The pH of a neutralized solution - Chemistry Stack Exchange most recent 30 from chemistry.stackexchange.com 2019-08-19T02:12:10Z https://chemistry.stackexchange.com/feeds/question/19808 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://chemistry.stackexchange.com/q/19808 9 The pH of a neutralized solution ahorn https://chemistry.stackexchange.com/users/9934 2014-11-21T08:34:01Z 2017-04-24T22:57:36Z <p>If pH is defined as the concentration of hydrogen ions in solution, then how can a ‘neutralized’ solution (defined as having an equal amount of hydrogen and hydroxide ions) have a pH other than 7?</p> <p><a href="http://en.wikipedia.org/wiki/Neutralization_(chemistry)" rel="nofollow noreferrer">Wikipedia</a> writes: “In a reaction in water, neutralization results in there being no excess of hydrogen or hydroxide ions present in solution.” In my mind, an equivalent amount of hydrogen ions and hydroxide ions means a pH of 7 (in water), but Wikipedia carries on to write: “The pH of the neutralized solution depends on the acid strength of the reactants.”</p> <p><a href="https://chemistry.stackexchange.com/questions/8048/shouldnt-the-ph-at-the-equivalence-point-always-be-7">This question</a> doesn’t seem to answer my question.</p> https://chemistry.stackexchange.com/questions/19808/-/19814#19814 10 Answer by Martin - マーチン for The pH of a neutralized solution Martin - マーチン https://chemistry.stackexchange.com/users/4945 2014-11-21T10:49:16Z 2017-04-24T22:57:36Z <p><strong>TL;DR</strong><br> The neutral point is not the same as the equivalence point.<br> A neutral aqueous solution at room temperature, $25~^\circ\mathrm{C}$ and standard pressure $1~\mathrm{atm}$, has always $\ce{pH}=7$.</p> <hr> <p>If you look for credible sources of definitions of neutral solutions on the internet, most likely you will find something along the lines of this: </p> <blockquote> <p>Neutral solution<br> (Science) Has a $\ce{pH}$ level of $7$: a solution in which the concentration of hydrogen ions and hydroxide ions are equal (<a href="http://www.biology-online.org/dictionary/Neutral_solution" rel="nofollow noreferrer">biology-online.org</a>)</p> </blockquote> <p>Or even worse:</p> <blockquote> <p>Neutral Solution Definition:<br> An aqueous solution with a $\ce{pH}$ of $7.0$ $(\ce{[H^{+}]} = 1.0 \times 10^{-7}~\mathrm{M})$. (<a href="http://chemistry.about.com/od/chemistryglossary/a/neutralsoldef.htm" rel="nofollow noreferrer">chemistry.about.com</a>)</p> </blockquote> <p>The second one especially is negligent of a lot of features.<br> Unfortunately the IUPAC does not provide an actual definition of a neutral solution. There are two possible definitions, which come to the same conclusion (compare the above), given the same external conditions.</p> <ol> <li>The lazy definition:<br> The concentrations of hydronium and hydroxide ions are identical. $$c(\ce{OH-})= c(\ce{H3O+})$$</li> <li>In terms of $\ce{pH}, \ce{pOH}, \mathrm{p}K_w$ one arrives at a more complete side.<br> Pure water is a neutral solution. It's autoprotolysis provides \begin{align} \ce{2H2O &amp;~&lt;=&gt;~ OH- + H3O+}.\tag{1}\\ \end{align} Now we can formulate the <a href="http://goldbook.iupac.org/E02177.html" rel="nofollow noreferrer">equilibrium constant</a> and furthermore assume that autoprotolysis is small compared to the overall concentration of water. \begin{align} K_c &amp;= \frac{c(\ce{OH-})\cdot c(\ce{H3O+})}{c^2(\ce{H2O})}\\ K_w &amp;= c(\ce{OH-})\cdot c(\ce{H3O+})\tag{2}\\ \end{align} Equation $(1)$ also provides the lazy definition. $$c(\ce{OH-})= c(\ce{H3O+})\tag3$$ We plug that into $(2)$ and we arrive at $$c(\ce{H3O+})=\sqrt{K_w}\tag{4}$$ Consider the actual <a href="http://goldbook.iupac.org/P04524.html" rel="nofollow noreferrer">definition</a> of $$\ce{pH} = −\lg a(\ce{H+}) = −\lg\left( m(\ce{H+}) \gamma_m(\ce{H+}) / m^\circ\right)\tag{5}$$ rewritten using concentrations $$\ce{pH} = −\lg a(\ce{H+}) = −\lg\left( c(\ce{H+}) \gamma_c(\ce{H+}) / c^\circ\right)\tag{5a}$$ The identities used here are $a(\ce{H+})$ for the activity of a proton in aqueous solution, $\ce{H+ (aq)}$ and we will consider $\ce{H+ (aq) = H3O+}$ to be the same. Now we are going to assume, that the activity coefficient is $\gamma_c(\ce{H+})\approx 1$ for very diluted systems. Using the <a href="http://goldbook.iupac.org/S05909.html" rel="nofollow noreferrer">standard concentration</a> $c^\circ$ we do not have to care about units. $$\ce{pH} = −\lg\left( \frac{c(\ce{H+})}{c^\circ}\right)\tag{5b}$$ Now we can substitute in $(4)$ and we will have a nice definition of the $\ce{pH}$ of a neutral solution. $$\ce{pH} = −\lg\left( \frac{\sqrt{K_w}}{c^\circ}\right)\tag{6}$$</li> </ol> <p>The second formulation includes a very crucial point. The autoprotolysis $(1)$ is temperature, $T$, dependent, which is obvious following the definition of the <a href="http://goldbook.iupac.org/S05915.html" rel="nofollow noreferrer">standard equilibrium constant</a> $$K^\circ = \exp\left\{\frac{-\Delta G^\circ}{\mathcal{R}T}\right\}\approx K_c.$$ Therefore also the ion product of water is temperature dependent, $K_w(T)$. <a href="http://en.wikipedia.org/wiki/Self-ionization_of_water#Dependence_on_temperature.2C_pressure_and_ionic_strength" rel="nofollow noreferrer">Wikipedia</a> actually has a couple of values for the $\mathrm{p}K_w$. Reaction $(1)$ is endothermic. A higher temperature means providing energy, means a higher $\mathrm{p}K_w$. For example, in the human body, $37~^\circ\mathrm{C}$, this value is slightly higher than for the one we usually assume as the "neutral point" $\mathrm{p}K_w(25~^\circ\mathrm{C})=14$.</p> <p>Since $(6)$ is more correct in the following form, $$\ce{pH}(T) = −\lg\left( \frac{\sqrt{K_w(T)}}{c^\circ}\right)\tag{6a},$$ the neutral $\ce{pH}(T)$ therefore changes with temperature.</p> <p>Another note is that it is also pressure dependent, but that might take it a little too far.</p> <p>The <a href="http://en.wikipedia.org/wiki/Equivalence_point" rel="nofollow noreferrer">equivalence point</a> is usually defined for an arbitrary chemical reaction between an acid and a base, and it refers to the situation where there are stoichiometric quantities of acid and base are present. $$\ce{AH + B &lt;=&gt;[\ce{H2O}] A^- + HB+}$$ This means, that at the equivalence point the following statement holds: $$c_\text{initial}(\ce{HA}) = c_\text{final}(\ce{HB+}).$$ Therefore the $\ce{pH}$ at the equivalence point will only be governed by the reactions of $\ce{HB+}$ and might not be neutral.</p> <hr> <p>The issue of solvent dependency is addressed by Fred Senese quite concise on <a href="http://antoine.frostburg.edu/chem/senese/101/acidbase/faq/what-is-pH.shtml" rel="nofollow noreferrer">antoine.frostburg.edu</a>:</p> <blockquote> <p>pH is often used to compare solution acidities. For example, a solution of pH 1 is said to be 10 times as acidic as a solution of pH 2, because the hydrogen ion concentration at pH 1 is ten times the hydrogen ion concentration at pH 2. This is correct as long as the solutions being compared both use the same solvent. You can't use pH to compare the acidities in different solvents because the neutral pH is different for each solvent. For example, the concentration of hydrogen ions in pure ethanol is about 1.58 × 10-10 M, so ethanol is neutral at pH 9.8. A solution with a pH of 8 would be considered acidic in ethanol, but basic in water!</p> </blockquote> https://chemistry.stackexchange.com/questions/19808/-/19828#19828 0 Answer by RE60K for The pH of a neutralized solution RE60K https://chemistry.stackexchange.com/users/5531 2014-11-21T17:40:04Z 2014-11-21T17:40:04Z <p>Simple contradiction is salt hydrolysis:</p> <p>The neutralization Reaction:</p> <blockquote> <p>$$\ce{CH3COOH +NaOH-&gt;CH3COONa + H2O}$$</p> </blockquote> <p>Now the following reaction happen due to low acidity of the acid, thus the reversible reaction a little favored:</p> <blockquote> <p>$$\ce{CH3COO- + H2O-&gt;CH3COOH + OH-}$$</p> </blockquote> <p>Though the reaction reaches equivalence/neutralization point, the solution will be little basic, as even though none, hydronium or hydroxyl ions, is in excess but one may become in excess with the advent of salt hydrolysis(kinda in situ).</p> https://chemistry.stackexchange.com/questions/19808/-/33777#33777 5 Answer by pH13 - Yet another Philipp for The pH of a neutralized solution pH13 - Yet another Philipp https://chemistry.stackexchange.com/users/16622 2015-07-09T15:27:16Z 2016-12-07T23:28:39Z <p>In addition to all other good answers, I'd like to actually <em>show</em> you why the "neutralized solution" is not equal to a neutral solution.</p> <p>Whenever we want to describe a neutralisation reaction (that is nothing else than a titration) we first need to find out where protons come from and where they go. Let's examine a simple titration of a monoprotic acid with a monoprotic base:</p> <p>$$c(\ce{H3O+})=c(\ce{OH-})+c(\ce{A-})-c(\ce{BH+})$$</p> <p>Protons come from the autoprotolysis of water and the acid residue anions and they will react with the titration base. Extending the parts of this equation by their $\mathrm{pH}$, $c_0$ and $k_\mathrm a$ containing counterparts, we get:</p> <p>$$c(\ce{H3O+})=\frac{k_\mathrm w}{c(\ce{H3O+})}+\frac{c_0(\ce{HA})~k_\mathrm a}{k_\mathrm a+c(\ce{H3O+})}-\frac{c_0(\ce{B})~k_\mathrm b~c(\ce{H3O+})}{k_\mathrm w+k_\mathrm b~c(\ce{H3O+})}$$</p> <p>At the point of inflection, the equivalence point, the amount of both moles need to be equal and the total volume is the addition of previous acidic volume plus the added base volume $V_\mathrm{tot}=V_{\ce{A}}+V_{\ce{B}}$. The ratio of both concentrations $c(\ce{HA})$ and $c(\ce{B})$ is therefor equal to $1$. \begin{align} n_{\ce{A}}&amp;=n_{\ce{B}}\\ \Leftrightarrow c_\mathrm A~V_\mathrm a&amp;=c_\mathrm B~V_\mathrm b\\ \xrightarrow{V_\mathrm{tot}=V_\mathrm A+V_\mathrm B} \frac{c_B}{c_A}&amp;=1=\tau~\text{or}~\gamma\end{align}</p> <p>Knowing this, rearranging the second equation to $c_\mathrm A/c_\mathrm B$ gives us:</p> <p>$$\tau=\frac{c_\mathrm B}{c_\mathrm A}=\left(1+\frac{k_\mathrm w}{k_\mathrm b~c(\ce{H3O+})}\right)\left(\frac{k_\mathrm w}{c(\ce{H3O+})}-c(\ce{H3O+})+\frac{k_\mathrm a}{c(\ce{H3O+})+k_\mathrm a}\right)$$</p> <p>which we now somehow have to solve for the proton concentration after setting $\tau=1$. As this is rather annoying I did that for the titration of any more or less relevant acids for $\mathrm pK_\mathrm a$ values between $-2$ and $16$, with $\ce{NaOH}$ giving the following graph.</p> <p>$\hskip1.2in$ <img src="https://i.stack.imgur.com/OU66t.png" alt="EP for titration of acids with NaOH"></p> <p>You can see that strong acids will be neutralized a pH 7 and extremely weak acids at pH 14. In between there is a linear range in which one can calculate the pH at the equivalence point by the simple equation $$\mathrm pH_\mathrm{eq}=7+0.5~\mathrm pK_\mathrm a$$</p> <p>This can be expanded for the neutralization of every monoprotic acid with every monoprotic base and again there is a simple equation for calculating the pH at the equivalence point.</p> <p>$\hskip1.2in$ <img src="https://i.stack.imgur.com/yAotY.png" alt="enter image description here"></p> <p>$$\mathrm pH_\mathrm {eq}=7+0.5~\mathrm pK_\mathrm a-0.5~\mathrm pK_\mathrm b$$</p>