For a reaction `R_(1), Delta G = x KJ mol^(-1)`. For a reaction `R_(2), Delta G = y KJ mol^(-1)`. Reaction `R_(1)` is non-spontaneous but along with `R_(2)` it is spontaneous. This means that

Options

A. x is -ve, y is +ve but in magnitude `x gt y`
B. x is +ve, y is -ve but in magnitude `y gt x`
C. Both x and y are -ve but not equal
D. Both x and y +ve but not equal

Answer

To solve the problem, we need to analyze the conditions given for the reactions R1 and R2 in terms of their Gibbs free energy changes (ΔG).

### Step-by-Step Solution:

1. **Understanding Gibbs Free Energy (ΔG)**:
- For a reaction to be spontaneous, the Gibbs free energy change (ΔG) must be negative. If ΔG is positive, the reaction is non-spontaneous.

2. **Given Information**:
- For reaction R1, ΔG = x kJ/mol (non-spontaneous, hence x > 0).
- For reaction R2, ΔG = y kJ/mol (unknown spontaneity).

3. **Combining Reactions**:
- The problem states that R1 is non-spontaneous, but when combined with R2, the overall reaction becomes spontaneous. This means:
\[ \Delta G_{\text{total}} = \Delta G_{R1} + \Delta G_{R2} = x + y < 0 \]
- This implies that the sum of the ΔG values must be negative.

4. **Analyzing the Conditions**:
- Since R1 is non-spontaneous, we know x > 0.
- For the overall reaction to be spontaneous (x + y < 0), it follows that:
\[ y < -x \]
- This indicates that y must be negative and in magnitude greater than x.

5. **Conclusion**:
- From the analysis, we can conclude:
- x is positive (since R1 is non-spontaneous).
- y is negative and has a greater magnitude than x (since it must compensate for the positive x to make the total negative).
- Therefore, the correct option is:
- **x is positive, y is negative, and in magnitude, |y| > |x|**.

### Final Answer:
The correct conclusion is that **x is positive, y is negative, and |y| > |x|**.