Carbon dioxide and water react to form methanol and oxygen, like this: 2 CO2(9)+4 H,O(g)→2 CH;OH(1)+3 0,(g) At a certain temperature, a chemist finds that a 7.5 L reaction vessel containing a mixture of carbon dioxide, water, methanol, and oxygen at equilibrium has the following composition: compound amount CO2 2.24 g H,O 4.82 g CH; OH 4.11 g O2 2.03 g Calculate the value of the equilibrium constant K, for this reaction. Round your answer to 2 significant digits. K = 0

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### Reaction Equilibrium and K\(_c\) Calculation

**Carbon dioxide and water react to form methanol and oxygen, as shown in the balanced chemical equation:**

\[ 2 \text{CO}_2(g) + 4 \text{H}_2\text{O}(g) \rightarrow 2 \text{CH}_3\text{OH}(l) + 3 \text{O}_2(g) \]

At a certain temperature, a chemist finds that a 7.5 L reaction vessel containing a mixture of carbon dioxide, water, methanol, and oxygen at equilibrium has the following composition:

| compound | amount |
|----------|-------------|
| CO\(_2\)  | 2.24 g      |
| H\(_2\)O  | 4.82 g      |
| CH\(_3\)OH | 4.11 g     |
| O\(_2\)  | 2.03 g      |

Calculate the value of the equilibrium constant \(K_c\) for this reaction. Round your answer to 2 significant digits.

\[ K_c = \]

**Interactive Interface:**

An input box is provided for entering the value of \(K_c\). Additional options are available for users to ensure their calculations are correct or to seek hints if needed.

### Details:

To calculate \(K_c\), we would convert the given masses of the substances to moles, determine their concentrations by dividing by the volume of the reaction vessel, and plug these values into the equilibrium expression.
Transcribed Image Text:### Reaction Equilibrium and K\(_c\) Calculation **Carbon dioxide and water react to form methanol and oxygen, as shown in the balanced chemical equation:** \[ 2 \text{CO}_2(g) + 4 \text{H}_2\text{O}(g) \rightarrow 2 \text{CH}_3\text{OH}(l) + 3 \text{O}_2(g) \] At a certain temperature, a chemist finds that a 7.5 L reaction vessel containing a mixture of carbon dioxide, water, methanol, and oxygen at equilibrium has the following composition: | compound | amount | |----------|-------------| | CO\(_2\) | 2.24 g | | H\(_2\)O | 4.82 g | | CH\(_3\)OH | 4.11 g | | O\(_2\) | 2.03 g | Calculate the value of the equilibrium constant \(K_c\) for this reaction. Round your answer to 2 significant digits. \[ K_c = \] **Interactive Interface:** An input box is provided for entering the value of \(K_c\). Additional options are available for users to ensure their calculations are correct or to seek hints if needed. ### Details: To calculate \(K_c\), we would convert the given masses of the substances to moles, determine their concentrations by dividing by the volume of the reaction vessel, and plug these values into the equilibrium expression.
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