equilibrium constant for the reaction mentioned below at a certain tempereture is 0.914 NO2 + NO ⇌ N2O + O2 if initially 0.4 moles of NO2 is available how many moles of NO should be added to the vessel to have 0.15 mol of N2O(g) at equilibrium ?
To determine how many moles of NO should be added to the vessel to have 0.15 mol of N2O(g) at equilibrium, we need to use the equilibrium constant and the stoichiometry of the reaction. Here's how you can solve it step by step:
Step 1: Write the balanced chemical equation for the reaction:
NO2 + NO ⇌ N2O + O2
Step 2: Set up the expression for the equilibrium constant (K) using the concentration or partial pressure of the species involved. In this case, the reaction is in the gas phase, so we'll use the partial pressure. The equilibrium constant expression is given as:
K = (P(N2O) * P(O2)) / (P(NO2) * P(NO))
Step 3: Plug in the known values into the expression. Given that the equilibrium constant (K) is 0.914 and the equilibrium concentration of N2O is 0.15 mol, we have:
0.914 = (0.15 * P(O2)) / (0.4 * P(NO))
Step 4: Solve the equation for P(O2):
P(O2) = (0.914 * 0.4 * P(NO)) / 0.15
Step 5: Since we want to find the number of moles of NO required to reach the equilibrium concentration of N2O, we'll convert the partial pressure of NO to moles:
P(NO) = (n(NO) / V), where n(NO) is the number of moles of NO added and V is the volume of the vessel.
Step 6: Substitute P(NO) into the equation from step 4:
P(O2) = (0.914 * 0.4 * (n(NO) / V)) / 0.15
Step 7: Rearrange the equation to solve for the number of moles of NO (n(NO)):
n(NO) = (P(O2) * V * 0.15) / (0.914 * 0.4)
Step 8: Substitute the given values into the equation from step 7. Assuming the volume (V) is constant and using the given value for P(O2), you can calculate the number of moles of NO required.
By following these steps, you can find the number of moles of NO that should be added to the vessel to achieve the desired equilibrium concentration of N2O.