A protein is found to contain 2.29% Tryptophan(molecular weight 204). What is the minimum molecular weight of the protein?

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If we want the minimum molecular weight of the protein, then we have to assume that the 2.29% of the entire mass represents a single tryptophan molecule. Therefore we need to set up a ratio for the mass of one unit of tryptophan to the mass of the protein and set it equal to the ratio given by the percentage, 2.29%. 

If we have a mass percent of 2.29%, then that tells us that if the protein weighs 100 g, 2.29 g of that will be due to tryptophan.  Since we have to have whole units of amino acids to build proteins, the minimum we could have is 1 unit of tryptophan.

(2.29 g tryptophan / 100 g protein) = (204 amu tryptophan / x amu of protein)

x = 8908 amu protein

If we want to look at this in terms of grams, we have to use the conversion of 1 amu = 1.66 x 10^-24 g

8908 amu protein (1.66 x 10^-24 g / 1 amu) = 8.91 x 10^-21 g of protein for a single unit of protein

If we want it in terms of moles, then we need to multiply the mass of a single protein unit by Avogadro's number, 6.022 x 10^23, to find the g/mol which would be

8.91 x 10^-21 g * 6.022 x 10^23 = 5.36 x 10^3 g/mol


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