HCN is a weak acid `(K_a=6.2xx10^(-10)).NH_4` OH is a weak base `(K_b=1.8xx10^(-5)).` A 1 M solution of `NH_4CN` would be

Options

A. strongly acidic
B. weakly acidic
C. neutral
D. weakly basic

Answer

To determine the nature of a 1 M solution of NH₄CN, we need to analyze the weak acid (HCN) and the weak base (NH₄OH) that are formed from its components. Here is a step-by-step solution:

### Step 1: Identify the components of NH₄CN
NH₄CN dissociates in water to form NH₄⁺ (ammonium ion) and CN⁻ (cyanide ion).

### Step 2: Determine the properties of NH₄⁺ and CN⁻
- NH₄⁺ is the conjugate acid of NH₃ (ammonia) and can donate protons, making it a weak acid.
- CN⁻ is the conjugate base of HCN (hydrogen cyanide) and can accept protons, making it a weak base.

### Step 3: Calculate the pKa of HCN
Given \( K_a \) for HCN is \( 6.2 \times 10^{-10} \):
\[ pK_a = -\log(K_a) = -\log(6.2 \times 10^{-10}) \approx 9.2 \]

### Step 4: Calculate the pKb of NH₄OH
Given \( K_b \) for NH₄OH is \( 1.8 \times 10^{-5} \):
\[ pK_b = -\log(K_b) = -\log(1.8 \times 10^{-5}) \approx 4.74 \]

### Step 5: Calculate pKw
The value of \( pK_w \) at 25°C is 14:
\[ pK_w = 14 \]

### Step 6: Calculate the pH of the solution
Using the formula for pH of a solution containing both a weak acid and a weak base:
\[ pH = \frac{1}{2} (pK_w + pK_a - pK_b) \]
Substituting the values:
\[ pH = \frac{1}{2} (14 + 9.2 - 4.74) = \frac{1}{2} (18.46) \approx 9.23 \]

### Step 7: Determine the nature of the solution
Since the calculated pH (9.23) is greater than 7, the solution is basic. Therefore, a 1 M solution of NH₄CN is a weakly basic solution.

### Final Answer
The 1 M solution of NH₄CN would be weakly basic.

---