Given : Enthalpy of ioinization of two acids :
`triangleH^(@)(HCN)=45.2 KJ mol^(-)`
`triangleH^(@)(CH_(3)COOH)=2.1 KJ mol^(-)`
which relationshop for the two acids is true ?

Options

A. `pK_(a)(HCN)=pK_(a)(CH_(3)COOH)`
B. `pK_(a)(HCN)gtpK_(a)(CH_(3)COOH)`
C. `pK_(a)(HCN)ltpK_(a)(CH_(3)COOH)`
D. `pK_(a)(HCN)=(45.2)/(2.1)pK_(a)(CH_(3)COOH)`

Answer

To determine the relationship between the two acids HCN (hydrocyanic acid) and CH₃COOH (acetic acid) based on their enthalpy of ionization, we can follow these steps:

### Step 1: Understand the Concept of Enthalpy of Ionization
The enthalpy of ionization (ΔH) is the energy required to dissociate an acid into its ions. A lower enthalpy of ionization indicates that the acid is stronger because it requires less energy to ionize, while a higher enthalpy indicates a weaker acid.

### Step 2: Compare the Given Enthalpies
We are given:
- ΔH°(HCN) = 45.2 kJ/mol
- ΔH°(CH₃COOH) = 2.1 kJ/mol

### Step 3: Analyze the Values
Since the enthalpy of ionization for HCN (45.2 kJ/mol) is significantly higher than that for acetic acid (2.1 kJ/mol), we can conclude that:
- HCN requires more energy to ionize compared to acetic acid.
- Therefore, HCN is a weaker acid than acetic acid.

### Step 4: Relate to pKa Values
The strength of an acid can also be related to its pKa value:
- A stronger acid has a lower pKa value.
- A weaker acid has a higher pKa value.

Since HCN is a weaker acid than acetic acid, it will have a higher pKa value compared to acetic acid.

### Step 5: Conclusion
Based on the analysis, we can conclude:
- The pKa of HCN > pKa of CH₃COOH.

Thus, the correct relationship is that HCN is a weaker acid than acetic acid, which means its pKa value is greater than that of acetic acid.

### Final Answer
**The relationship that is true for the two acids is: pKa (HCN) > pKa (CH₃COOH).**

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