The enthalpy change for the formation of NaCl from its elements is -411 kJ.

At constant pressure, the enthalpy change is given by ΔH = ΔU + PΔV.

The standard enthalpy change for the formation of ammonia is -92.4 kJ.

The formation of water from hydrogen and oxygen is an exothermic reaction, thus the enthalpy change is negative.

The enthalpy change for the formation of 2 moles of water is -571.6 kJ.

The enthalpy change for the formation of CO2 from carbon and oxygen is -393.5 kJ/mol.

The enthalpy change for the formation of CO2 from its elements is -393.5 kJ/mol.

The decomposition of calcium carbonate is an endothermic reaction, requiring heat input.

The standard enthalpy change for the formation of water from its elements is -241.8 kJ/mol.

The formation of ammonia from nitrogen and hydrogen is an exothermic reaction, thus the enthalpy change is negative.

The enthalpy change when 1 mole of NaCl is dissolved in water is approximately -3.87 kJ.

The condensation of water vapor to liquid water releases heat, making the enthalpy change negative.

The entropy change for a reversible isothermal expansion of an ideal gas is ΔS = nR ln(Vf/Vi).

The entropy change for a reversible isothermal process is ΔS = nR ln(Vf/Vi).

For a reversible process, the entropy change can be zero if the process is isothermal and reversible.

During a phase transition at constant temperature, the change in entropy is given by ΔS = Q/T, where Q is the heat absorbed or released.

The entropy change for an ideal gas during an isothermal expansion is ΔS = nR ln(Vf/Vi).

The entropy change for an isothermal expansion is given by ΔS = nR ln(V2/V1). For 1 mole, ΔS = R ln(V2/V1).

The entropy change for the mixing of two ideal gases at constant temperature is ΔS = nR ln(2) for equal moles of each gas.

The change in entropy when heating an ideal gas at constant volume is given by ΔS = nC_v ln(T2/T1). For 1 mole, it simplifies to ΔS = R ln(T2/T1).

The change in entropy at constant volume is given by ΔS = nC_v ln(T2/T1). For 1 mole, ΔS = R ln(T2/T1).

The phase change from ice to water at 0°C involves an increase in disorder, thus resulting in a positive change in entropy.

The change in entropy for an isothermal compression is ΔS = nR ln(V1/V2). For 2 moles, ΔS = 2R ln(V1/V2), which is negative since V1 < V2.

The displacement of a damped harmonic oscillator is given by x(t) = A e^(-bt) cos(ωt), where b is the damping coefficient.

Using the standard form, the equation is (x + 1)² + (y - 2)² = 4² = 16.

The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

The equation of a circle with center at (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.

The standard form of the equation of an ellipse with horizontal major axis is x^2/a^2 + y^2/b^2 = 1.

The equation of motion for a damped harmonic oscillator is m d²x/dt² + b dx/dt + kx = 0.

The equation of motion for SHM is x(t) = A cos(ωt) or x(t) = A sin(ωt).