A protein subunit from an enzyme is part of a research study and needs to be characterized. A total of 0.135g of this subunit was dissolved in enough water to produce 2.00 mL of solution. At 28 ∘C the osmotic pressure produced by the solution was 0.138 atm. What is the molar mass of the protein?

To find the molar mass of the protein subunit, we can use the ideal gas law equation:

πV = nRT

Where:
π = osmotic pressure (0.138 atm)
V = volume of solution (2.00 mL = 0.00200 L)
n = moles of solute (protein subunit)
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (28 °C = 28 + 273 = 301 K)

Let's solve for n:

n = (πV) / (RT)

n = (0.138 atm * 0.00200 L) / (0.0821 L.atm/mol.K * 301 K)
n ≈ 0.00119 mol

The molar mass of the protein subunit can then be calculated as:

Molar mass = mass / moles

Molar mass = 0.135 g / 0.00119 mol
Molar mass ≈ 113.44 g/mol

Therefore, the molar mass of the protein subunit is approximately 113.44 g/mol.

To determine the molar mass of the protein subunit, we can use the equation for osmotic pressure:

π = MRT

Where:
π is osmotic pressure
M is the molarity of the solution
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature in Kelvin

First, we need to calculate the molarity of the solution:

Molarity (M) = moles of solute / volume of solution (in L)

Given that 0.135 g of the protein subunit was dissolved in enough water to produce 2.00 mL (or 0.00200 L) of solution, we need to calculate the moles of the protein subunit.

Moles of solute = given mass of solute / molar mass of solute

Next, we can determine the molar mass of the protein subunit using the rearranged equation:

Molar mass of solute = given mass of solute / moles of solute

Finally, substitute the values into the osmotic pressure equation to solve for the molar mass.

Let's calculate each step:

Step 1: Calculate the moles of the protein subunit:
Moles of solute = 0.135 g / molar mass of solute

Step 2: Calculate the molar mass of the protein subunit:
Molar mass of solute = 0.135 g / moles of solute

Step 3: Plug the values into the osmotic pressure equation:
0.138 atm = M (molarity) * R * T

Given that the temperature is 28 °C, we need to convert it to Kelvin:
T = 28 °C + 273.15 = 301.15 K

Now we can solve for M (molarity):
M = 0.138 atm / (R * T)

Finally, substitute the molarity value into the molar mass equation to find the molar mass of the protein subunit:

Molar mass of the protein subunit = 0.135 g / moles of solute

Follow these steps, and you will be able to determine the molar mass of the protein subunit in the research study.

pi = MRT

pi = 0.138 atm
M = ?
R = 9.08205 L*atm/mol*K
T = 273.15 + 28 = ?
Solve for M.
Then M = mols/L. You know L and M, solve for mols.
Then mols = grams/molar mass. You know mols and grams, solve for molar mass.

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