Question

Northern cod produce proteins that protect their cells from damage caused by subzero temperatures. Measurements of the osmotic pressure for two “antifreeze” proteins at 18°C yielded the data listed below. Use this information to calculate the molar mass for each of the proteins. Assume these proteins are nonelectrolytes and use the value i = 1.If a 45.9 mg sample of protein B in 1.75 mL of water has an osmotic pressure of 0.218 atm, what is the molar mass of protein B?________ g/mol

Answer 1

Answer:

$2,875.94\text{ g/mol}$

Explanation:

Here, we want to calculate the molar mass of protein B

Mathematically:

$\Pi\text{ = iMRT}$

where:

Π is the osmotic pressure which is 0.218 atm

i is the Vantt Hoff factor which is 1

M is the molarity

T is the temperature in Kelvin. The temperature given is in Celsius. We convert to Kelvin by adding 273.15 K : 273.15 + 18 = 291.15 K

R is the molar gas constant which is 0.0821 L.atm/mol.k

Substituting the values:

$\begin{gathered} 0.218\text{ = 1}\times\text{ M}\times\text{ 0.0821 }\times\text{ 291.15} \\ M\text{ = 0.00912 M} \end{gathered}$

Now, we have to make some conversions

We need to get the number of moles from the molarity

We can do that by multiplying the volume by the number of moles

Mathematically:

$\begin{gathered} 1.75\text{ mL = 0.00175 L} \\ number\text{ of moles = 0.00175 }\times\text{ 0.00912 = 0.00001596 moles} \end{gathered}$

Finally, to get the molar mass, we have to divide the mass by the number of moles

$\begin{gathered} 45.9\text{ mg = 0.0459 g \lparen we divide the mg value by 1000\rparen} \\ The\text{ mass is:} \\ \frac{0.0459}{0.00001596}\text{ = 2,875.94 g/mol} \end{gathered}$