Askiitians Tutor Team
Last Activity: 4 Months ago
To find the density of LiBH4, we can use the formula for density, which is mass divided by volume. Given the information about the unit cell dimensions and the molar mass, we can calculate the density step by step.
Understanding the Unit Cell
LiBH4 crystallizes in an orthorhombic system, which means its unit cell has three different lengths: a, b, and c. The dimensions provided are:
- a = 6.8 Å
- b = 4.4 Å
- c = 7.2 Å
Calculating the Volume of the Unit Cell
The volume (V) of the unit cell can be calculated using the formula:
V = a × b × c
Substituting the values:
V = 6.8 Å × 4.4 Å × 7.2 Å
Calculating this gives:
V = 6.8 × 4.4 × 7.2 = 214.464 ų
Converting Volume to cm³
Since 1 ų = 10-24 cm³, we can convert the volume:
V = 214.464 ų × 10-24 cm³/ų = 2.14464 × 10-22 cm³
Calculating the Mass of the Unit Cell
Next, we need to determine the mass of the unit cell. Since there are 4 molecules of LiBH4 per unit cell and the molar mass is given as 21.76 g/mol, we can find the mass of the unit cell:
Mass of unit cell = (Number of molecules) × (Molar mass / Avogadro's number)
Using Avogadro's number (approximately 6.022 × 1023 mol-1):
Mass = 4 × (21.76 g/mol / 6.022 × 1023 mol-1)
Calculating this gives:
Mass = 4 × (3.61 × 10-23 g) = 1.444 × 10-22 g
Finding the Density
Now, we can calculate the density (D) using the formula:
D = Mass / Volume
Substituting the values we calculated:
D = (1.444 × 10-22 g) / (2.14464 × 10-22 cm³)
This simplifies to:
D ≈ 0.672 g/cm³
Choosing the Correct Option
From the options provided:
- (a) 0.6708 gm/cm³
- (b) 1.6708 gm/cm³
- (c) 2.6708 gm/cm³
- (d) All of the above
The calculated density of approximately 0.672 g/cm³ closely matches option (a) 0.6708 gm/cm³. Therefore, the correct answer is:
(a) 0.6708 gm/cm³
