(a) Sketch, in a cubic unit cell, a [111] and a [112] lattice direction. (b) Use a trigonometric calculation to determine the an
gle between these two directions. (c) Use Equation 3.3 to determine the angle between these two directions.
1 answer:
Answer and Explanation:
a) The direction is shown in the cube diagram attached to this solution.
b) the angle between two planes (h₁, k₁, l₁) and (h₂, k₂, l₂) is given by the formula,
Cos Φ = (h₁h₂ + k₁k₂ + l₁)/√((h₁² + k₁² + l₁²)(h₂² + k₂² + l₂²))
For (111) and (112)
Cos Φ = (1.1 + 1.1 + 1.2)/√((1² + 1² + 1²)(1² + 1² + 2²))
Cos Φ = (1 + 1 + 2)/√((1+1+1)(1+1+4))
Cos Φ = 4/√(3×6)
Cos Φ = 4/√18
Φ = cos⁻¹ (4/√18) = 19.56°
c) equation 3.3 is missing from the question, I would be back to provide the answers to that as soon as the equation is provided!
Hope this Helps!!
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Answer:
A mixture of 100. mL of 0.1 M HC3H5O3 and 50. mL of NaOH
Explanation:
The pH of a buffer solution is calculated using following relation
Thus the pH of buffer solution will be near to the pKa of the acid used in making the buffer solution.
The pKa value of HC₃H₅O₃ acid is more closer to required pH = 4 than CH₃NH₃⁺ acid.
pKa = -log [Ka]
For HC₃H₅O₃
pKa = 3.1
For CH₃NH₃⁺
pKa = 10.64
pKb = 14-10.64 = 3.36 [Thus the pKb of this acid is also near to required pH value)
A mixture of 100. mL of 0.1 M HC3H5O3 and 50. mL of NaOH
Half of the acid will get neutralized by the given base and thus will result in equal concentration of both the weak acid and the salt making the pH just equal to the pKa value.