At constant pressure, ΔH = q = -250 J.

ΔU = q - W = 300 J - 100 J = 200 J.

ΔH for 0.5 moles = 200 kJ * 0.5 = 100 kJ.

Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

Gas particles do not occupy a definite volume; they fill the container they are in.

According to Boyle's Law, at constant temperature, pressure is inversely proportional to volume. If the volume is doubled, the pressure is halved.

According to Boyle's Law, at constant temperature, pressure is inversely proportional to volume. Halving the volume doubles the pressure.

The Kelvin scale starts at absolute zero, which is 0 K or -273.15°C.

ΔH = q/n = 500 J / 2 mol = 250 J/mol.

Dipole moment (p) = charge (q) × distance (d) = (1.6 x 10^-19 C) × (1.5 x 10^-10 m) = 2.4 x 10^-29 C·m.

Dipole moment (μ) = charge (q) × distance (d). μ = 0.33 e × 1.27 × 10^-10 m = 4.2 × 10^-29 C·m = 1.1 D.

ΔH = [2(201) + 498] - [2(941)] = -220 kJ.

Formal charge = Valence electrons - (Non-bonding electrons + 1/2 Bonding electrons) = 5 - (0 + 1/2*6) = 0.

Formal charge = valence electrons - (non-bonding electrons + 1/2 bonding electrons). For nitrogen in NO3-, it is 5 - (0 + 1/2(6)) = 0.

ΔG = -nFE° = -2 * 96485 C/mol * 0.75 V = -144.73 kJ.

Ionization energy is the energy required to remove an electron from the ground state. For hydrogen, it is 13.6 eV.

Ionization energy is the energy required to remove the electron from the ground state. For hydrogen, it is 13.6 eV.

In a tetrahedral geometry, the bond angles are approximately 109.5° due to the arrangement of four electron pairs.

The half-life (t1/2) of a first-order reaction is given by t1/2 = 0.693/k. Rearranging gives k = 0.693/t1/2 = 0.693/10 min = 0.0693 min^-1.

The half-life of a first-order reaction is independent of concentration; it remains 10 minutes.

The bond energy for a double bond (bond order = 2) is typically around 600 kJ/mol for C=C.

For a first-order reaction, t = (ln(2)/k) * ln([A]0/[A]t). To reach 25%, t = (ln(2)/0.1) * ln(4) = 20 seconds.

According to Le Chatelier's principle, increasing the concentration of products will shift the equilibrium position to the left to counteract the change.

According to Le Chatelier's principle, increasing temperature shifts the equilibrium to favor the endothermic direction (right).

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

For first-order reactions, the half-life is inversely proportional to the rate constant (t1/2 = 0.693/k).

The overall order of a reaction is the sum of the orders with respect to each reactant. Here, it is 1 (for A) + 2 (for B) = 3.

A negative ΔH and a positive ΔS indicate that the reaction is spontaneous at high temperatures, as ΔG will be negative.

The half-life for a first-order reaction is given by t1/2 = 0.693/k. Thus, t1/2 = 0.693/0.1 = 6.93 s.