Question

What volume of 0.2 M $N{H}_{4}Cl$ solution should be added to 100 ml of 0.1 M $N{H}_{4}OH$ solution to produce a buffer solution of $pH=8.7$?
Given : $p{K}_{b}ofN{H}_{4}OH=4.7;\text{antilog (0.6)}=4$

• A. 50 ml
• B. 100 ml
• C. 200 ml
• D. None of the above

Answer 1

The correct option is C 200 ml

Given: $pH=8.7,p{K}_b\left(N{H}_{4}OH\right)=4.7$
$\Rightarrow pOH=14-8.7=5.3$
Now Henderson equation for basic buffer is
$\Rightarrow pOH=p{K}_b+log\frac{\left[\text{Salt}\right]}{\left[\text{Base}\right]}$
$\Rightarrow pOH-p{K}_b=log\frac{\left[\text{Salt}\right]}{\left[\text{Base}\right]}\Rightarrow 5.3-4.7=log\frac{\left[\text{Salt}\right]}{\left[\text{Base}\right]}\Rightarrow 0.6=log\frac{\left[\text{Salt}\right]}{\left[\text{Base}\right]}$

$\Rightarrow \frac{\text{mmoles of salt}}{\text{mmoles of base}}=4$
If volume of salt = V ml
$\Rightarrow \frac{V\times 0.2}{100\times 0.1}=4$
$\Rightarrow V=200ml$