How many cubes (1 nm on each side) can be carved out of a cubic parent (1 m on e
ID: 976046 • Letter: H
Question
How many cubes (1 nm on each side) can be carved out of a cubic parent (1 m on each side)? What is the surface area of each nanometer-sized cube? Compare the surface area of all carved out cubes and a cubic parent. Briefly describe the nano effects in catalysis. What are the specific factors that control the activity and selectivity of nanocatalysts? Gold nanoparticles with core size of ~2.1 nm (AU_309) were used for the oxidation of CO to CO_2. The electro-oxidation reaction of 15 mmol of CO was completed in 30 min using 5 mg of gold nanoparticle catalysts. Calculate the turnover frequency (TOF) of gold nanoparticles based on active surface atoms. In catalytic converters which clean up petrol engine exhaust gases, a catalyst promotes the reduction of nitrogen oxides using another polluting gas as reductant. State a suitable catalyst for this task, identify the reductant, and write an equation for the reaction.Explanation / Answer
5.
We have 1 cube of 1 m on each side. Its surface area will be 6 m^2 as cube has six sides.
First we will calculate number of nano-cubes that can be carved out of parent cube.
1 nm = 1 * 10^-9 m
Therefore, volume of nanocube is (1 * 10^-9 m)^3 = 1 * 10^-27 m3
Number of nanocubes = 1 m3 / 1 * 10^-27 m3 = 1 * 10^27 nanocubes.
Surface area of each nano sized cube is = (1 * 10^-9 m)^2 *6 = 6 * 10^-18 m2
Total surface area of all cubes = 1 * 10^27 nanocubes * 6 * 10^-18 m2 = 6 * 10^9 m2 = 6000 km2
The total surface area of nano sized cubes is a billion times that of the 1-m cube.
6.
There are three types of nano-effects in catalysis.
(i) shape-catalytic effects, the effect of the shape of the confining material or the reduced dimensionality of the porous space;
(ii) physical effects including the influence of dispersion and electrostatic interactions with the confining material
(iii) chemical effects that involve significant electron rearrangement, including the formation and breaking of chemical bonds with the confining material.
Factors that control the activity and selectivity.
Orientation – In case of filamentous carbon nanostructures, orientations play important role in synthesis.
Thermal conditions – As the size of system decreases thermal control becomes more important.
7.
We need to calculate turn over number first.
Turn over number = moles of product formed / moles of catalyst = 15 mmol / 0.025 mmoles gold
= 600
Turn over frequency = turn over number / time of reaction = 600 / 30 min = 600 / 1800
= 0.333 s-1
8.
Reductant used in catalytic converters is CO carbon monoxide.
Carbon monoxide can act as strong reducing agent in presence of suitable catalyst.
Catalysts used are metals as Platinum, Palladium, rhodium and gold.
2NOx à xO2 + N2
2CO + O2 à CO2
4CO + 2NOx à 4COx + N2
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