A sample of potato starch was ground in a ball mill to give a starchlike molecule of lower molecular weight. The product analysed 0086% phosphorus. If each molecule is assumed to contain one atom of phosphorus, what is the molecular weight of the material?

Answer

To determine the molecular weight of the starch-like molecule that contains phosphorus, we can follow these steps:

### Step 1: Understand the given data
We know that the sample contains 0.086% phosphorus. This means that in 100 grams of the sample, there are 0.086 grams of phosphorus.

### Step 2: Find the mass of phosphorus in grams
Since the percentage is given, we can directly interpret that:
- Mass of phosphorus in 100 grams of the sample = 0.086 grams

### Step 3: Use the atomic weight of phosphorus
The atomic weight of phosphorus (P) is approximately 31 grams/mole. This means that 1 mole of phosphorus weighs 31 grams.

### Step 4: Calculate the number of moles of phosphorus in the sample
To find the number of moles of phosphorus in 0.086 grams, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles of P} = \frac{0.086 \text{ g}}{31 \text{ g/mol}} \]

### Step 5: Calculate the number of moles
Calculating the above expression:
\[ \text{Number of moles of P} = \frac{0.086}{31} \approx 0.002774 \text{ moles} \]

### Step 6: Relate the number of moles of phosphorus to the molecular weight of the compound
Since we assume that each molecule of the starch-like compound contains one atom of phosphorus, the number of moles of the compound will also be 0.002774 moles.

### Step 7: Calculate the molecular weight of the compound
The molecular weight (M) of the compound can be calculated using the formula:
\[ M = \frac{\text{mass of sample (g)}}{\text{number of moles}} \]
Since we are considering 100 grams of the sample:
\[ M = \frac{100 \text{ g}}{0.002774 \text{ moles}} \]

### Step 8: Calculate the molecular weight
Calculating the above expression:
\[ M \approx \frac{100}{0.002774} \approx 36053.4 \text{ g/mol} \]

### Final Result
The molecular weight of the starch-like compound is approximately **36053.4 g/mol**.

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