At \(900^{\circ} \mathrm{C}, K_{\mathrm{C}}=0.0108\) for the reaction $$\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$ A mixture of \(\mathrm{CaCO}_{3}, \mathrm{CaO},\) and \(\mathrm{CO}_{2}\) is placed in a 10.0 - \(\mathrm{L}\) vessel at \(900^{\circ} \mathrm{C}\) . For the following mixtures, will the amount of \(\mathrm{CaCO}_{3}\) increase, decrease, or remain the same as the system approaches equilibrium? \begin{equation} \begin{array}{l}{\text { (a) } 15.0 \mathrm{g} \mathrm{CaCO}_{3}, 15.0 \mathrm{g} \mathrm{CaO}, \text { and } 4.25 \mathrm{gCO}_{2}} \\ {\text { (b) } 2.50 \mathrm{g} \mathrm{CaCO}_{3}, 25.0 \mathrm{g} \mathrm{CaO}, \text { and } 5.66 \mathrm{g} \mathrm{CO}_{2}} \\ {\text { (a) } 30.5 \mathrm{g} \mathrm{CaCO}_{3}, 25.5 \mathrm{g} \mathrm{CaO}, \text { and } 6.48 \mathrm{g} \mathrm{CO}_{2}}\end{array} \end{equation}

Step by step solution

01

(a) Calculate moles of CO2 in the first mixture

Given, 4.25 g of CO2. To determine the number of moles, we will use the formula: moles = mass / molar mass moles = 4.25 g / 44.01 g/mol = 0.0966 mol

02

(b) Calculate moles of CO2 in the second mixture

Given, 5.66 g of CO2. To determine the number of moles, we will use the formula: moles = mass / molar mass moles = 5.66 g / 44.01 g/mol = 0.1286 mol

03

(c) Calculate moles of CO2 in the third mixture

Given, 6.48 g of CO2. To determine the number of moles, we will use the formula: moles = mass / molar mass moles = 6.48 g / 44.01 g/mol = 0.1472 mol ##Step 2: Compute the reaction quotient Qc for each mixture## Next, we will calculate the reaction quotient Qc for each mixture using the formula: Qc = [CO2]

04

(a) Calculate Qc for the first mixture

Qc = [0.0966 mol CO2 / 10 L] = 0.00966

05

(b) Calculate Qc for the second mixture

Qc = [0.1286 mol CO2 / 10 L] = 0.01286

06

(c) Calculate Qc for the third mixture

Qc = [0.1472 mol CO2 / 10 L] = 0.01472 ##Step 3: Compare Qc to Kc to determine the change in CaCO3## Finally, we will compare the Qc value of each mixture to the Kc value (0.0108) to determine if the CaCO3 will increase, decrease, or remain the same as the system approaches equilibrium:

07

(a) Determine the change in CaCO3 for the first mixture

Qc < Kc, therefore the reaction will proceed to the right to reach equilibrium. This means that the amount of CaCO3 will decrease.

08

(b) Determine the change in CaCO3 for the second mixture

Qc > Kc, therefore the reaction will proceed to the left to reach equilibrium. This means that the amount of CaCO3 will increase.

09

(c) Determine the change in CaCO3 for the third mixture

Qc > Kc, therefore the reaction will proceed to the left to reach equilibrium. This means that the amount of CaCO3 will increase.

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