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Chapter 14: Q14.2-15 E (page 828)

Explain why a sample of pure water at \({40^ \circ }{\rm{C}}\) is neutral even though \(\left( {{{\rm{H}}_3}{{\rm{O}}^ + }} \right) = 1.7 \times {10^{ - 7}}M.\) \({K_{\rm{w}}}{\rm{\;is\;}}2.9 \times \)\({10^{ - 14}}{\rm{\;at\;}}{40^ \circ }{\rm{C}}.\)

Short Answer

Expert verified

It is neutral because concentrations of hydronium ion and hydroxide ion are the same.

Step by step solution

01

Data given

Ionization constant of water is\(2.9 \times {10^{ - 14}}\), and it says in the task that concentration of \({{\rm{H}}_3}{{\rm{O}}^ + }\) equals \(1.7 \times {10^{ - 7}}\)M. Equation of water ionization is as follows:

\({{\rm{H}}_2}{\rm{O}}(l) + {{\rm{H}}_2}{\rm{O}}(l) \to {{\rm{H}}_3}{{\rm{O}}^ + }(aq) + {\rm{O}}{{\rm{H}}^ - }(aq)\)

02

Explain why a sample of pure water is neutral

Ionization constant is:

\({K_w} = c\left( {{{\rm{H}}_3}{{\rm{O}}^ + }} \right) \cdot c\left( {{\rm{O}}{{\rm{H}}^ - }} \right)\)

So, concentration of OH - is:

\(\begin{aligned}{c\left( {O{H^ - }} \right) = \frac{{{K_w}}}{{c\left( {{H_3}{O^ + }} \right)}}}\\{\,\,c\left( {O{H^ - }} \right) = \frac{{2.9 \times {{10}^{ - 14}}}}{{1.7 \times {{10}^{ - 7}}}}}\\{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,c\left( {O{H^ - }} \right) = 1.7 \times {{10}^{ - 7}}{\rm{\;mold}}{{\rm{m}}^{ - 3}}{\rm{\;}}}\end{aligned}\)

Having the same concentration of \({{\rm{H}}_3}{{\rm{O}}^ + }\)and OH- means that the solution is neutral

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Most popular questions from this chapter

Saccharin, \({{\bf{C}}_{\bf{7}}}{{\bf{H}}_{\bf{4}}}{\bf{NS}}{{\bf{O}}_{\bf{3}}}{\bf{H}}\), is a weak acid\(\left( {{\bf{Ka = 2}}{\bf{.1 \times 1}}{{\bf{0}}^{{\bf{ - 2}}}}} \right)\). If \({\bf{0}}.{\bf{250}}{\rm{ }}{\bf{L}}\) of diet cola with a buffered pH of \({\bf{5}}.{\bf{48}}\) was prepared from \({\bf{2}}.{\bf{00}}{\rm{ }} \times {\rm{ }}{\bf{1}}{{\bf{0}}^{ - {\bf{3}}}}{\bf{g}}\) of sodium saccharide, \({\bf{Na}}\left( {{{\bf{C}}_{\bf{7}}}{{\bf{H}}_{\bf{4}}}{\bf{NS}}{{\bf{O}}_{\bf{3}}}} \right)\), what are the final concentrations of saccharine and sodium saccharide in the solution?

Novocaine, \({C_{13}}{H_{21}}{O_2}\;{N_2}Cl\), is the salt of the base procaine and hydrochloric acid. The ionization constant for procaine is \(7 \times 1{0^{ - 6}}\). Is a solution of novocaine acidic or basic? What are \(\left( {{H_3}{O^ + }} \right),\left( {O{H^ - }} \right)\), and \(pH\) of a \(2.0\% \) solution by mass of novocaine, assuming that the density of the solution is \(1.0\;g/mL\).

What concentration of\(N{H_4}N{O_3}\)is required to make\(\left( {O{H^ - }} \right) = 1.0 \times 1{0^{ - 5}}\)in a\(0.200 M\)solution of\(N{H_3}\)?

What is the ionization constant at 25oC for the weak acid \(C{H_3}NH_3^ + \), the conjugate acid of the weak base \(C{H_3}N{H_2}\)\({K_b} = 4.4 \times 1{0^{ - 4}}\) ,.

Gastric juice, the digestive fluid produced in the stomach, contains hydrochloric acid, and HCl. Milk of Magnesia, a suspension of solid Mg(OH)2 in an aqueous medium, is sometimes used to neutralize excess stomach acid. Write a complete balanced equation for the neutralization reaction, and identify the conjugate acid-base pairs
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