A positive ΔG° indicates that the reaction is non-spontaneous in the forward direction.

For a first-order reaction, the rate of reaction is directly proportional to the concentration of the reactant, given by Rate = k[A].

Using t = 1 / (k[A₀]) * (1/[A] - 1/[A₀]), t = 1 / (0.02 * 0.5) * (1/0.25 - 1/0.5) = 25 s.

Using the Arrhenius equation, k = Ae^(-Ea/RT). Calculate k using the given values.

Increasing the temperature generally increases the rate of reaction significantly due to higher kinetic energy.

To find the temperature at which the reaction becomes spontaneous, set ΔG = 0: 0 = ΔH - TΔS. Thus, T = ΔH/ΔS = (100,000 J)/(200 J/K) = 500 K.

To find the temperature at which the reaction becomes spontaneous, set ΔG = 0: 0 = ΔH - TΔS, thus T = ΔH/ΔS = 100,000 J / 200 J/K = 500 K.

To find the temperature at which the reaction becomes spontaneous, set ΔG = 0: 0 = ΔH - TΔS, thus T = ΔH/ΔS = (50,000 J/mol) / (100 J/mol·K) = 500 K.

The moment of inertia of a rectangular plate about an axis through its center parallel to side a is I = 1/12 Mb^2.

For a reversible process, the change in entropy is given by ΔS = Q/T, where Q is the heat exchanged and T is the temperature.

For a reversible process, the change in entropy (ΔS) is given by ΔS = Q/T, where Q is the heat absorbed and T is the temperature.

The change in entropy (ΔS) for a reversible process is given by ΔS = Q/T, where Q is the heat absorbed and T is the temperature.

For a reversible process, the change in entropy of the universe is zero, as the system and surroundings are in equilibrium.

The efficiency of a Carnot engine is given by η = 1 - (T2/T1), where T1 is the temperature of the hot reservoir and T2 is the temperature of the cold reservoir.

For a satellite in a circular orbit, the kinetic energy is less than the potential energy, as K.E. = -1/2 P.E.

Low Earth orbit satellites typically operate at altitudes ranging from about 200 km to 2000 km above the Earth's surface.

For a satellite in a stable orbit, the centripetal force required for circular motion equals the gravitational force acting on the satellite.

The angular position of the first minimum is given by sin θ = λ/a.

The magnetic field inside a solenoid is given by B = μ₀nI.

Using Ampere's Law, B = μ₀nI where n is the number of turns per unit length.

The moment of inertia of a solid disk about an axis through its center is I = 1/2 MR^2.

The moment of inertia of a solid disk about an axis through its center is I = 1/2 MR^2.

According to Raoult's Law, the vapor pressure of the solution is P_A = X_A * P_A^0 = 0.6 * 100 mmHg = 60 mmHg.

For a solution to obey Raoult's Law, the interactions between solute and solvent must be similar to those in the pure components.

The electric field outside a spherical charge distribution behaves as if all the charge were concentrated at the center, so E = Q/4πε₀r².

For a spontaneous process, the total entropy change of the universe (system + surroundings) must be positive.

The relationship is given by ΔG = ΔH - TΔS, where ΔG must be negative for a spontaneous process.

The correct relationship is ΔG = ΔH - TΔS, where ΔG must be negative for a spontaneous process.

For a process to be spontaneous, the change in Gibbs free energy (ΔG) must be negative.

The moment of inertia for a system of particles is calculated as I = Σ(m_i * r_i^2), where m_i is the mass and r_i is the distance from the axis.