pepsin is an enzyme involved in the process of digestion. its molar mass is about 3.50 x 10^-4 g/mol. what is thr osmotic pressure in mm Hg at 30 degree oC of a 0.400g sample of pepsin in 55.0mL of an aqueous solution?
Here is how you work the problem BUT I don't believe the molar mass is as small as you have it. Check your numbers.
mol pepsin = grams/molar mass = 0.400/? = ?
M = mols/0.055L = ?
pi = MRT
pi in atm.
M = from above
R = 0.08206
T = 273 + 30 = ? K.
Convert atm to mm Hg; atm x 760 = ?
To calculate the osmotic pressure, we need to use the formula:
Osmotic pressure (π) = (n/V)RT
Where:
n = moles of solute
V = volume of solvent (in liters)
R = ideal gas constant (0.0821 L·atm/(K·mol))
T = temperature in Kelvin
First, let's find the moles of pepsin. The molar mass of pepsin is given as 3.50 x 10^-4 g/mol:
molar mass = 3.50 x 10^-4 g/mol
mass of pepsin = 0.400 g
moles of pepsin = mass of pepsin / molar mass
= 0.400 g / (3.50 x 10^-4 g/mol)
Next, we need to convert the volume from milliliters to liters:
volume = 55.0 mL = 55.0 mL / 1000 mL/L
= 0.055 L
Now, we can substitute the values into the formula:
Osmotic pressure (π) = (n/V)RT
Osmotic pressure = [(moles of pepsin) / (volume)] x (R) x (temperature)
temperature = 30°C = 30 + 273 = 303 K
Osmotic pressure = [(0.400 g / (3.50 x 10^-4 g/mol)) / (0.055 L)] x (0.0821 L·atm/(K·mol)) x (303 K)
Simplifying the equation, you can use the calculator to find the osmotic pressure.
To calculate the osmotic pressure, you will need to use the ideal gas law equation, which is given by:
π = (n/V)RT
Where:
π = osmotic pressure
n = number of moles of solute
V = volume of solution in liters
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
To find the number of moles (n) of pepsin, you will need to convert the mass of the sample given (0.400g) into moles by dividing it by the molar mass of pepsin.
First, let's convert the temperature from Celsius to Kelvin:
T = 30°C + 273.15 = 303.15 K
Now let's find the number of moles (n):
n = mass / molar mass
= 0.400g / (3.50 x 10^-4 g/mol)
= 1142.86 mol
Next, convert the volume of the solution (55.0 mL) into liters:
V = 55.0 mL / 1000
= 0.055 L
Now we can substitute the values into the equation:
π = (n/V)RT
= (1142.86 mol / 0.055 L) * (0.0821 L·atm/(mol·K)) * 303.15 K
Calculating the osmotic pressure:
π = (2.078 x 10^4 mol/L·atm) * (0.0821 L·atm/(mol·K)) * 303.15 K
≈ 509.27 atm
To convert the osmotic pressure to mmHg, multiply by the conversion factor:
1 atm = 760 mmHg
π = 509.27 atm * 760 mmHg/atm
≈ 387,175 mmHg
Therefore, the osmotic pressure at 30°C of a 0.400g sample of pepsin in a 55.0mL solution is approximately 387,175 mmHg.