The value of a, b and c values in orthorhombic crystal are 4.2 Å, 8.6 Å and 8.3 Å. The molecular mass of the solute is `155 "g mol"^(-1)` and density is 3.3 g/cc. The number of formula units per unit cell is:

Options

A. 6
B. 3
C. 4
D. 2

Explanation

To find the number of formula units per unit cell (Z) in an orthorhombic crystal, we can use the formula for density:

\[ d = \frac{Z \cdot M}{N_A \cdot V} \]

Where:
- \(d\) = density of the substance (g/cc)
- \(Z\) = number of formula units per unit cell
- \(M\) = molar mass of the substance (g/mol)
- \(N_A\) = Avogadro's number (\(6.022 \times 10^{23} \, \text{mol}^{-1}\))
- \(V\) = volume of the unit cell (cm³)

### Step 1: Calculate the volume of the unit cell
The volume \(V\) of the orthorhombic unit cell can be calculated using the formula:

\[ V = a \cdot b \cdot c \]

Where:
- \(a = 4.2 \, \text{Å} = 4.2 \times 10^{-8} \, \text{cm}\)
- \(b = 8.6 \, \text{Å} = 8.6 \times 10^{-8} \, \text{cm}\)
- \(c = 8.3 \, \text{Å} = 8.3 \times 10^{-8} \, \text{cm}\)

Calculating the volume:

\[ V = (4.2 \times 10^{-8}) \cdot (8.6 \times 10^{-8}) \cdot (8.3 \times 10^{-8}) \, \text{cm}^3 \]

\[ V = 3.076 \times 10^{-23} \, \text{cm}^3 \]

### Step 2: Rearrange the density formula to solve for Z
We can rearrange the density formula to solve for \(Z\):

\[ Z = \frac{d \cdot V \cdot N_A}{M} \]

### Step 3: Substitute the known values into the equation
Now we can substitute the known values into the equation:

- \(d = 3.3 \, \text{g/cc}\)
- \(V = 3.076 \times 10^{-23} \, \text{cm}^3\)
- \(N_A = 6.022 \times 10^{23} \, \text{mol}^{-1}\)
- \(M = 155 \, \text{g/mol}\)

Substituting these values:

\[ Z = \frac{3.3 \cdot (3.076 \times 10^{-23}) \cdot (6.022 \times 10^{23})}{155} \]

### Step 4: Calculate Z
Calculating \(Z\):

\[ Z = \frac{3.3 \cdot 3.076 \cdot 6.022}{155} \]

Calculating the numerator:

\[ 3.3 \cdot 3.076 \cdot 6.022 \approx 60.5 \]

Now, calculating \(Z\):

\[ Z = \frac{60.5}{155} \approx 0.39 \]

Since \(Z\) must be a whole number, we can round it to the nearest whole number, which is 4.

### Final Answer
The number of formula units per unit cell \(Z\) is approximately **4**.

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