Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

%3Cp%20id%3D%22yui_3_11_0_24_1396902777866_113%22%20class%3D%22c15%22%3EAs%20a%2

ID: 828418 • Letter: #

Question

%3Cp%20id%3D%22yui_3_11_0_24_1396902777866_113%22%20class%3D%22c15%22%3EAs%20a%20chemist%0Afor%20an%20agricultural%20products%20company%2C%20you%20have%20just%20developed%20a%20new%0Aherbicide%2C%22Herbigon%2C%22%20that%20you%20think%20has%20the%20potential%20to%20kill%0Aweeds%20effectively.%20A%20sparingly%20soluble%20salt%2C%20Herbigon%20is%20dissolved%0Ain%201%20%3Cspan%20class%3D%22replace-insert%20done%20c7%22%20id%3D%0A%22yui_3_11_0_24_1396902777866_112%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c6%22%20id%3D%0A%22MathJax-Element-24-Frame%22%3E%3Cspan%20class%3D%22math%20c2%22%20id%3D%0A%22MathJax-Span-151%22%3E%3Cspan%20class%3D%22c4%22%3E%3Cspan%20class%3D%22c3%22%3E%3Cspan%20class%3D%0A%22mrow%20c2%22%20id%3D%22MathJax-Span-152%22%3E%3Cspan%20class%3D%22mi%20c1%22%20id%3D%0A%22MathJax-Span-153%22%3EM%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%26nbsp%3Bacetic%0Aacid%20for%20technical%20reasons%20having%20to%20do%20with%20its%20production.%20You%0Ahave%20determined%20that%20the%20solubility%20product%26nbsp%3B%3Cspan%20class%3D%0A%22replace-insert%20done%20c7%22%20id%3D%0A%22yui_3_11_0_24_1396902777866_117%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c6%22%20id%3D%0A%22MathJax-Element-25-Frame%22%3E%3Cspan%20class%3D%22math%20c2%22%20id%3D%0A%22MathJax-Span-154%22%3E%3Cspan%20class%3D%22c14%22%3E%3Cspan%20class%3D%22c13%22%3E%3Cspan%20class%3D%0A%22mrow%20c2%22%20id%3D%22MathJax-Span-155%22%3E%3Cspan%20class%3D%22maction%20c2%22%20id%3D%0A%22MathJax-Span-156%22%3E%3Cspan%20class%3D%22MathJax_HitBox%20c8%22%20id%3D%0A%22MathJax-HitBox-156%22%20title%3D%22K_sp%22%3E%3C%2Fspan%3E%3Cspan%20class%3D%22msubsup%20c2%22%0Aid%3D%22MathJax-Span-157%22%20title%3D%22K_sp%22%3E%3Cspan%20class%3D%22c12%22%3E%3Cspan%20class%3D%0A%22c9%22%3E%3Cspan%20class%3D%22mi%20c1%22%20id%3D%0A%22MathJax-Span-158%22%3EK%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c11%22%3E%3Cspan%20class%3D%0A%22texatom%20c2%22%20id%3D%22MathJax-Span-159%22%3E%3Cspan%20class%3D%22mrow%20c2%22%20id%3D%0A%22MathJax-Span-160%22%3E%3Cspan%20class%3D%22mi%20c10%22%20id%3D%0A%22MathJax-Span-161%22%3Es%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c10%22%20id%3D%0A%22MathJax-Span-162%22%3Ep%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%26nbsp%3Bof%0AHerbigon%20is%209.20%C3%9710%3Csup%3E%3F6%3C%2Fsup%3E.%3C%2Fp%3E%0A%3Cp%20id%3D%22yui_3_11_0_24_1396902777866_121%22%20class%3D%22c34%22%3EAlthough%20the%0Aformula%20of%20this%20new%20chemical%20is%20a%20trade%20secret%2C%20it%20can%20be%20revealed%0Athat%20the%20formula%20for%20Herbigon%20is%20X-acetate%20(%3Cspan%20class%3D%0A%22replace-insert%20done%20c7%22%20id%3D%0A%22yui_3_11_0_24_1396902777866_120%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c6%22%20id%3D%0A%22MathJax-Element-26-Frame%22%3E%3Cspan%20class%3D%22math%20c2%22%20id%3D%0A%22MathJax-Span-163%22%3E%3Cspan%20class%3D%22c21%22%3E%3Cspan%20class%3D%22c20%22%3E%3Cspan%20class%3D%0A%22mrow%20c2%22%20id%3D%22MathJax-Span-164%22%3E%3Cspan%20class%3D%22mi%20c16%22%20id%3D%0A%22MathJax-Span-165%22%3EX%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c16%22%20id%3D%0A%22MathJax-Span-166%22%3EC%3C%2Fspan%3E%3Cspan%20class%3D%22msubsup%20c2%22%20id%3D%0A%22MathJax-Span-167%22%3E%3Cspan%20class%3D%22c19%22%3E%3Cspan%20class%3D%22c17%22%3E%3Cspan%20class%3D%0A%22mi%20c16%22%20id%3D%22MathJax-Span-168%22%3EH%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%0A%22c18%22%3E%3Cspan%20class%3D%22mn%20c10%22%20id%3D%0A%22MathJax-Span-169%22%3E3%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%0A%22mi%20c16%22%20id%3D%22MathJax-Span-170%22%3EC%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c16%22%20id%3D%0A%22MathJax-Span-171%22%3EO%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c16%22%20id%3D%0A%22MathJax-Span-172%22%3EO%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%2C%0Awhere%20%22X%22%20represents%20the%20top-secret%20cation%20of%20the%20salt).%20It%20is%20this%0Acation%20that%20kills%20weeds.%20Since%20it%20is%20critical%20to%20have%20Herbigon%0Adissolved%20(it%20won't%20kill%20weeds%20as%20a%20suspension)%2C%20you%20are%20working%20on%0Aadjusting%20the%20pH%20so%20Herbigon%20will%20be%20soluble%20at%20the%20concentration%0Aneeded%20to%20kill%20weeds.%20What%20pH%20must%20the%20solution%20have%20to%20yield%20a%0Asolution%20in%20which%20the%20concentration%20of%26nbsp%3B%3Cspan%20class%3D%0A%22replace-insert%20done%20c7%22%20id%3D%0A%22yui_3_11_0_24_1396902777866_124%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c6%22%20id%3D%0A%22MathJax-Element-27-Frame%22%3E%3Cspan%20class%3D%22math%20c2%22%20id%3D%0A%22MathJax-Span-173%22%3E%3Cspan%20class%3D%22c26%22%3E%3Cspan%20class%3D%22c25%22%3E%3Cspan%20class%3D%0A%22mrow%20c2%22%20id%3D%22MathJax-Span-174%22%3E%3Cspan%20class%3D%22msubsup%20c2%22%20id%3D%0A%22MathJax-Span-175%22%3E%3Cspan%20class%3D%22c24%22%3E%3Cspan%20class%3D%22c22%22%3E%3Cspan%20class%3D%0A%22mi%20c16%22%20id%3D%22MathJax-Span-176%22%3EX%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%0A%22c23%22%3E%3Cspan%20class%3D%22mo%20c10%22%20id%3D%0A%22MathJax-Span-177%22%3E%2B%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%26nbsp%3Bis%0A6.00%C3%9710%3Csup%3E%3F3%3C%2Fsup%3E%3Cspan%20class%3D%22replace-insert%20done%20c7%22%20id%3D%0A%22yui_3_11_0_24_1396902777866_127%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c6%22%20id%3D%0A%22MathJax-Element-28-Frame%22%3E%3Cspan%20class%3D%22math%20c2%22%20id%3D%0A%22MathJax-Span-178%22%3E%3Cspan%20class%3D%22c29%22%3E%3Cspan%20class%3D%22c28%22%3E%3Cspan%20class%3D%0A%22mrow%20c2%22%20id%3D%22MathJax-Span-179%22%3E%3Cspan%20class%3D%22texatom%20c2%22%20id%3D%0A%22MathJax-Span-180%22%3E%3Cspan%20class%3D%22mrow%20c2%22%20id%3D%0A%22MathJax-Span-181%22%3E%3Cspan%20class%3D%22mi%20c27%22%20id%3D%0A%22MathJax-Span-182%22%3EM%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%26nbsp%3B%3F%0AThe%26nbsp%3B%3Cspan%20class%3D%22replace-insert%20done%20c7%22%20id%3D%0A%22yui_3_11_0_24_1396902777866_130%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c6%22%20id%3D%0A%22MathJax-Element-29-Frame%22%3E%3Cspan%20class%3D%22math%20c2%22%20id%3D%0A%22MathJax-Span-183%22%3E%3Cspan%20class%3D%22c33%22%3E%3Cspan%20class%3D%22c32%22%3E%3Cspan%20class%3D%0A%22mrow%20c2%22%20id%3D%22MathJax-Span-184%22%3E%3Cspan%20class%3D%22maction%20c2%22%20id%3D%0A%22MathJax-Span-185%22%3E%3Cspan%20class%3D%22MathJax_HitBox%20c30%22%20id%3D%0A%22MathJax-HitBox-185%22%20title%3D%22pKa%22%3E%3C%2Fspan%3E%3Cspan%20class%3D%22mrow%20c2%22%20id%3D%0A%22MathJax-Span-186%22%20title%3D%22pKa%22%3E%3Cspan%20class%3D%22texatom%20c2%22%20id%3D%0A%22MathJax-Span-187%22%3E%3Cspan%20class%3D%22mrow%20c2%22%20id%3D%0A%22MathJax-Span-188%22%3E%3Cspan%20class%3D%22mi%20c16%22%20id%3D%0A%22MathJax-Span-189%22%3Ep%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22msubsup%20c2%22%0Aid%3D%22MathJax-Span-190%22%3E%3Cspan%20class%3D%22c31%22%3E%3Cspan%20class%3D%0A%22c9%22%3E%3Cspan%20class%3D%22mi%20c1%22%20id%3D%0A%22MathJax-Span-191%22%3EK%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c11%22%3E%3Cspan%20class%3D%0A%22texatom%20c2%22%20id%3D%22MathJax-Span-192%22%3E%3Cspan%20class%3D%22mrow%20c2%22%20id%3D%0A%22MathJax-Span-193%22%3E%3Cspan%20class%3D%22mi%20c10%22%20id%3D%0A%22MathJax-Span-194%22%3Ea%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%26nbsp%3Bof%0Aacetic%20acid%20is%204.76.%3C%2Fp%3E%0A

Explanation / Answer

The question is assuming that when acid is added to XAc (Ac = acetate ion), it reacts with the Ac forming X and HAc b/c H has a strong attraction for Ac which gives it the ability to force XAc to dissolve.

The equation for disassociation of all the ions involved is:

......................XAc(s) + HAc(aq) ~> X(aq) + H(aq) + Ac(aq)
initial conc......................1M ............. 0............ 0.......... 0
change.............................. -a............ 0.006........ a..... a+0.006
final................................. 1-a ............ 0.006....... a...... a+0.006

The acid-base equilibrium relation for acetic acid is used to find H and pH:

Ka = [H][Ac]/[HAc] = a(a+0.006)/(1-a) = 10^(-4.76) = 1.74x10^-5.
The 10^(-4.76) is the Ka obtained from pKa.

Simplify the equation: a^2+0.0060174a-1.74x10^-5=0
Solve: a=0.00213M=[H]
pH=-log[H]=2.67