ChemistryOne litre of water contains 10-7 moles of H+ ions. Degree of ionisation of water (in percentage) is

One litre of water contains 10^-7 moles of H⁺ ions. Degree of ionisation of water (in percentage) is

A
$large 1.8, times {10^{ - 7}}$
B
$1.8, times {10^{ - 9}}$
C
$3.6, times {10^{ - 7}}$
D
$3.6, times {10^{ - 9}}$

Solution:

[H⁺] = 10^-7M = C₀α

large {H_2}Oleft( ell right) rightleftharpoons {H^ + }left( {aq} right) + O{H^ - }left( {aq} right)

t=t_eq C₀ - C₀α C₀α C₀α

large {K_i} = frac{{{C_0}{alpha ^2}}}{{1 - alpha }} sim{C_0}{alpha ^2}left[ {alpha < < < 1} right]

large {alpha} = sqrt{frac{K_i}{C_0}}

K_i (dissociation constant of water) can be expressed as

large {H_2}Oleft( ell right) rightleftharpoons {H^ + }left( {aq} right) + O{H^ - }left( {aq} right)

large {K_i} = frac{{left[ {{H^ + }} right]left[ {O{H^ - }} right]}}{{left[ {{H_2}O} right]}} = frac{{{K_w}}}{{55.55M}}

large {K_i} = frac{{{{10}^{ - 14}}{M^2}}}{{55.55M}} = 1.8 times {10^{ - 16}}M

Concentration of pure water at 25^oC is constant and equal to 55.55 M.

K_i = 1.8 $\times$ 10^-16

large alpha = sqrt {frac{{1.8 times {{10}^{ - 16}}}}{{55.55}}} = 0.18 times {10^{ - 8}} = 1.8 times {10^{ - 9}}

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