Methane crystallises in a cubic unit cell with a = 0.598 nm. Calculate the theoretical density of methane assuming Z = 1, 2 and 4. If the density of liquid methane is `0.466"g cm"^(-3)` and assume that density of solid is the same as that of the liquid at a given temperature, predict which type of unit cell result?

Explanation

To solve the problem, we will calculate the theoretical density of methane for three different values of Z (1, 2, and 4) using the formula for density in a cubic unit cell. Then, we will compare the calculated densities with the given density of liquid methane to determine the type of unit cell.

### Step 1: Understand the formula for density
The formula for the density (D) of a crystalline solid is given by:
\[ D = \frac{Z \cdot M}{A^3 \cdot N_A} \]
where:
- \( Z \) = number of formula units per unit cell
- \( M \) = molar mass of the substance (for methane, \( M = 16 \, \text{g/mol} \))
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