Question

Number of hydrogen ions present in $10millio{n}^{th}$ part of $1.33c{m}^3$ of pure water at $25^{\circ }C$ is

• A. 6.023 million
• B. 60 million
• C. 8.01 million
• D. 80.23 million

Answer 1

Answer: (C)

10 million $=10^{-7}$
$\therefore 10$ million ${}^{\text{th }}$ part of $1.33c{m}^3$
$=1.33\times 10^{-7}c{m}^3$
For pure water, $$\begin{gathered} =1.33\times 10^{-7}mL \\ \left[H^{+}\right]=10^{-7}mol/L \end{gathered}$$
$\Rightarrow 1L$ water contains $H^{+}]=10^{-7}mol$
or $1mL$ water contains $\left[H^{+}\right]=\frac{10^{-7}}{1000}=10^{-10}mol$
or 10 million ${}^{\text{th }}$ part of $1\cdot 33c{m}^3$ water contains
$\left[H^{+}\right]=1\cdot 33\times 10^{-7}\times 10^{-10}mol$
$=1\cdot 33\times 10^{-17}mol$
$\therefore$ Number of $H^{+}$ions
$=1.33\times 10^{-17}\times N_A$
$=1.33\times 10^{-17}\times 6.022\times 10^{23}$
$=8.009\times 10^6=8.01$ million