Lithium β is a solid phase of lithium still unknown to science. The only difference between it and ordinary lithium is that Lithium β forms a crystal with an fcc unit cell and a lattice constant =a0.430 nm. Calculate the density of Lithium β

The density of Lithium β is 0.5798 g/cm³

Explanation:

For a face centered cubic (FCC) structure, there are total number of 4 atoms in the unit cell.

we need to calculate the mass of these atoms because density is mass per unit volume.

Atomic mass of Lithium is 6.94 g/mol

Then we calculate the mass of four atoms;

⇒next, we estimate the volume of the unit cell in cubic centimeter

given the edge length or lattice constant a = 0.43nm

a = 0.43nm = 0.43 X 10⁻⁹ m = 0.43 X 10⁻⁹ X 10² cm = 4.3 X 10⁻⁸cm

Volume of the unit cell = a³ = (4.3 X 10⁻⁸cm)³ = 7.9507 X 10⁻²³ cm³

⇒Finally, we calculate the density of Lithium β

Density = mass/volume

Density = (4.6097 X 10⁻²³ g)/(7.9507 X 10⁻²³ cm³)

Density = 0.5798 g/cm³

n2(g) + 3h2-> 2nh3(g)   this is the balanced equation

note the mole ratio between n2, h2 and nh3.   it is 1 : 3 : 2   this will be important.

moles n2 present = 28.0 g n2 x 1 mole n2/28 g = 1 mole n2 present

moles h2 present = 25.0 g h2 x 1 mole h2/2 g = 12.5 moles h2 present

based on mole ratio, n2 is limiting in this situation because there is more than enough h2 but not enough n2.

moles nh3 that can be produced = 1 mole n2 x 2 moles nh3/mole n2 = 2 moles nh3 can be produced

grams of nh3 that can be produced = 2 moles nh3 x 17 g/mole = 34 grams of nh3 can be produced

note:   the key to this problem is recognizing that n2 is limiting, and therefore limits how much nh3 can be produced.

answer: a tank of height h is filled with water and sits on the ground. water squirts from a hole at a height y above the ground and has a range r. for two y values, 0 and h, r is zero. determine the value of y for which the range will be a maximum.

explanation: