Two reactions are given below :
(i) `CO_((g))+(1)/(2)O_(2(g))rarrCO_(2(g))`
(ii) `Ag_(2)O_((s)) rarr 2Ag_((s))+(1)/(2)O_(2(g))`
Which of the following statements is true ?

Options

A. For (i) `DeltaH lt DeltaU` and for (ii) `DeltaH gt DeltaU`
B. For (i) `DeltaH gt DeltaU` and for (ii) `DeltaH lt DeltaU`
C. For both (i) and (ii) `DeltaH gt DeltaU`
D. For both (i) and (ii) `DeltaH lt DeltaU`

Explanation

To determine the correct relationship between ΔH (enthalpy change) and ΔU (internal energy change) for the given reactions, we will use the equation:

\[ \Delta H = \Delta U + n_g RT \]

where \(n_g\) is the change in the number of moles of gas, \(R\) is the universal gas constant, and \(T\) is the temperature in Kelvin.

### Step 1: Analyze Reaction 1

The first reaction is:

\[ CO_{(g)} + \frac{1}{2} O_{2(g)} \rightarrow CO_{2(g)} \]

**Calculate \(n_g\)**:

- **Products**: 1 mole of \(CO_2\) (gaseous)
- **Reactants**: 1 mole of \(CO\) + \(\frac{1}{2}\) mole of \(O_2\) = \(1 + \frac{1}{2} = \frac{3}{2}\) moles of gas

Thus,

\[ n_g = \text{moles of products} - \text{moles of reactants} = 1 - \frac{3}{2} = -\frac{1}{2} \]

**Substituting into the equation**:

\[ \Delta H = \Delta U + \left(-\frac{1}{2}\right) RT \]

This implies:

\[ \Delta H = \Delta U - \frac{1}{2} RT \]

From this, we can conclude:

\[ \Delta H < \Delta U \]

### Step 2: Analyze Reaction 2

The second reaction is:

\[ Ag_2O_{(s)} \rightarrow 2Ag_{(s)} + \frac{1}{2} O_{2(g)} \]

**Calculate \(n_g\)**:

- **Products**: \(\frac{1}{2}\) mole of \(O_2\) (gaseous)
- **Reactants**: 0 moles of gas (since \(Ag_2O\) is solid)

Thus,

\[ n_g = \text{moles of products} - \text{moles of reactants} = \frac{1}{2} - 0 = \frac{1}{2} \]

**Substituting into the equation**:

\[ \Delta H = \Delta U + \left(\frac{1}{2}\right) RT \]

This implies:

\[ \Delta H = \Delta U + \frac{1}{2} RT \]

From this, we can conclude:

\[ \Delta H > \Delta U \]

### Conclusion

For the two reactions, we have determined:

1. For Reaction 1: \(\Delta H < \Delta U\)
2. For Reaction 2: \(\Delta H > \Delta U\)

Thus, the correct statement is:

**Option A**: For Reaction 1, \(\Delta H\) is less than \(\Delta U\) and for Reaction 2, \(\Delta H\) is greater than \(\Delta U\).