I thought about using Kp=Kc(RT)^(delta n) but I’m not sure what to do with the two given Kc values.
The Correct Answer and Explanation is:
When you’re given two values for the equilibrium constant KcK_cKc and you want to relate them using the equation Kp=Kc(RT)ΔnK_p = K_c (RT)^{\Delta n}Kp=Kc(RT)Δn, it’s important to first understand the components of the equation.
- KpK_pKp: The equilibrium constant in terms of partial pressures.
- KcK_cKc: The equilibrium constant in terms of concentrations.
- RRR: The ideal gas constant, which is usually 0.0821 L\cdotpatm/mol\cdotpK0.0821 \, \text{L·atm/mol·K}0.0821L\cdotpatm/mol\cdotpK if you’re using pressure in atmospheres and volume in liters.
- TTT: Temperature in Kelvin.
- Δn\Delta nΔn: The change in the number of moles of gas from reactants to products. This is calculated by subtracting the moles of gaseous reactants from the moles of gaseous products.
If you’re given two KcK_cKc values at different temperatures, you can use the Van’t Hoff equation to find the relationship between the constants: ln(Kc2Kc1)=−ΔH∘R(1T2−1T1)\ln \left( \frac{K_{c2}}{K_{c1}} \right) = – \frac{\Delta H^\circ}{R} \left( \frac{1}{T_2} – \frac{1}{T_1} \right)ln(Kc1Kc2)=−RΔH∘(T21−T11)
Where:
- Kc1K_{c1}Kc1 and Kc2K_{c2}Kc2 are the equilibrium constants at temperatures T1T_1T1 and T2T_2T2.
- ΔH∘\Delta H^\circΔH∘ is the standard enthalpy change for the reaction.
In this case, the first step is to identify the relationship between the two KcK_cKc values. You can calculate Δn\Delta nΔn from the balanced chemical equation, then use Kp=Kc(RT)ΔnK_p = K_c (RT)^{\Delta n}Kp=Kc(RT)Δn to convert between the concentration-based equilibrium constant and the pressure-based equilibrium constant if the equation involves gases. If the temperatures are different, and you’re only given the two KcK_cKc values, using the Van’t Hoff equation can help you connect them.
