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.