Examples of calculating Kp from Kc and vice versa

📚 Quick Study Guide

• ⚖️ Equilibrium Constants: $K_c$ represents the equilibrium constant in terms of concentrations, while $K_p$ represents it in terms of partial pressures.
• ➗ Ideal Gas Law: The relationship between pressure and concentration is derived from the ideal gas law: $PV = nRT$, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
• ➮ Key Formula: The formula to convert between $K_p$ and $K_c$ is: $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ is the change in the number of moles of gas (moles of gaseous products - moles of gaseous reactants).
• 🌡️ Temperature: Ensure the temperature (T) is always in Kelvin when using the formula. Convert Celsius to Kelvin by adding 273.15.
• 📝 Calculating $\Delta n$: Only consider gaseous species when calculating $\Delta n$. Ignore solids and liquids.
• 💡 R Value: The value of the ideal gas constant, R, depends on the units used for pressure. If pressure is in atm, use R = 0.0821 L·atm/mol·K.

🧪 Practice Quiz

1. For the reaction $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$, if $K_c = 0.5$ at 400K, what is the value of $K_p$?

   1. 0.5
   2. 1.64
   3. 0.00012
   4. 0.00018

2. Given $K_p = 4.0$ for the reaction $CO(g) + Cl_2(g) \rightleftharpoons COCl_2(g)$ at 300K, calculate $K_c$.

   1. 4.0
   2. 163.0
   3. 0.163
   4. 9.75 x 10^-5

3. For the reaction $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$, $K_c = 50$ at 700K. What is the value of $K_p$?

   1. 50
   2. 2800
   3. 0.02
   4. It cannot be determined

4. Consider the reaction $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$. If $K_c = 2.8 \times 10^2$ at 1000K, what is $K_p$?

   1. $2.8 \times 10^2$
   2. $3.4 \times 10^4$
   3. 3.4
   4. 2.29 x 10^-3

5. If $K_p = 0.04$ for the reaction $N_2O_4(g) \rightleftharpoons 2NO_2(g)$ at 300K, calculate $K_c$.

   1. 0.04
   2. 0.975
   3. 1.63 x 10^-3
   4. 1.63

6. For the equilibrium $C(s) + CO_2(g) \rightleftharpoons 2CO(g)$, $K_p = 167.7$ at 1000°C. Calculate $K_c$.

   1. 167.7
   2. 1.71
   3. 1.71 x 10^-2
   4. 1.41

7. Given the reaction $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$ with $K_c = 0.045$ at 500 K, find $K_p$.

   1. 0.045
   2. 1.85
   3. 2.75
   4. 3.7