A small protein molecule, code-named "sloth", has a MM of $\mathrm{1.50 x 10^4}$ g/mol. What is the osmotic pressure exerted at $\mathrm{24.0^oC}$ by 25.0 mL of an aqueous solution that contains $\mathrm{3.75 x 10^{10}}$ nanograms of "sloth"? R = 0.08206 (atm L)/(mol K).

The equation my professor gave me is: $\mathrm{O.P. = T*R*M}$. So I did:

$\mathrm{O.P. = (24.0 + 273) K * 0.08206 (atm*L)/(mol*K) * ([(3.75 x 10^{10})x 10^{-9} g] / 1.50 x 10^4 g/mol) / 0.025 L}$

I keep on trying and I get 2.44 atm, but my professor marked the correct answer as $\mathrm{2.44 x 10^{-3}}$ atm. I think he may have divided the moles of sloth by 25 instead of .025 L, which would make his answer $10^3$ smaller than mine. Did I do something wrong?

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Ok let's start with $\text{OP} = \text{T}\times\text{R}\times\text{M}$

$\text{T} = (24.0 + 273) \text{K} = 297 \text{K}$

$\text{R} = 0.08206 \dfrac{\text{atm}\cdot\text{L}}{\text{mol}\cdot\text{K}}$

$\text{M} = \dfrac{\text{moles}}{\text{L}} = \dfrac{\frac{37.5 \text{ g}}{1.50 \times 10^4 \text{ g/mol}}}{0.025 \text {L}} = \dfrac{2.50\times10^{-3}\text{ mol}}{0.025\text{ L}} = 0.100 \dfrac{\text{mol}}{\text{L}} $

$\text{OP} = 297\text{ K}\times0.08206 \dfrac{\text{atm}\cdot\text{L}}{\text{mol}\cdot\text{K}}\times0.100 \dfrac{\text{mol}}{\text{L}} = 2.44 \text{ atm} $

So I get your answer too...


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