Compute the theoretical density of ZnS given that the Zn-S distance and bond angle are 0.234 nm and 109.5o, respectively. The at
1 answer:
Answer: the theoretical density is 4.1109 g/cm³
Explanation:
first the image of one set of ZnS bonding in the crystal structure, we calculate the value of angle θ
θ + ∅ + 90° = 180°
θ = 90° - ∅
θ = 90° - ( 109.5° / 2 )
θ = 35.25°
next we calculate the value of x from the geometry
given that; distance angle d = 0.234
x = dsinθ
= 0.234 × sin35.25°)
= 0.135 nm = 0.135 × 10⁻⁷ cm
next we calculate the length of the unit cell
a = 4x
a = 4(0.135)
a = 0.54 nm = 0.54 × 10⁻⁷ cm
next we calculate number of formula units
n' = (no of corner atoms in unit ell × contribution of each corner atom in unit cell) + ( no of face center atom in a unit cell × contribution of each face center atom in a unit cell)
n' = 8 × 1/8) + ( 6 × 1/2)
= 1 + 3
= 4
next we calculate the theoretical density using this equation
P = [n'∑(Ac + AA)] / [Vc.NA]
= [n'∑(Ac + AA)] / [(a)³NA]
where the ∑Ac is sum of atomic weights of all cations in the formula unit( 65.41 g/mol)
∑AA is the sum of weights of all anions in the formula unit( 32.06 g/mol)
Na is the Avogadro’s number( 6.023 × 10²³ units/mole)
so we substitute
P = [4( 65.41 + 32.06)] / [ ( 0.54 × 10⁻⁷ )³ × (6.023 × 10²³)]
= 389.88 / 94.84
= 4.1109 g/cm³
therefore the theoretical density is 4.1109 g/cm³
You might be interested in
Answer:
F = 9.11 x 10³ N = 9.11 KN
Explanation:
The areas, lengths, young's modulus, and coefficient of linear thermal expansion are given in the diagram. First we find the equivalent change in length due to temperature change:
ΔL = (ΔL)steel + (ΔL)brass + (ΔL)Copper
ΔL = (∝s)(Ls)(ΔT) + (∝b)(Lb)(ΔT) + (∝c)(Lc)(ΔT)
where,
ΔL = Equivalent Change in Length = ?
ΔT = Change in Temperature = 25°C - 12°C = 13°C
Ls = Length of Steel Segment = 300 mm = 0.3 m
Lb = Length of Brass Segment = 200 mm = 0.2 m
Lc = Length of Copper Segment = 100 mm = 0.1 m
Therefore,
ΔL = (12 x 10⁻⁶ °C⁻¹)(0.3 m)(13 °C) + (21 x 10⁻⁶ °C⁻¹)(0.2 m)(13 °C) + (17 x 10⁻⁶ °C⁻¹)(0.1 m)(13 °C)
ΔL = 46.8 x 10⁻⁶ m + 54.6 x 10⁻⁶ m + 22.1 x 10⁻⁶ m
ΔL = 123.5 x 10⁻⁶ m ----------------------- equation (1)
Now, we calculate this deflection in terms of an applied force (F):
ΔL = (F)(Ls)/(Es)(As) + (F)(Lb)/(Eb)(Ab) + (F)(Lc)/(Ec)(Ac)
ΔL = (F)(0.3 m)/(200 x 10⁹ Pa)(200 x 10⁻⁶ m²) + (F)(0.2 m)/(100 x 10⁹ Pa)(450 x 10⁻⁶ m²) + (F)(0.1 m)/(120 x 10⁹ Pa)(515 x 10⁻⁶ m²)
ΔL = F(7.5 x 10⁻⁹ m/N + 4.44 x 10⁻⁹ m/N + 1.61 x 10⁻⁹ m/N)
ΔL = F(13.55 x 10⁻⁹ m/N) --------------------- equation (1)
Comparing equation (1) and equation (2):
123.5 x 10⁻⁶ m = F(13.55 x 10⁻⁹ m/N)
F = (123.5 x 10⁻⁶ m)/(13.55 x 10⁻⁹ m/N)
<u>F = 9.11 x 10³ N = 9.11 KN</u>
