A protein subunit from an enzyme is part of a research study and needs to be characterized. A total of 0.180 g of this subunit was dissolved in enough water to produce 2.00 mL of solution. At 28C the osmotic pressure produced by the solution was 0.138 atm. What is the molar mass of the protein?

This is what i used:

PV= nRT
PV= (m/M)RT
Molar mass= (0.180g)(0.0821)(30lk)/(0.000276kg)(0.138)
= 16115.942

Which is wrong can someone please help me.

oops sorry when i multiply (0.002 Litres)(0.138) the answer i get is 0.000276 and kg was an accident

Where did you get .000276 kg. Shouldnt you have volume there..... 0.002liters?

You have used the 0.138 twice. Once to multiply by 0.002 and again by sticking it in the denominator.Replace the 0.000276 with 0.002 L (that's the volume) and leave the 0.138 atm as is. I get something like 16,000 but you need to do it exactly.

To find the molar mass of the protein subunit, you first need to calculate the number of moles of the protein present in the solution. Then, you can divide the mass of the protein by the number of moles to determine the molar mass.

Let's break down the solution step-by-step:

Step 1: Convert the volume of the solution from mL to liters.
2.00 mL = 0.00200 L

Step 2: Apply the ideal gas law to calculate the number of moles of the protein subunit.
PV = nRT

Given:
Pressure (P) = 0.138 atm
Volume (V) = 0.00200 L
Gas constant (R) = 0.0821 L·atm/(mol·K)
Temperature (T) = 28°C = 301 K (convert to Kelvin by adding 273)

0.138 atm × 0.00200 L = n × 0.0821 L·atm/(mol·K) × 301 K

n = (0.138 atm × 0.00200 L) / (0.0821 L·atm/(mol·K) × 301 K)

Solving the equation gives:
n ≈ 0.00179 moles

Step 3: Calculate the molar mass of the protein subunit.
Molar mass (M) = mass (m) / moles (n)

Given:
Mass (m) = 0.180 g
Number of moles (n) = 0.00179 mol

Molar mass = 0.180 g / 0.00179 mol ≈ 100.56 g/mol

Therefore, the molar mass of the protein subunit is approximately 100.56 g/mol.