Subtracting 4x from both sides gives 3x - 3 = 6, then adding 3 gives 3x = 9, leading to x = 3.

Dividing both sides by 7 gives x = 3.

In this case, the reaction force at each support is half the load applied at the center.

The horizontal component is calculated as 10 N * cos(30°) = 8.66 N.

A ΔG of +5 kJ/mol indicates that the reaction is non-spontaneous.

ΔG = ΔH - TΔS = 100 kJ - 298 K * (-0.2 kJ/K) = 100 kJ + 59.6 kJ = 159.6 kJ.

Using Raoult's Law, the mole fraction of the solvent can be calculated as 80 mmHg / 100 mmHg = 0.8, which corresponds to a mole fraction of 0.75 for the solvent.

The quantum numbers correspond to the 2s orbital, where l=0 indicates an s orbital.

The spin quantum number can be either +1/2 or -1/2, so both values are possible.

For l=1, the electron occupies a p orbital.

For l=1, the orbital is a p orbital.

For l=1, m_l can take values -1, 0, +1.

For l=0, m_l can only be 0.

For l=2, m_l can take values -2, -1, 0, 1, 2. Therefore, all of the options are valid.

For l=2, the orbital type is d.

According to the Arrhenius equation, an increase in activation energy results in a decrease in the rate constant k.

The azimuthal quantum number l = 1 corresponds to p orbitals, which have a dumbbell shape.

According to Le Chatelier's principle, increasing the concentration of reactants will shift the equilibrium position to the right, favoring the formation of products.

If the enthalpy of a system increases, the process is considered endothermic.

An increase in enthalpy indicates that the system is gaining heat.

A negative enthalpy change indicates that the reaction releases heat, making it exothermic.

An increase in entropy indicates that the process is spontaneous, as per the second law of thermodynamics.

If entropy increases, ΔG decreases, making the reaction more favorable.

For equal roots, the discriminant must be zero. Thus, (-5)^2 - 4*1*k = 0 => 25 - 4k = 0 => k = 25/4 = 6.25.

The equilibrium constant for the reverse reaction is the reciprocal of the forward reaction, so Kc' = 1/Kc = 0.1.

A Kc value greater than 1 indicates that the products are favored at equilibrium.

A Kc value less than 1 indicates that at equilibrium, the concentration of reactants is greater than that of products, thus reactants are favored.

According to Le Chatelier's principle, increasing the temperature of an exothermic reaction shifts the equilibrium position to the left, favoring the reactants.

Mole fraction of solvent = 1 - mole fraction of solute = 1 - 0.2 = 0.8.

According to Raoult's Law, the vapor pressure of the solvent in the solution is 0.75 * 100 mmHg = 75 mmHg.