Math / Algebra

QuestionReview Constants
What is the equilibrium concentration of CO at 1000 K ? Express your answer in molarity to three significant figures.
MISSED THIS? Watch KCV 15.8, IWE 15.9; Read Section 15.8. You can click on the Review link to access the section in your eText.
For the following reaction, $K_{\mathrm{c}}=255$ at 1000 K . $\mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{COCl}_{2}(\mathrm{~g})$ A reaction mixture initially contains a CO concentration of 0.1530 M and a $\mathrm{Cl}_{2}$ concentration of 0.172 M at 1000 K .

Studdy Solution

STEP 1

1. The reaction is at equilibrium at 1000 K.
2. The equilibrium constant $K_c$ for the reaction is 255.
3. The initial concentration of CO is 0.1530 M.
4. The initial concentration of $\text{Cl}_2$ is 0.172 M.
5. We need to find the equilibrium concentration of CO.

STEP 2

1. Write the balanced chemical equation.
2. Set up the expression for the equilibrium constant.
3. Define the change in concentration using an ICE table.
4. Solve for the equilibrium concentration of CO.

STEP 3

Write the balanced chemical equation for the reaction:
$\text{CO(g)} + \text{Cl}_2\text{(g)} \rightleftharpoons \text{COCl}_2\text{(g)}$

STEP 4

Set up the expression for the equilibrium constant $K_c$ :
$K_c = \frac{[\text{COCl}_2]}{[\text{CO}][\text{Cl}_2]}$

STEP 5

Define the change in concentration using an ICE table (Initial, Change, Equilibrium):
- Initial concentrations: $[ \text{CO} ] = 0.1530 \, \text{M}, [ \text{Cl}_2 ] = 0.172 \, \text{M}, [ \text{COCl}_2 ] = 0 \, \text{M}$ - Change in concentrations: $[ \text{CO} ] = -x, [ \text{Cl}_2 ] = -x, [ \text{COCl}_2 ] = +x$ - Equilibrium concentrations: $[ \text{CO} ] = 0.1530 - x, [ \text{Cl}_2 ] = 0.172 - x, [ \text{COCl}_2 ] = x$

STEP 6

Substitute the equilibrium concentrations into the equilibrium constant expression and solve for $x$ :
$255 = \frac{x}{(0.1530 - x)(0.172 - x)}$

STEP 7

Solve the equation for $x$ using algebraic methods (e.g., quadratic formula or approximation if $x$ is small):
Assume $x$ is small compared to initial concentrations, so $0.1530 - x \approx 0.1530$ and $0.172 - x \approx 0.172$ :
$255 \approx \frac{x}{0.1530 \times 0.172}$
$x \approx 255 \times 0.1530 \times 0.172$
$x \approx 6.686 \times 10^{-3}$

STEP 8

Calculate the equilibrium concentration of CO:
$[\text{CO}]_{\text{eq}} = 0.1530 - x$
$[\text{CO}]_{\text{eq}} = 0.1530 - 6.686 \times 10^{-3}$
$[\text{CO}]_{\text{eq}} = 0.1463 \, \text{M}$
The equilibrium concentration of CO is:
$\boxed{0.146 \, \text{M}}$

Was this helpful?

Studdy Solution

STEP 1

1. The reaction is at equilibrium at 1000 K.
2. The equilibrium constant $K_c$ for the reaction is 255.
3. The initial concentration of CO is 0.1530 M.
4. The initial concentration of $\text{Cl}_2$ is 0.172 M.
5. We need to find the equilibrium concentration of CO.

STEP 2

1. Write the balanced chemical equation.
2. Set up the expression for the equilibrium constant.
3. Define the change in concentration using an ICE table.
4. Solve for the equilibrium concentration of CO.

STEP 3

Write the balanced chemical equation for the reaction:
$\text{CO(g)} + \text{Cl}_2\text{(g)} \rightleftharpoons \text{COCl}_2\text{(g)}$

STEP 4

Set up the expression for the equilibrium constant $K_c$ :
$K_c = \frac{[\text{COCl}_2]}{[\text{CO}][\text{Cl}_2]}$

STEP 5

STEP 6

Substitute the equilibrium concentrations into the equilibrium constant expression and solve for $x$ :
$255 = \frac{x}{(0.1530 - x)(0.172 - x)}$

STEP 7

STEP 8

Calculate the equilibrium concentration of CO:
$[\text{CO}]_{\text{eq}} = 0.1530 - x$
$[\text{CO}]_{\text{eq}} = 0.1530 - 6.686 \times 10^{-3}$
$[\text{CO}]_{\text{eq}} = 0.1463 \, \text{M}$
The equilibrium concentration of CO is:
$\boxed{0.146 \, \text{M}}$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

1. The reaction is at equilibrium at 1000 K.2. The equilibrium constant Kc K_c Kc​ for the reaction is 255.3. The initial concentration of CO is 0.1530 M.4. The initial concentration of Cl2 \text{Cl}_2 Cl2​ is 0.172 M.5. We need to find the equilibrium concentration of CO.

STEP 2

1. Write the balanced chemical equation.2. Set up the expression for the equilibrium constant.3. Define the change in concentration using an ICE table.4. Solve for the equilibrium concentration of CO.

STEP 3

Write the balanced chemical equation for the reaction:CO(g)+Cl2(g)⇌COCl2(g) \text{CO(g)} + \text{Cl}_2\text{(g)} \rightleftharpoons \text{COCl}_2\text{(g)} CO(g)+Cl2​(g)⇌COCl2​(g)

STEP 4

Set up the expression for the equilibrium constant Kc K_c Kc​:Kc=[COCl2][CO][Cl2] K_c = \frac{[\text{COCl}_2]}{[\text{CO}][\text{Cl}_2]} Kc​=[CO][Cl2​][COCl2​]​

STEP 5

STEP 6

Substitute the equilibrium concentrations into the equilibrium constant expression and solve for x x x:255=x(0.1530−x)(0.172−x) 255 = \frac{x}{(0.1530 - x)(0.172 - x)} 255=(0.1530−x)(0.172−x)x​

STEP 7

STEP 8

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The reaction is at equilibrium at 1000 K.
2. The equilibrium constant $K_c$ for the reaction is 255.
3. The initial concentration of CO is 0.1530 M.
4. The initial concentration of $\text{Cl}_2$ is 0.172 M.
5. We need to find the equilibrium concentration of CO.

1. Write the balanced chemical equation.
2. Set up the expression for the equilibrium constant.
3. Define the change in concentration using an ICE table.
4. Solve for the equilibrium concentration of CO.

Write the balanced chemical equation for the reaction:
$\text{CO(g)} + \text{Cl}_2\text{(g)} \rightleftharpoons \text{COCl}_2\text{(g)}$

Set up the expression for the equilibrium constant $K_c$ :
$K_c = \frac{[\text{COCl}_2]}{[\text{CO}][\text{Cl}_2]}$

Substitute the equilibrium concentrations into the equilibrium constant expression and solve for $x$ :
$255 = \frac{x}{(0.1530 - x)(0.172 - x)}$