Cellobiose(a nonvolative, nonelectrolyte) is a sugar obtained by degratation of cellulose. If 200.mL of an aqueous solution containing 1.500g of cellobiose at 25C give rise to an osmotic pressure of 407.2mmHg. What is the molecular mass of Cellobiose?
I converted the osmotic pressure to atm. then used the equation pi =iMRT, i plugged in the numbers but i am calculating it wrong.
.5357894737 = 1.500g/X/.200L(.0821)(298.15) if that's correct
but when i plug it in to my calculator i get a different answer instead of the actual answer which is 342.6g/mol
To find the molecular mass of cellobiose, we can use the formula for osmotic pressure:
π = (n/V)RT
Where:
π = osmotic pressure in mmHg
n = number of moles
V = volume 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:
Volume = 200 mL = 0.2 L
Pressure = 407.2 mmHg
Temperature = 25°C = 298 K
Rearranging the formula, we have:
n = (πV) / (RT)
Substituting the given values, we get:
n = (407.2 mmHg * 0.2 L) / (0.0821 L•atm/(mol•K) * 298 K)
n ≈ 4.17 mol
To find the molecular mass of cellobiose, we can use the formula:
Molecular mass = mass / moles
Given the mass of cellobiose is 1.500 g, we can calculate the molecular mass:
Molecular mass = 1.500 g / 4.17 mol
Molecular mass ≈ 359.64 g/mol
Therefore, the molecular mass of cellobiose is approximately 359.64 g/mol.
To find the molecular mass of cellobiose, we can use the formula for osmotic pressure:
π = (n/V)RT
where π is the osmotic pressure, n is the number of moles of solute, V is the volume of the solution in liters, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin.
First, let's convert the given values to the appropriate units:
Volume (V) = 200 mL = 0.2 L
Osmotic pressure (π) = 407.2 mmHg
Next, we rearrange the formula to solve for the number of moles (n):
n = (π * V) / (RT)
Now we can calculate the number of moles of cellobiose:
n = (407.2 mmHg * 0.2 L) / (0.0821 L·atm/(mol·K) * 298 K)
n ≈ 3.837 mol
Finally, we can calculate the molecular mass (M) of cellobiose using the formula:
M = m/n
where m is the mass of solute (1.500 g) and n is the number of moles (3.837 mol):
M = 1.500 g / 3.837 mol
M ≈ 0.390 g/mol
Therefore, the molecular mass of cellobiose is approximately 0.390 g/mol.