Sia
Question
Chemistry
Posted 10 months ago
LiBr have the density of
3
.
4
6
4
g
/
cm
3
,
rock salt structure, shown in figure
1
.
The atomic weight of Li
=
6
.
9
4
1
and Br
=
7
9
.
9
0
4
.
Caculate
(
a
)
the molar volumn of LiBr
(
b
)
the unit cell volumn
(
cm
3
/
unit
)
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Answer from Sia
Posted 10 months ago
Solution
1
Calculate the molar mass of LiBr: To find the molar volume, we first need to calculate the molar mass of LiBr using the atomic weights of lithium (Li) and bromine (Br)
M_{\text{LiBr}} = M_{\text{Li}} + M_{\text{Br}} = 6.941 \text{ g/mol} + 79.904 \text{ g/mol} = 86.845 \text{ g/mol}
2
Calculate the molar volume of LiBr: The molar volume is the volume occupied by one mole of a substance. We can calculate it using the density and the molar mass
V_{\text{molar}} = \frac{M_{\text{LiBr}}}{\text{density}} = \frac{86.845 \text{ g/mol}}{3.464 \text{ g/cm}^3} = 25.07 \text{ cm}^3/\text{mol}
3
Calculate the unit cell volume of LiBr: The rock salt structure has a face-centered cubic (FCC) unit cell with 4 formula units per unit cell. The molar volume divided by Avogadro's number gives the volume of one formula unit, which we multiply by 4 to find the unit cell volume
V_{\text{unit cell}} = \frac{V_{\text{molar}}}{N_A} \times 4 = \frac{25.07 \text{ cm}^3/\text{mol}}{6.022 \times 10^{23} \text{ formula units/mol}} \times 4 = 1.66 \times 10^{-22} \text{ cm}^3/\text{unit cell}
1 Answer
The molar volume of LiBr is 25.07 cm³/mol
2 Answer
The unit cell volume of LiBr is 1.66 × 10⁻²² cm³/unit cell
Key Concept
Molar volume is calculated using the molar mass and density of a substance. The unit cell volume in a crystal structure can be found by dividing the molar volume by Avogadro's number and multiplying by the number of formula units per unit cell.
Explanation
The molar volume is derived from the density and molar mass, providing the volume occupied by one mole of the substance. For crystalline substances with known structures, the unit cell volume can be calculated by relating the molar volume to the number of entities in a unit cell, using Avogadro's number to convert moles to individual formula units.
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