CaC03(s) → CaO(s) + C02(g),∆fH° [CaO(s)] = -635.1 kJ mol–1,∆fH° [COz(g)] = -393.5 kJ mol–1,∆fH° [CaC03(s)] = -1206.9 kJ mol–1 Predict the effect of temperature on the equilibrium constant of the above reaction.

To predict the effect of temperature on the equilibrium constant (KK) of the given reaction, we can use the relationship between the standard Gibbs free energy change (ΔG∘ΔG∘) and the equilibrium constant:

ΔG∘=−RTln⁡KΔG∘=−RTlnK

where:

• ΔG∘ΔG∘ is the standard Gibbs free energy change,
• RR is the gas constant (8.314 J/mol·K),
• TT is the temperature in Kelvin,
• KK is the equilibrium constant.

At equilibrium, ΔG∘ΔG∘ is zero. Therefore, we can rearrange the equation to solve for KK:

K=e−ΔG∘RTK=e−RTΔG∘

Given that the reaction is:

CaCO3(s)→CaO(s)+CO2(g)CaCO3(s)→CaO(s)+CO2(g)

with the given standard enthalpy changes (ΔH∘ΔH∘):

ΔHCaCO3∘=−1206.9 kJ/molΔHCaCO3∘=−1206.9kJ/mol ΔHCaO∘=−635.1 kJ/molΔHCaO∘=−635.1kJ/mol ΔHCO2∘=−393.5 kJ/molΔHCO2∘=−393.5kJ/mol

we can use these values to calculate the change in standard Gibbs free energy (ΔG∘ΔG∘) using the equation:

ΔG∘=ΔHproducts∘−ΔHreactants∘ΔG∘=ΔHproducts∘−ΔHreactants∘

ΔG∘=(−635.1+(−393.5))−(−1206.9) kJ/molΔG∘=(−635.1+(−393.5))−(−1206.9)kJ/mol ΔG∘=118.3 kJ/molΔG∘=118.3kJ/mol

Now, we can calculate KK at two different temperatures and compare their values:

1. At T1=298 KT1=298K: K1=e−118.3×1038.314×298K1=e−8.314×298118.3×103

2. At T2=350 KT2=350K: K2=e−118.3×1038.314×350K2=e−8.314×350118.3×103

To determine the effect of temperature on KK, we can compare the values of K1K1 and K2K2. If K2>K1K2>K1, then increasing the temperature increases the equilibrium constant KK, indicating that the reaction shifts towards the products at higher temperatures. Conversely, if K2<K1K2<K1, then increasing the temperature decreases the equilibrium constant KK, indicating that the reaction shifts towards the reactants at higher temperatures.

By calculating K1K1 and K2K2 using the above equations, we can determine the effect of temperature on the equilibrium constant KK of the given reaction.