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.

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.

The mole fraction of the solvent is 1 - X_solute = 1 - 0.2 = 0.8.

Molarity = π / (RT) = 3.0 / (0.0821 * 298) = 0.12 M

Molarity = π / (RT) = 3.0 / (0.0821 * 298) = 0.12 M

The maximum number of electrons in a subshell is given by 2(2l + 1). For l = 2, it is 2(2*2 + 1) = 10.

For n=4, l can take values 0, 1, 2, or 3.

For n=4, l can take values from 0 to n-1, which are 0, 1, 2, and 3.

The discriminant must be less than zero: k^2 - 4*1*9 < 0 => k^2 < 36 => |k| < 6.

Using the Arrhenius equation, a rule of thumb states that for every 10°C increase in temperature, the rate doubles if Ea is around 40 kJ/mol.

For real and distinct roots, the discriminant must be positive: 3^2 - 4*1*k > 0 => 9 - 4k > 0 => k < 9.

Using Vieta's formulas, k = (-2)(-3) = 6.

Using Vieta's formulas, k = 2 * 4 = 8.

Ksp = [Ag+][Cl-] = s^2, thus s = sqrt(1.77 x 10^-10) = 1.77 x 10^-5 M.

According to Charles's Law, at constant pressure, the volume of a gas is directly proportional to its temperature.

As the temperature of a system increases, the kinetic energy of the particles increases, leading to greater disorder and thus an increase in entropy.

Using Raoult's Law, P_solution = X_solvent * P_pure_solvent; 60 mmHg = X_solvent * 80 mmHg; X_solvent = 60/80 = 0.75.

Using Raoult's Law, P_solution = X_solvent * P_solvent^0; 80 = X_solvent * 120; X_solvent = 80/120 = 0.67.

Using Raoult's Law, P_solution = X_A * P_A^0 = 0.6 * 100 mmHg = 60 mmHg.

According to Raoult's Law, the vapor pressure of the solution is 0.5 * 100 mmHg = 50 mmHg.

Using Raoult's Law, the vapor pressure of the solution is P_solution = P_solvent * X_solvent = 120 * (1/(1+0.2)) = 120 * (1/1.2) = 100 mmHg.

Subtracting 4 from both sides gives x = 6.