Calculate - H -of solution obtained by mixing equal volume of 0-02 M HNO 2 a weak acid and 0-2 M CH 3 COOH solution- Given that-K a 1 HNO 2-2 - 10-4K a 2 CH 3 COOH -2 - 10-5Where- K a 1 and K a 2 are the dissociation constants of HNO 2 and CH 3 COOH respectively-A- 2 - 10-3 MB- 4 - 10-4 M- 6 - 10-3 MD- 8 - 10-4 M

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Factors Affecting Alpha

Calculate [ H...

Question

Calculate $[H^{+}]$ of solution obtained by mixing equal volume of 0.02 M $H N O_{2}$ ( a weak acid) and 0.2 M $C H_{3} C O O H$ solution.
Given that:
$K_{a_{1}} (H N O_{2}) = 2 \times 10^{- 4}$
$K_{a_{2}} (C H_{3} C O O H) = 2 \times 10^{- 5}$
Where , $K_{a_{1}} a n d K_{a_{2}}$ are the dissociation constants of $H N O_{2} a n d C H_{3} C O O H$ respectively.

2 \times 10^{- 3} M

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4 \times 10^{- 4} M

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6 \times 10^{- 3} M

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8 \times 10^{- 4} M

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2 \times 10^{- 3} M$
Denoting a for $H N O_{2}$ and b for $C H_{3} C O O H$ .
Let the equal volumes of solution a and b as V , i.e. $V_{a} = V_{b} = V$
So, $C_{1} = \frac{C_{a} V_{a}}{V_{a} + V_{b}} = \frac{0.02 \times V}{V + V} C_{1} = 0.01 M$
Similarly, $C_{2} = \frac{C_{b} \times V_{b}}{V_{a} + V_{b}} = \frac{0.2 \times V}{V + V} C_{2} = 0.1 M$
Now,
$\begin{matrix} H N O_{2} (a q) & ⇌ & H^{+} (a q) & + & N O_{2}^{-} (a q) C_{1} (1 - α_{1}) & C_{1} α_{1} + C_{2} α_{2} & C_{1} α_{1} \end{matrix}$
$[N O_{2}^{-}] = C_{1} α_{1} = 0.01 \times 10^{- 1} = 1 \times 10^{- 3}$
$\begin{matrix} C H_{3} C O O H & ⇌ & H^{+} & + & C H_{3} C O O^{-} C_{2} (1 - α_{2}) & C_{1} α_{1} + C_{2} α_{2} & C_{2} α_{2} \end{matrix}$

Dissociation constant for $H N O_{2}$ i.e. $K_{a_{1}}$ :
$K_{a_{1}} = \frac{(C_{1} α_{1} + C_{2} α_{2}) (C_{1} α_{1})}{C_{1} (1 - α_{1})}$

Dissociation constant for $C H_{3} C O O H$ i.e. $K_{a_{2}}$ :
$K_{a_{2}} = \frac{(C_{1} α_{1} + C_{2} α_{2}) (C_{2} α_{2})}{C_{2} (1 - α_{2})}$
Since, both are weak acids so $α_{1} a n d α_{2}$ are very small in comparison to unity for weak monoprotic acids. So $1 - α_{1} \approx 1 a n d 1 - α_{2} \approx 1$ .
$C_{1} K_{a_{1}} + C_{2} K_{a_{2}} = (C_{1} α_{1} + C_{2} α_{2})^{2}$
$[H^{+}] = C_{1} α_{1} + C_{2} α_{2} = \sqrt{C_{1} K_{a_{1}} + C_{2} K_{a_{2}}}$

$[H^{+}] = \sqrt{K_{a_{1}} C_{1} + K_{a_{2}} C_{2}} = \sqrt{2 \times 10^{- 4} \times 0.01 + 2 \times 10^{- 5} \times 0.1} [H^{+}] = \sqrt{2 \times 10^{- 6} + 2 \times 10^{- 6}} [H^{+}] = 2 \times 10^{- 3} M$

Suggest Corrections

Similar questions

Q. Calculate

[H^{+}]

of solution obtained by mixing equal volume of 0.02 M

H N O_{2}

( a weak acid) and 0.2 M

C H_{3} C O O H

solution.
Given that:

K_{a_{1}} (H N O_{2}) = 2 \times 10^{- 4}

K_{a_{2}} (C H_{3} C O O H) = 2 \times 10^{- 5}

Where ,

K_{a_{1}} a n d K_{a_{2}}

are the dissociation constants of

H N O_{2} a n d C H_{3} C O O H

respectively.

Q. Calculate the ratio

\frac{α_{1}}{α_{2}}

of a solution obtained by mixing equal volume of 0.02 M

H O C l

( a weak acid) and 0.2 M

C H_{3} C O O H

solution.
where,

α_{1}

is the degree of dissociation of

H O C l

α_{2}

is the degree of dissociation of

C H_{3} C O O H

Given that:

K_{a_{1}} (H O C l) = 2 \times 10^{- 7}

K_{a_{1}} (C H_{3} C O O H) = 2 \times 10^{- 5}

Q. Calculate the ratio

\frac{α_{1}}{α_{2}}

of a solution obtained by mixing equal volume of 0.02 M

H O C l

( a weak acid) and 0.2 M

C H_{3} C O O H

solution.
where,

α_{1}

is the degree of dissociation of

H O C l

α_{2}

is the degree of dissociation of

C H_{3} C O O H

Given that:

K_{a_{1}} (H O C l) = 2 \times 10^{- 7}

K_{a_{1}} (C H_{3} C O O H) = 2 \times 10^{- 5}

Q. Calculate the degree of dissociation

(α_{1})

, in a solution obtained by mixing equal volume of 0.02 M AOH and 0.2 M BOH solution.
Where,

α_{1}

is the degree of dissociation of weak base AOH and

α_{2}

is the degree of dissociation of weak base BOH.
Given that,

K_{b} (A O H) = 1 \times 10^{- 8} M

K_{b} (B O H) = 2 \times 10^{- 9} M

Q. Calculate the pH of a solution obtained by mixing equal volume of 0.02M HOCl & 0.2M

{C H}_{3} C O O H

solutions.

Given that

K_{a} (H O C l) = 2 \times 10^{- 4}

and

K_{a} (C H_{3} C O O H) = 2 \times 10^{- 5}

Join BYJU'S Learning Program

Explore more

Factors Affecting Alpha

Standard XII Chemistry

Join BYJU'S Learning Program

Calculate [H+] of solution obtained by mixing equal volume of 0.02 M HNO2 ( a weak acid) and 0.2 M CH3COOH solution. Given that: Ka1(HNO2)=2×10−4 Ka2(CH3COOH)=2×10−5 Where , Ka1and Ka2 are the dissociation constants of HNO2 and CH3COOH respectively.