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# OwlSolutions - Kw for the answers below Use the rules for...

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The gas phase decomposition of dimethyl ether at 500 o C CH 3 OCH 3 (g) CH 4 (g) + H 2 (g) + CO(g) is first order in CH 3 OCH 3 . During one experiment it was found that when the initial concentration of CH 3 OCH 3 was 0.118 M, the concentration of CH 3 OCH 3 dropped to 2.02E-2 M after 2794 s had passed. Based on this experiment, the rate constant for the reaction is 6.32E-4 s -1 . Feedback: For a first order reaction of the form A products, the equation that relates concentration to time is ln [A] = ln [A] o - kt In this case: [A] o = 0.118 M [A] = 2.02E-2 M t = 2794 s Substituting into the above equation gives ln [ 2.02E-2 ] = ln( 0.118 ) - (k s -1 )( 2794 s ) k = 6.32E-4 s -1 The pK w of a solution is defined by the equation: ... pK w = - log K w ... ... Where: K w = water dissociation constant NOTE: Write K w as Kw

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Unformatted text preview: Kw for the answers below. Use the rules for logarithms and exponents to solve for K w in terms of pK w . ... K w = Correct answer: Your response: If ... pK w = 7.15 ... then ... K w = 7.08E-8 Feedback: In order to solve for K w you must clear the logarithm. Step 1 ... Multiply both sides of the equation by (-1) .- pK w = log K w Step 2 Raise both sides of the equation to the base 10 . 10- pK w = 10 (log K w ) Step 3 Simplify the right side of this equation using the rule 10 log a = a. 10 (log K w ) = K w The resulting equation is: K w = 10-pKw If ... pK w = 7.15 ... then ... K w = 10-7.15 = 7.1E-8 K w is equal to 1.0 x 10-7 at 25 o C. It changes slightly with temperature....
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