Consider the equilibrium set up :
`2H_(2(g))+CO_((g))hArrCH_(3)OH_((g))`
What will be the effect of the following on the equilibrium of the reaction ?
(i) Addition of `H_(2)` (ii) Addition of `CH_(3)OH`
(iii) Removal of CO (iv) Removal of `CH_(3)OH`

Options

A. `{:(,(i),(ii),(iii),(iii)),((a),"Forward direction","Backward direction","Backward direction","Forward direction"):}`
B. `{:(,(i),(ii),(iii),(iii)),((a),"Backward direction","Backward direction","Forward direction","Forward direction"):}`
C. `{:(,(i),(ii),(iii),(iii)),((a),"Forward direction","Forward direction","Backward direction","Backward direction"):}`
D. `{:(,(i),(ii),(iii),(iii)),((a),"Backward direction","Forward direction","Forward direction","Backward direction"):}`

Explanation

To analyze the effects of various changes on the equilibrium of the reaction:

\[ 2H_{2(g)} + CO_{(g)} \rightleftharpoons CH_{3}OH_{(g)} \]

we will apply Le Chatelier's principle, which states that if an external change is applied to a system at equilibrium, the system will adjust itself to counteract that change and restore a new equilibrium.

### Step-by-Step Solution:

**(i) Addition of \( H_2 \)**

1. **Identify the change**: Adding \( H_2 \) increases its concentration.
2. **Apply Le Chatelier's principle**: The system will respond by favoring the forward reaction to consume the added \( H_2 \).
3. **Effect on equilibrium**: The equilibrium will shift to the right, producing more \( CH_3OH \).

**(ii) Addition of \( CH_3OH \)**

1. **Identify the change**: Adding \( CH_3OH \) increases the concentration of the product.
2. **Apply Le Chatelier's principle**: The system will respond by favoring the reverse reaction to consume the added \( CH_3OH \).
3. **Effect on equilibrium**: The equilibrium will shift to the left, producing more \( H_2 \) and \( CO \).

**(iii) Removal of \( CO \)**

1. **Identify the change**: Removing \( CO \) decreases its concentration.
2. **Apply Le Chatelier's principle**: The system will respond by favoring the forward reaction to produce more \( CO \).
3. **Effect on equilibrium**: The equilibrium will shift to the right, producing more \( CH_3OH \).

**(iv) Removal of \( CH_3OH \)**

1. **Identify the change**: Removing \( CH_3OH \) decreases its concentration.
2. **Apply Le Chatelier's principle**: The system will respond by favoring the forward reaction to produce more \( CH_3OH \).
3. **Effect on equilibrium**: The equilibrium will shift to the right, producing more \( CH_3OH \).

### Summary of Effects on Equilibrium:

- **Addition of \( H_2 \)**: Shifts equilibrium to the right (producing more \( CH_3OH \)).
- **Addition of \( CH_3OH \)**: Shifts equilibrium to the left (producing more \( H_2 \) and \( CO \)).
- **Removal of \( CO \)**: Shifts equilibrium to the right (producing more \( CH_3OH \)).
- **Removal of \( CH_3OH \)**: Shifts equilibrium to the right (producing more \( CH_3OH \)).