Question

Find the factors of 3m² + 9m + 6.​

Answer 1

Step-by-step explanation:

The kinetics of the oxidation of sulphur dioxide with oxygen using a commercial vanadium pentoxide catalyst has been investigated. Experimental conditions have been chosen such that the reaction has been carried out isothermally in a flow‐type reactor at temperatures (360° to 450°) and conversions (up to 10%) where the reverse reaction may be ignored.

The results, analysed in conjunction with the relevant adsorption isotherms and rates of adsorption on the clean catalyst, indicate that the rate‐determining step is the rate of reaction between gaseous oxygen and chemisorbed sulphur dioxide.

The adsorption isotherms, which are Langmuir in character, indicate the presence of at least two different types of active centres. Both oxygen and sulphur dioxide are reversibly chemisorbed, oxygen being weakly bound with a heat of adsorption of 6·4 kcal. and sulphur dioxide strongly bound with a heat of 28·8 kcal. There is evidence that both adsorbed species possess considerable mobility on the surface.

Measurements of the rates of adsorption of SO2 and O2 on the clean surface indicate that oxygen is adsorbed by a second‐order mechanism at a slower rate than the observed rate of reaction, whereas sulphur dioxide is adsorbed by a third‐order mechanism at a much faster rate than the rate of reaction. Adsorption equilibrium of SO2 may be assumed, under the conditions of reaction, without sensible error.

Adsorption‐rate measurements of both SO2 and O2 indicate that the number of active centres (defects) increases with temperature, according to a relationship of the type d ln L/dT = A/RT2 where L = no. of active centres, as suggested by Volkenstein (1949).

With SO2, reaction between it and an active centre requires no activation energy, the increase in rate with increase in temperature being due entirely to the increase in the number of active centres. With O2, a small activation energy may be required, although the main increase in rate of adsorption with temperature is similarly due to the increase in the number of active centres with temperature.

Some interesting comparisons are made between the results of these adsorption measurements and recent work on the semi‐conductivity of oxide catalysts, notably by Bevan & Anderson (1950) and Garner, Gray & Stone (1950). Several points of similarity are noted which indicate lines for further work.

Finally, a mechanism for the catalytic oxidation of sulphur dioxide is proposed, the main features of which are:

chemical structure image

Answer 2

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Find the factors of 3m² + 9m + 6.

$\huge \sf {\orange {\underline {\pink{\underline{Answer :-}}}}}$

★Hwre we notice that 3 is a common factor of all the terms.

Therefore,

$\sf{3m^2 + 9m + 6 = 3(m^2 + 3m +2)}$

Now,

$\sf{m^2 + 3m +2 = m^2 + m + 2m + 2}$

$\boxed{\sf{\orange{(as 2 = 1\times 2)}}}$

⠀⠀⠀⠀⠀⠀⠀ ⠀$\sf{= m(m + 1)+ 2(m + 1)}$

⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{= (m + 1) (m + 2)}$

Therefore,

$\sf{3m^2 + 9m + 6 = 3(m + 1) (m + 2)}$

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