a solution of glycol containing 1.82g/litre has an osmotic pressure of 51.8 cm of mercury at 18 degrees Celsius what is the molecular weight of glycol

To find the molecular weight of glycol, we can use the formula for osmotic pressure:

π = n/V * R * T

where: π is the osmotic pressure, n is the number of moles of the solute, V is the volume of the solution in liters, R is the ideal gas constant, and T is the temperature in Kelvin.

First, we need to convert the given values to the appropriate units.

The osmotic pressure (π) is given as 51.8 cm of mercury. We need to convert this to atmospheres because the value of R we will be using is in atmospheres. 1 atm is approximately equal to 760 cm of mercury, so:

π = 51.8 cm Hg * (1 atm / 760 cm Hg) = 0.06816 atm

The temperature (T) is given as 18 degrees Celsius. We need to convert this to Kelvin by adding 273.15:

T = 18°C + 273.15 = 291.15 K

The volume (V) of the solution is 1 liter.

We can now substitute these values into the formula and solve for n, the number of moles of glycol:

0.06816 atm = n/1 L * 0.0821 L·atm/(K·mol) * 291.15 K

Solving for n gives:

n = 0.06816 atm / (0.0821 L·atm/(K·mol) * 291.15 K) = 0.0027 mol

The mass of glycol in the solution is given as 1.82 g. The molecular weight (MW) of glycol is the mass of the glycol divided by the number of moles:

MW = 1.82 g / 0.0027 mol = 674.07 g/mol

So, the molecular weight of glycol is approximately 674.07 g/mol.