Ratio `K_(p)//K_(c)` of the reaction `2 SO_(2) + O_(2)hArr 2 SO_(3) ` is equal to `……… .`

Answer

To find the ratio \( \frac{K_p}{K_c} \) for the reaction:

\[ 2 \text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2 \text{SO}_3(g) \]

we can use the relationship between \( K_p \) and \( K_c \):

\[ K_p = K_c \cdot R T^{\Delta N_g} \]

where:
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( \Delta N_g \) is the change in the number of moles of gas, calculated as:

\[ \Delta N_g = \text{moles of gaseous products} - \text{moles of gaseous reactants} \]

**Step 1: Identify the moles of gaseous products and reactants.**

In the given reaction:
- Moles of gaseous products (SO3) = 2
- Moles of gaseous reactants (SO2 + O2) = 2 + 1 = 3

**Step 2: Calculate \( \Delta N_g \).**

\[ \Delta N_g = \text{moles of products} - \text{moles of reactants} = 2 - 3 = -1 \]

**Step 3: Substitute \( \Delta N_g \) into the equation for \( K_p \).**

Using the relationship:

\[ K_p = K_c \cdot R T^{\Delta N_g} \]

we can express \( \frac{K_p}{K_c} \):

\[ \frac{K_p}{K_c} = R T^{\Delta N_g} \]

**Step 4: Substitute \( \Delta N_g \) into the ratio.**

Since \( \Delta N_g = -1 \):

\[ \frac{K_p}{K_c} = R T^{-1} = \frac{R}{T} \]

Thus, the ratio \( \frac{K_p}{K_c} \) for the reaction is:

\[ \frac{K_p}{K_c} = \frac{R}{T} \]

### Final Answer:
\[ \frac{K_p}{K_c} = \frac{R}{T} \]

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