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

According to Le Chatelier's principle, increasing the volume of the container decreases the pressure. The equilibrium will shift towards the side with more moles of gas, which is the left side (2 moles of SO2 + 1 mole of O2).

N2 is reduced to NH3 as it gains electrons.

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

For an exothermic reaction, increasing the temperature shifts the equilibrium to the left, favoring the reactants, as the system tries to absorb the added heat.

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.

Magnetic field lines emerge from the north pole and enter the south pole of a bar magnet.

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

Gas particles have the highest energy compared to solids and liquids, allowing them to move freely and occupy more space.

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).

Using the integrating factor method, we find the solution y = (3/5) + Ce^(5x).

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 first-order linear equation. The integrating factor method gives the solution y = 2 - Ce^(-6x).

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 Arrhenius equation relates the rate constant (k) to temperature (T) and activation energy (Ea).

Frequency is defined as the number of cycles per unit time, hence its dimensional formula is [T^-1].

Velocity is defined as displacement per unit time, hence its dimensional formula is [M^0 L^1 T^-1].

The force on a charged particle moving in a magnetic field is maximum when the angle between the velocity and the magnetic field is 90 degrees.

The force on a charged particle moving in a magnetic field is maximum when the particle moves perpendicular to the field.

Time period (T) = 1 / frequency (f) = 1 / 440 Hz ≈ 0.00227 s.

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