a solution of 4.65 of a carbohydrate in 100.0g of water has a density of 1.016g/mL and an osmotic pressure of 3.18 atm at 20.0 degrees celcius. calculate the molar mass of the carbohydrate.
Note the correct spelling of celsius.
pi = MRT
Solve for M = molarity. M = moles/L soln
Use density to determine the volume of 100 g of the soln, then calculate moles. Finally, moles = grams/molar mass.You know g and moles, solve for molar mass.
To calculate the molar mass of the carbohydrate, we need to use the formula for osmotic pressure:
Π = (n/V)RT
Where:
Π = osmotic pressure (in atm)
n = number of moles of solute
V = volume of the solution (in L)
R = ideal gas constant (0.0821 L·atm/(K·mol))
T = temperature (in Kelvin)
We are given the osmotic pressure (Π = 3.18 atm), and we can determine the volume of the solution.
The mass of the solution is given as 100.0 g, and we know the density of the solution is 1.016 g/mL. So, the volume can be calculated by dividing the mass by density:
Volume (V) = mass/density
= 100.0 g / 1.016 g/mL
Next, we need to convert the volume from mL to Liters by dividing by 1000 since there are 1000 mL in a liter.
Now, we can substitute the given values into the osmotic pressure equation and solve for the number of moles (n):
3.18 atm = (n / volume) * (0.0821 L·atm/(K·mol)) * (293 K)
Solving for n:
n = (3.18 atm * volume) / (0.0821 L·atm/(K·mol) * 293 K)
Finally, we can calculate the molar mass (M) using the relationship:
Molar mass (M) = mass (m) / moles (n)
The mass of the carbohydrate given is 4.65 g, and the number of moles (n) was calculated.
Substitute the values and calculate the Molar Mass (M).