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Equilibrium

Question
CBSEENCH11006544

Calculate the pH of a 1·0 × 10–8 M solution of HCl.

Solution
The [H3O+] is obtained from the following two ionisation reactions:
left parenthesis straight i right parenthesis space HCl space left parenthesis aq right parenthesis space plus space straight H subscript 2 straight O left parenthesis l right parenthesis space space rightwards harpoon over leftwards harpoon space space space straight H subscript 3 straight O to the power of plus left parenthesis aq right parenthesis space plus space OH to the power of minus left parenthesis aq right parenthesis
left parenthesis ii right parenthesis space 2 straight H subscript 2 straight O space rightwards harpoon over leftwards harpoon space space space space straight H subscript 3 straight O to the power of plus space left parenthesis aq right parenthesis space plus space OH to the power of minus left parenthesis aq right parenthesis
space space space therefore space space space From space acid semicolon space space space open square brackets straight H subscript 3 straight O to the power of plus close square brackets space equals space 10 to the power of negative 8 end exponent straight M
From space water semicolon space space open square brackets straight H subscript 3 straight O to the power of plus close square brackets space equals space open square brackets OH to the power of minus close square brackets space equals space straight x space mol space straight L to the power of negative 1 end exponent left parenthesis aq right parenthesis

Thus space in space solution comma space we space have
space space space space open square brackets straight H subscript 3 straight O to the power of plus close square brackets space equals space left parenthesis 10 to the power of negative 8 end exponent space plus space straight x right parenthesis space straight M space and space open square brackets OH to the power of minus close square brackets space equals space straight x space straight M
We know,
 open square brackets straight H subscript 3 straight O to the power of plus close square brackets space open square brackets OH to the power of minus close square brackets space equals straight K subscript straight w space equals space 10 to the power of negative 14 end exponent
<pre>uncaught exception: <b>Http Error #404</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 61<br />#0 [internal function]: com_wiris_plugin_impl_HttpImpl_0(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Http Error #404')
#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/php/Boot.class.php(769): call_user_func_array('com_wiris_plugi...', Array)
#2 [internal function]: _hx_lambda->execute('Http Error #404')
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(532): call_user_func_array(Array, Array)
#4 [internal function]: haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Http Error #404')
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/php/Boot.class.php(769): call_user_func_array('haxe_Http_5', Array)
#6 [internal function]: _hx_lambda->execute('Http Error #404')
#7 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(27): call_user_func_array(Array, Array)
#8 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Http Error #404')
#9 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), NULL, NULL)
#10 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(40): haxe_Http->request(true)
#11 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(80): com_wiris_plugin_impl_HttpImpl->request(true)
#12 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#13 {main}</pre>
straight i. straight e. space open square brackets OH to the power of minus close square brackets space equals space 9.5125 space cross times space 10 to the power of negative 8 end exponent straight M
or space space space space space space straight p subscript OH space equals space minus log space open square brackets OH to the power of minus close square brackets
space space space space space space space space space space space space space space space equals space minus log left parenthesis 9.5125 space cross times space 10 to the power of negative 8 end exponent right parenthesis
space space space space space space space space space space space space space space space equals space 8 minus 0.9783 space equals space 7.02
pH space equals space 14 minus space straight p subscript OH space equals 14 minus 7.02 space equals 6.98