How many moles of ptoton weigh 1 Kg?

Options

A. `10^(3)`
B. `N_(A)`
C. `(1)/(N_(A)) xx 10^(3)`
D. `(10^(8))/(9.11 xx 6.022)`

Answer

To find out how many moles of protons weigh 1 kg, we can follow these steps:

### Step 1: Determine the mass of a single proton
The mass of a single proton is given as:
\[ \text{Mass of 1 proton} = 1.67 \times 10^{-27} \text{ kg} \]

### Step 2: Calculate the mass of one mole of protons
To find the mass of one mole of protons, we use Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) (the number of particles in one mole). The mass of one mole of protons can be calculated as follows:
\[ \text{Mass of 1 mole of protons} = \text{Mass of 1 proton} \times \text{Avogadro's number} \]
\[ = 1.67 \times 10^{-27} \text{ kg} \times 6.022 \times 10^{23} \]

### Step 3: Perform the multiplication
Now, we perform the multiplication:
\[ \text{Mass of 1 mole of protons} = 1.67 \times 6.022 \times 10^{-4} \text{ kg} \]
Calculating this gives:
\[ \text{Mass of 1 mole of protons} \approx 1.00 \times 10^{-3} \text{ kg} \]

### Step 4: Calculate the number of moles in 1 kg
To find out how many moles of protons weigh 1 kg, we use the formula:
\[ \text{Number of moles} = \frac{\text{Total mass}}{\text{Mass of 1 mole}} \]
Substituting the values we have:
\[ \text{Number of moles} = \frac{1 \text{ kg}}{1.00 \times 10^{-3} \text{ kg}} \]

### Step 5: Perform the division
Now, calculating the number of moles:
\[ \text{Number of moles} = 1 \times 10^{3} \]

### Final Answer
Therefore, the number of moles of protons that weigh 1 kg is:
\[ \text{Number of moles} = 1000 \text{ moles} \]

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