When 0.10 g of insulin is dissolved in 0.200 L of water, the osmotic pressure is 2.30 Torr at 20°C. What is the molar mass of insulin?
I tried using the van't hoff equation, converting Torr into atm; but not sure how to do it. my teacher didn't really explain this type of prob yet it's on my homework.
pi = osmotic pressure.
pi = MRT
Convert 2.30 torr to atmospheres (divide by 760), use 0.08206 for R and plug in Kelvin (293 K) for T. Solve for M = molarity.
M = moles/L
You have M from the above, and you have L from the problem, solve for moles.
You know n = grams/molar mass and the problem gives you grams. Calculate molar mass. Post your work if you get stuck.
Do you have to divide again by 760?
To determine the molar mass of insulin, we can use the van't Hoff equation, which relates osmotic pressure to molar concentration. The van't Hoff equation is given by:
π = MRT
Where:
π is the osmotic pressure,
M is the molar concentration of the solute,
R is the ideal gas constant (0.0821 L·atm/K·mol),
T is the temperature in Kelvin.
First, let's convert the given osmotic pressure from Torr to atm:
1 atm = 760 Torr
Therefore, the osmotic pressure is:
π = 2.30 Torr / 760 Torr/atm
π = 0.0030263 atm
Now let's rearrange the van't Hoff equation to solve for the molar concentration (M):
M = π / (RT)
We need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 20°C + 273.15
T(K) = 293.15 K
Now we can substitute the values into the equation:
M = 0.0030263 atm / (0.0821 L·atm/(K·mol) * 293.15 K)
M = 0.0030263 atm / 24.0283 (L·K/(mol*atm))
M = 0.00012597 mol/L
Now, we can calculate the number of moles of insulin (n) using the given mass of insulin (0.10 g) and the molar concentration (M):
n = M * V
n = (0.00012597 mol/L) * 0.200 L
n = 0.000025194 mol
Finally, we can calculate the molar mass (Molar Mass = Mass / Moles):
Molar Mass = 0.10 g / 0.000025194 mol
Molar Mass = 3967 g/mol
Therefore, the molar mass of insulin is approximately 3967 g/mol.
To find the molar mass of insulin, we can use the van't Hoff equation. The van't Hoff equation relates the osmotic pressure (π) of a solution to the concentration of the solute (in this case, insulin).
The van't Hoff equation is written as:
π = iMRT
Where:
π = osmotic pressure (in atm)
i = van't Hoff factor (the number of particles into which the solute dissociates, for insulin, this is typically 1)
M = molar concentration of the solute (in mol/L)
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
In this problem, we are given the following information:
- The mass of insulin = 0.10 g
- The volume of water = 0.200 L
- The osmotic pressure = 2.30 Torr
- The temperature = 20°C (which is 293 K)
First, we need to convert the osmotic pressure from Torr to atm. Since 1 atm is equal to 760 Torr, we have:
2.30 Torr / 760 Torr/atm = 0.00303 atm
Next, we need to calculate the molar concentration (M) of insulin. This is given by:
M = n/V
Where:
M = molar concentration (in mol/L)
n = moles of insulin
V = volume of solution (in L)
To find the moles of insulin, we can use the molar mass (Molar mass = mass/moles). Rearranging the equation gives:
moles = mass / molar mass
Since we are trying to find the molar mass, we can rewrite the equation as:
molar mass = mass / moles
Now, let's plug in the given values and solve the equation step by step:
First, we need to convert the mass of insulin from grams to moles. We know that the molar mass of insulin is unknown, so let's call it "Molar mass (insulin)" and set it as "x" for now.
moles = mass / molar mass
moles = 0.10 g / x
Next, we can substitute the given concentration and volume values to solve for x:
M = moles / V
0.00303 atm = (0.10 g / x) / 0.200 L
Simplifying the equation further:
0.00303 atm = 0.5 g / (x * 0.2 L)
0.00303 atm = 2.5 g / x
Cross-multiplying the equation:
0.00303 atm * x = 2.5 g
x = 2.5 g / 0.00303 atm
x ≈ 825.08
Therefore, the molar mass of insulin is approximately 825.08 g/mol.