Exercise 14.55 Consider the reaction: NiO(s)+CO(g)⇌Ni(s)+CO2(g) Kc=4000.0 at 1500 K When calculating the answer, do not round to the appropriate number of significant figures until the last calculation step..
I don't see a question here.
To calculate the answer for this question, we need to use the given equilibrium constant (Kc) and the stoichiometry of the reaction. Here's how you can approach it step by step:
Step 1: Write the balanced chemical equation for the reaction:
NiO(s) + CO(g) ⇌ Ni(s) + CO2(g)
Step 2: Define the initial and equilibrium concentrations of the reactants and products:
Let's assume the initial concentrations of NiO, CO, Ni, and CO2 are [NiO]0, [CO]0, [Ni]0, and [CO2]0, respectively. At equilibrium, these concentrations are [NiO], [CO], [Ni], and [CO2].
Step 3: Express the equilibrium concentrations in terms of the initial concentrations and changes:
Using the stoichiometry of the balanced equation, we can express the equilibrium concentrations in terms of the initial concentrations and the extent of reaction (x). The changes in concentrations can be written as follows:
[NiO] = [NiO]0 - x
[CO] = [CO]0 - x
[Ni] = [Ni]0 + x
[CO2] = [CO2]0 + x
Step 4: Set up the equilibrium constant expression using the equilibrium concentrations:
The equilibrium constant (Kc) expression can be written as:
Kc = [Ni] * [CO2] / ([NiO] * [CO])
Substituting the equilibrium concentrations from Step 3, we get:
Kc = ([Ni]0 + x) * ([CO2]0 + x) / ([NiO]0 - x) * ([CO]0 - x)
Step 5: Substitute the given value of Kc and solve for x:
As per the given question, Kc = 4000.0. Plug in this value into the Kc expression and solve for x algebraically. This step may involve some algebraic manipulations and solving a quadratic equation. In general, it is recommended to use numerical methods or software for solving such equations.
Step 6: Calculate the equilibrium concentrations:
Once you find the value of x, substitute it back into the expressions from Step 3 to calculate the equilibrium concentrations [NiO], [CO], [Ni], and [CO2].
Step 7: Round the final answer:
As mentioned in the question, do not round to the appropriate number of significant figures until the last calculation step. Once you have the final answer for the equilibrium concentrations, you can round them to the appropriate number of significant figures.
Remember to double-check your calculations and ensure that all units are consistent throughout the calculation.