Ammonium hydrogen sulfide, a stink bomb ingredient, decomposes to ammonia and hydrogen sulfide: Calculate the standard free-energy change for the rection at 25 °C if the total pressure resulting from the solid NH4S placed in an evacuated container is 0.658 atm at 25 °C. (a) -43.8 kJ (b) +1.04 kJ (c) -462 kJ (d) +5.51 kJ

Verified step by step guidance

1. Write the balanced chemical equation for the decomposition of ammonium hydrogen sulfide into ammonia and hydrogen sulfide: \(\text{NH}_4\text{HS(s)} \rightarrow \text{NH}_3\text{(g)} + \text{H}_2\text{S(g)}\).
2. Understand that the standard free-energy change (\(\Delta G^\circ\)) can be calculated using the equation: \(\Delta G^\circ = -RT \ln K_p\), where \(R\) is the gas constant (8.314 J/mol\cdot K), \(T\) is the temperature in Kelvin, and \(K_p\) is the equilibrium constant in terms of pressure.
3. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \(25^\circ\text{C} = 298.15 \text{K}\).
4. Calculate the equilibrium constant (\(K_p\)) using the given total pressure of the gases. Since the reaction produces equal moles of \(\text{NH}_3\) and \(\text{H}_2\text{S}\), each will exert half of the total pressure, i.e., \(0.658 \text{ atm}/2\). Use the relation \(K_p = (p_{\text{NH}_3})(p_{\text{H}_2\text{S}})\).
5. Substitute the values of \(R\), \(T\), and \(K_p\) into the free-energy equation to find \(\Delta G^\circ\).

Key Concepts

Standard Free Energy Change (ΔG°)

The standard free energy change (ΔG°) is a thermodynamic quantity that indicates the spontaneity of a reaction under standard conditions (1 atm, 25 °C). A negative ΔG° suggests that the reaction is spontaneous, while a positive ΔG° indicates non-spontaneity. It is calculated using the Gibbs free energy equation, which relates enthalpy, entropy, and temperature.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) describes the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas. In this context, it helps determine the amount of gaseous products formed from the decomposition of ammonium hydrogen sulfide. Understanding this law is crucial for calculating the partial pressures of the gases involved in the reaction.

Decomposition Reaction

A decomposition reaction is a type of chemical reaction where a single compound breaks down into two or more simpler products. In this case, ammonium hydrogen sulfide decomposes into ammonia and hydrogen sulfide. Analyzing the stoichiometry of the reaction is essential for calculating the free energy change and understanding the quantities of reactants and products involved.