# The number of hydroxyl ions in 10cm3 of 0.2M HCl solution is 1)5×10^-4 2)3×10^8 3)3×10^12 4)5×10^-12

To solve this, we need to find the number of moles of hydroxyl ions. To find that, we need to find the concentration of hydroxyl ions.

Now,

HCl is a strong acid. So it dissociates completely.

$So,\phantom{\rule{0ex}{0ex}}\left[{H}^{+}\right]=0.2M\phantom{\rule{0ex}{0ex}}pH=-\mathrm{log}\left[{H}^{+}\right]=0.6989\phantom{\rule{0ex}{0ex}}p{K}_{w}=pH+pOH\phantom{\rule{0ex}{0ex}}pOH=14-0.6989\phantom{\rule{0ex}{0ex}}pOH=13.3012=-\mathrm{log}\left[O{H}^{-}\right]\phantom{\rule{0ex}{0ex}}So,\left[O{H}^{-}\right]=anti\mathrm{log}[-13.3012]=4.98x{10}^{-14}M\phantom{\rule{0ex}{0ex}}Now,MolarityofO{H}^{-}ions=4.98x{10}^{-14}M\phantom{\rule{0ex}{0ex}}Volume=10c{m}^{3}=10ml=0.01L\phantom{\rule{0ex}{0ex}}So,\phantom{\rule{0ex}{0ex}}Numberofmoles=MolarityxVolume=4.98x{10}^{-14}x{10}^{-2}=4.98x{10}^{-12}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}So,numberofions=numberofmolesx{N}_{A}=4.98x{10}^{-12}x6.022x{10}^{23}=29.989x{10}^{11}=2.99x{10}^{12}\approx 3x{10}^{12}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

Thus, the number of hydroxyl ions is 3 x 10

^{12}.

Thus, the correct answer is option (3)

Hope it helps.

Regards

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