osmotic pressure of a solution containing 7g of protein in 100ml of solution is 20mmhg at37celsius calculate molecular mass of the protein
Use pi = nRT
pi = 20/760
T = 273 + 37
R = 0.08206
Solve for n = number of mols.
Then n = grams/molar mass. You have n and grams, solve for molar mass.
To calculate the molecular mass of the protein, we need to use the formula for osmotic pressure:
π = (MRT) / V
Where:
π is the osmotic pressure,
M is the molar concentration of the protein (in moles/L),
R is the ideal gas constant (0.0821 L·atm/(mol·K)),
T is the temperature in Kelvin,
and V is the volume of the solution (in liters).
First, let's convert the given values to the appropriate units:
Mass of protein = 7g
Volume of solution = 100mL = 0.1L
Temperature = 37 Celsius = 310 Kelvin (37 + 273)
We can rearrange the formula to solve for the molar concentration (M):
M = (π * V) / (R * T)
Now, substitute the values into the equation:
M = (20 mmHg * 0.1L) / (0.0821 L·atm/(mol·K) * 310 K)
M = 0.2 atm/L / (25.482 L·mol/(atm·K))
M ≈ 0.00784 mol/L
Since the molar concentration is given as moles/L, the molecular mass of the protein can be calculated by dividing the mass of protein by the molar concentration:
Molecular mass = Mass / Molar concentration
Molecular mass = 7g / 0.00784 mol/L
Molecular mass ≈ 892.9 g/mol
Therefore, the approximate molecular mass of the protein is 892.9 g/mol.
To calculate the molecular mass of the protein, we can use the formula:
Molecular mass = (osmotic pressure × V × RT) / (n × P)
Where:
osmotic pressure = 20 mmHg (given)
V = volume of the solution = 100 mL = 0.1 L
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature in Kelvin = 37°C + 273.15 = 310.15 K
n = number of moles of the protein
P = osmotic pressure constant = 760 mmHg
To calculate the number of moles (n) of the protein, we need to know the molar mass (M) of the protein. Given that there are 7 grams of protein in 100 mL of solution, we can find the molar mass using the following equation:
Molar mass = mass / moles
Since we know the mass (7 g) and we can calculate the number of moles using the formula:
moles = mass / molar mass
We can rearrange the formula and solve for the molar mass:
molar mass = mass / moles
Let's plug the values into the equation and calculate the molecular mass of the protein:
Molecular mass = (20 mmHg × 0.1 L × 0.0821 L·atm/(mol·K) × 310.15 K) / (moles × 760 mmHg)
First, let's calculate the number of moles:
moles = mass / molar mass = 7 g / molar mass
Now, plug this value back into the equation:
Molecular mass = (20 mmHg × 0.1 L × 0.0821 L·atm/(mol·K) × 310.15 K) / ((7 g) / molar mass × 760 mmHg)
Simplifying:
Molecular mass = (2.48216 × molar mass) / 760
To calculate the molecular mass, we need to rearrange the equation:
Molecular mass = (760 × molecular mass) / 2.48216
Now we can substitute the value of osmotic pressure (20 mmHg) into the equation to calculate the molecular mass.