Consider the reaction `2CO(g)+O_(2)(g)hArr2CO_(2)(g)+Heat`
Under what conditions shift is undeterminable ?

Options

A. Addition of `O_(2)` and decrease in volume
B. Addition of CO and removal of `CO_(2)` at constant volume
C. Increase in temperature and decrease in volume
D. Addition of CO and increase in temperature at constant volume

Answer

To determine the conditions under which the shift in the equilibrium of the reaction

\[ 2CO(g) + O_2(g) \rightleftharpoons 2CO_2(g) + \text{Heat} \]

is undeterminable, we will analyze the effects of various changes on the equilibrium position according to Le Chatelier's principle.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
- The reaction involves the conversion of carbon monoxide (CO) and oxygen (O₂) into carbon dioxide (CO₂) with the release of heat. This is an exothermic reaction.

2. **Identifying the Factors Affecting Equilibrium**:
- According to Le Chatelier's principle, if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the equilibrium will shift in a direction that counteracts the change.

3. **Analyzing Each Condition**:
- **Condition 1**: Addition of oxygen and decrease in volume.
- Adding oxygen increases the concentration of reactants, shifting the equilibrium to the right (towards products).
- Decreasing volume shifts the equilibrium towards the side with fewer moles of gas (from 3 moles on the left to 2 moles on the right).
- Both changes favor the formation of products, making the shift determinable.

- **Condition 2**: Addition of carbon monoxide and removal of carbon dioxide at constant volume.
- Adding CO increases reactant concentration, shifting equilibrium to the right.
- Removing CO₂ decreases product concentration, shifting equilibrium to the right.
- Both changes favor product formation, making the shift determinable.

- **Condition 3**: Increase in temperature and decrease in volume.
- Increasing temperature for an exothermic reaction shifts the equilibrium to the left (towards reactants).
- Decreasing volume shifts the equilibrium to the right (towards products).
- These changes are contradictory, making the shift undeterminable.

- **Condition 4**: Addition of CO and increase in temperature at constant volume.
- Adding CO shifts the equilibrium to the right (towards products).
- Increasing temperature shifts the equilibrium to the left (towards reactants).
- These changes are also contradictory, making the shift undeterminable.

4. **Conclusion**:
- The conditions under which the shift is undeterminable are:
- **Condition 3**: Increase in temperature and decrease in volume.
- **Condition 4**: Addition of CO and increase in temperature at constant volume.

### Final Answer:
The shift in equilibrium is undeterminable under the following conditions:
- Increase in temperature and decrease in volume.
- Addition of CO and increase in temperature at constant volume.