (M) can be calculated using the formula:

M = mass of solute / number of moles

Since we have the mass percentage of the solute (2.1%) and the mass of the solution is not given, we cannot calculate the molar mass with the information provided.

solution