The coefficient of x^2 is C(4,2)(3)^2(-4)^2 = 6 * 9 * 16 = -864.

Zinc (Zn) is oxidized to Zn2+, so its oxidation state is +2.

Iron (Fe) is oxidized as it loses electrons to form FeCl3.

Fe2O3 is reduced to Fe, as it gains electrons during the reaction.

Magnesium is oxidized as it loses electrons and its oxidation state increases from 0 to +2.

N2 is reduced to NH3 as it gains electrons.

Iron (Fe) is oxidized as it loses electrons to form Fe2O3.

Copper (Cu) is reduced as it gains electrons from zinc.

Cu is oxidized to Cu2+ as it loses electrons in the reaction.

Zn is oxidized to Zn2+ as it loses electrons.

In C2O4^2-, the oxidation state of carbon is +3.

Adsorption is widely used in water purification processes to remove impurities.

Particles in a solid have the least amount of energy compared to liquids, gases, and plasma.

In gases, particles move freely and are far apart compared to solids and liquids.

Integrating both sides, we get y = ∫(2x + 1)dx = x^2 + x + C.

Using an integrating factor, we find the solution is y = Ce^(2x) - 3/2.

This is a separable equation. Integrating gives y = Cx.

This is a linear first-order equation. The solution is y = 5/2 + Ce^(-2x).

The characteristic equation is r^2 - 3r + 2 = 0, which factors to (r - 1)(r - 2) = 0. The general solution is y = C1e^(x) + C2e^(2x).

This is a separable equation. Separating variables and integrating gives y = Cx.

Using the integrating factor e^(∫(1/x)dx) = x, we solve to get y = x + C/x.

The half-life of a first-order reaction is independent of the initial concentration and is directly proportional to the rate constant.

The half-life of a first-order reaction is given by the formula t1/2 = 0.693/k, where k is the rate constant.

The Langmuir isotherm assumes that adsorption occurs at specific sites, leading to a monolayer coverage of the adsorbate.

In the Langmuir isotherm, the maximum coverage of adsorbate on the adsorbent is referred to as a monolayer.

The rate constant of a reaction is affected by the nature of the reactants, temperature, and the presence of catalysts.

Dividing the equation by 3 gives x² - 4x + 4 = 0, which factors to (x - 2)² = 0, hence the root is 2.

The roots can be found using the factorization method: (x - 2)(x - 3) = 0, hence the roots are 2 and 3.

Enthalpy refers to the heat content of a system at constant pressure, defined as internal energy plus pressure times volume.

According to the second law of thermodynamics, the entropy of an isolated system always increases over time.