# Hydrazine (N 2 H 4 ) is like CO 3 2− in that it is a polyprotic base ( K b1 = 85 × 10 −7 and K b2 = 8.9 × 10 −16 ) . The two conjugate acids are N 2 H 5 + and N 2 H 6 2+ . What is the expected pH of a 0.025 M solution of N 2 H 4 ? (a) 3.83 (b) 8.32 (c) 10.16

### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

Chapter
Section

### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 16.8, Problem 1RC
Textbook Problem
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## Hydrazine (N2H4) is like CO32− in that it is a polyprotic base (Kb1 = 85 × 10−7 and Kb2 = 8.9 × 10−16). The two conjugate acids are N2H5+ and N2H62+. What is the expected pH of a 0.025 M solution of N2H4? (a) 3.83 (b) 8.32 (c) 10.16

Interpretation Introduction

Interpretation:

The hydrazine (N2H4) pH range should be calculate and identified using the Kb values for respective statements. Concept introduction:

pKa: It is introduced as an index to express the acidity of weak acids, where pKa is defined as fallows, we consider the Ka constant for acetic acid 1.8×105(pKa) but pKa constant for is 4.8 which is a simpler expression. Furthermore the smaller pKa value has strongest acid.

An acid-base reaction reaction is represented as written below.

HA(aq)+B(aq)   BH+(aq)  +    A(aq)(acid)    (base)        (conjugate     acid)   (conjugate     base)

pH concept of hydronium ions: A strong acid completely dissociates into its constituent ions in aqueous solution, as a result, the concentration of its ion is same as the initial concentration of that strong acid.

For example, strong acid dissociates as follows in water,

HA(aq)+H2O(l)H3O+(aq)+A(aq)

[H3O+]=[A]=[HA]

The pH of a solution is basically the measure of the molar concentration of the H+ or H3O+ ion in the solution. More the concentration of H+ or H3O+ ion in the solution, lesser will be the pH value and more acidic will be the solution.

The expression for pH is given as,

pH=log[H3O+]

The concentration of OH ions is calculated by using the ionic product of water.

Kw=[H3O+][OH]

The value of Kw is 1.0×1014 .

If pH<7 then, the solution is acidic in nature.

If pH<7 then, the solution is basic in nature.

If pH<7 then, the solution is neutral in nature.

### Explanation of Solution

The value of pH for hydrazine ion (N2H4) solution 10.16 and the concentration of ion in the solution is calculated below.

Given

The initial concentration of (N2H4) solution is 0.025 M .

Method 1:

N2H4 is a week acid it bomes a stong base and it dissociates as follows in water,

N2H4(aq)+H2O(l)N2H5+(aq)+OH(aq)

The ICE table is as follows,

EquilibriumN2H4(aq)+H2O(l)N2H5+(aq)+OH(aq)Initial(M)0.02500Change(M)x+x+xEquilibrium(M)(0.025x)xx

TheequilibriumexpressionshownbelowKa=[N2H5+][OH][N2H4][1]GivenKb1valueofN2H4=8.5×107Thisvaluehassubstitutedaboveequation8.5×107=[x][x][0.025x]Hence(0.025x)=(0.025)8.5×107=[x][x][0.025]=[x]2[0.025]x2=[0.025]×8.5×107TakingforsquarerootforbothsidesX=2.125×108X=1.457×104MTheconcentrationofhydrazineion(N2H5+)=1.457×104M

Using this value of [OH-] you can calculate the (pOH) of the solution

Theconcentreationof(N2H5+)=1.457×104HencepOH=log[N2H5+]=log[1.46×104]pOH=3.83andtherelationshippH+pOH=14tocalaculatethepH

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