An unknown amino acid has `0.32%` sulphur by mass . If each molecule has one sulphur atom only 1 g of amino acid has . . . . . . . Molecules :-

Options

A. `6.02xx10^(18)`
B. `6.02xx10^(19)`
C. `6.02xx10^(24)`
D. `6.02xx10^(23`

Answer

To solve the problem step-by-step, we will follow the reasoning provided in the video transcript.

### Step 1: Determine the Molar Mass of the Amino Acid
We know that the amino acid has 0.32% sulfur by mass. This means that in 100 grams of the amino acid, there are 0.32 grams of sulfur.

Let the molar mass of the amino acid be \( x \) grams/mole. Since there is one sulfur atom per molecule, we can set up the equation:

\[ \frac{0.32}{100} \times x = 32 \text{ grams (mass of one sulfur atom)} \]

### Step 2: Solve for the Molar Mass
Rearranging the equation gives us:

\[ 0.32x = 32 \implies x = \frac{32}{0.32} = 100 \text{ grams/mole} \]

### Step 3: Calculate the Number of Moles in 1 Gram of Amino Acid
Using the molar mass we found, we can now calculate the number of moles in 1 gram of the amino acid:

\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{1 \text{ gram}}{100 \text{ grams/mole}} = 0.01 \text{ moles} \]

### Step 4: Calculate the Number of Molecules
Using Avogadro's number, which is \( 6.022 \times 10^{23} \) molecules/mole, we can find the number of molecules in 0.01 moles:

\[ \text{Number of molecules} = 0.01 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \]

Calculating this gives:

\[ \text{Number of molecules} = 6.022 \times 10^{21} \text{ molecules} \]

### Final Answer
Thus, in 1 gram of the amino acid, there are approximately \( 6.022 \times 10^{21} \) molecules.

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