A spherical ball of radius 3 cm contains 66.66% iron. If density of ball is 1.5 g/`cm^3` then the number of mole of Fe present approximately is:

Options

A. 1
B. 2
C. 20
D. 10

Answer

To solve the problem step by step, we will follow the outlined process:

### Step 1: Calculate the Volume of the Spherical Ball
The formula for the volume \( V \) of a sphere is given by:

\[ V = \frac{4}{3} \pi r^3 \]

Where \( r \) is the radius of the sphere. Given that the radius \( r = 3 \) cm, we can substitute this value into the formula:

\[ V = \frac{4}{3} \pi (3)^3 \]

Calculating this gives:

\[ V = \frac{4}{3} \pi (27) = 36\pi \approx 113.1 \, \text{cm}^3 \]

### Step 2: Calculate the Mass of the Ball
We know that the density \( \rho \) of the ball is given as \( 1.5 \, \text{g/cm}^3 \). The mass \( m \) can be calculated using the formula:

\[ m = \rho \times V \]

Substituting the known values:

\[ m = 1.5 \, \text{g/cm}^3 \times 113.1 \, \text{cm}^3 \approx 169.65 \, \text{g} \]

### Step 3: Calculate the Mass of Iron in the Ball
The percentage of iron in the ball is given as \( 66.66\% \). To find the mass of iron, we can use the formula:

\[ \text{Mass of Iron} = \left(\frac{66.66}{100}\right) \times \text{Mass of Ball \]

This can be simplified to:

\[ \text{Mass of Iron} = \frac{2}{3} \times 169.65 \, \text{g} \approx 113.1 \, \text{g} \]

### Step 4: Calculate the Number of Moles of Iron
The molar mass of iron (Fe) is approximately \( 56 \, \text{g/mol} \). The number of moles \( n \) can be calculated using the formula:

\[ n = \frac{\text{Mass of Iron}}{\text{Molar Mass of Iron}} \]

Substituting the values we have:

\[ n = \frac{113.1 \, \text{g}}{56 \, \text{g/mol}} \approx 2.02 \, \text{mol} \]

### Conclusion
The number of moles of iron present in the spherical ball is approximately \( 2 \) moles.

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