The Kb for the nitrite ion (NO2 - (aq) is expressed as a.b x 10-cd. The values for a, b, c, and d are

To determine the values for \(a\), \(b\), \(c\), and \(d\) in the expression for the base dissociation constant (\(K_b\)) of the nitrite ion (\( \text{NO}_2^- \)), we can use the relationship between the base dissociation constant \(K_b\) and the acid dissociation constant \(K_a\) of the conjugate acid. 

The conjugate acid of \(\text{NO}_2^-\) is nitrous acid (\(\text{HNO}_2\)). The relationship between \(K_a\) and \(K_b\) is given by:

\[
K_a \times K_b = K_w
\]

Where \(K_w\) is the ionization constant of water, which is \(1.0 \times 10^{-14}\) at 25°C.

### Step 1: Find the \(K_a\) for \(\text{HNO}_2\).
The \(K_a\) value for nitrous acid (\(\text{HNO}_2\)) is commonly known and can be found in tables of acid dissociation constants. It is approximately:

\[
K_a = 4.5 \times 10^{-4}
\]

### Step 2: Calculate \(K_b\) for \(\text{NO}_2^-\).
Using the relationship \(K_a \times K_b = K_w\):

\[
K_b = \frac{K_w}{K_a} = \frac{1.0 \times 10^{-14}}{4.5 \times 10^{-4}}
\]

Now, let's calculate \(K_b\):

\[
K_b = \frac{1.0 \times 10^{-14}}{4.5 \times 10^{-4}} = 2.22 \times 10^{-11}
\]

### Step 3: Identify the values of \(a\), \(b\), \(c\), and \(d\).

In the expression \(a.b \times 10^{-cd}\), we have:

\[
K_b = 2.22 \times 10^{-11}
\]

Thus:
- \(a = 2\),
- \(b = 2\),
- \(c = 1\), and
- \(d = 1\).

So, the values are \(a = 2\), \(b = 2\), \(c = 1\), \(d = 1\).

Would you like further details on this calculation or have any other questions?

Here are some related questions:
1. How do the values of \(K_a\) and \(K_b\) relate to the strength of acids and bases?
2. Why is \(K_w\) temperature-dependent?
3. What is the significance of the \(pK_a\) value in acid-base chemistry?
4. How does the conjugate base's \(K_b\) affect the pH of a solution?
5. Can you explain how to determine \(K_b\) for polyprotic acids?

**Tip:** Always remember that strong acids have weak conjugate bases with very small \(K_b\) values and vice versa.

Learn how to calculate the base dissociation constant (Kb) for the nitrite ion (NO2-) in aqueous solution using the relationship between the acid dissociation constant (Ka) of its conjugate acid (nitrous acid) and the ionization constant of water (Kw). Step-by-step calculation provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation