At 500^∘ C, the equilibrium constant Kp for the synthesis of ammonia N2(g)+3 H2(g) ⇌2 NH3(g) is

step 1 formula here is kp is equal the k -c r t delta n we're told that the kp value is 1 .4 or 5 times

At 500^∘ C, the equilibrium constant Kp for the synthesis of...

At $500^{\circ} \mathrm{C},$ the equilibrium constant $K_{\mathrm{p}}$ for the synthesis of ammonia
$$
\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)
$$
is $1.45 \times 10^{-5} .$ What is the value of $K_{\mathrm{c}} ?$

Key Concepts

Equilibrium Constants

Equilibrium constants quantify the ratio of products to reactants in a reversible chemical reaction at equilibrium. They are defined based on either the concentrations of the species (Kc) or the partial pressures of the gases (Kp), and their values provide insight into the position of equilibrium and the extent of the reaction.

Relationship between Kp and Kc

Kp and Kc are related by the equation Kp = Kc(RT)^(?n), where R is the ideal gas constant, T is the absolute temperature, and ?n is the change in the number of moles of gas during the reaction. This relationship allows one to convert between concentration-based and pressure-based equilibrium constants, taking into account the effect of temperature and the difference in gas moles.

Change in Moles of Gas (?n)

?n represents the difference between the total moles of gaseous products and the total moles of gaseous reactants in a chemical reaction. This concept is essential when converting between Kc and Kp because the factor (RT)^(?n) in the conversion equation directly depends on how many moles of gas are produced or consumed during the reaction.

Ideal Gas Law and Temperature Dependence

The ideal gas law, which relates pressure, volume, temperature, and number of moles, underpins the conversion between concentration and pressure in gas-phase reactions. In the context of the Kp to Kc conversion, the temperature (T) plays a crucial role, since the term (RT)^(?n) links the change in moles of gas with the thermal energy available, thereby adjusting the equilibrium constant accordingly.

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