I have a couple of problems that I am needing help withplease..... 1) Geologists
ID: 691254 • Letter: I
Question
I have a couple of problems that I am needing help withplease.....1) Geologists can estimate the age of rocks by their uranium-238content. The Uranium is incorporated in the rock as it hardens andthen decays with first-order kinetics and a half-life of 4.5billion years. A rock is found to contain 84% of the amount ofuranium-238 that is contained when it was formed. (The amount thatthe rock contained when it was formed can be deduced from thepresence of the decay products of U-238) How old is the rock?
2) The hydrolysis of sucrose is C12H22O11 in glucose and fructosein acidic water has a rate constant 1.8*10^-4 s^-1 at 25 degrees C.Assuming the reaction is first order in sucrose, determine the massof sucrose that is hydrolyzed when 2.40L of a .160M sucrose isallowed to react for 200 minutes.
Your help would be greatly appreciated and would you please be sokind to indicate step by step how to solve the equation so that Iam able to understand how you came up with the solution. I amconfused,
Thank you very much.
Explanation / Answer
1. Step one.... Solve for k using known half like and amount decayedi.e 4.5 billion years and half sample decayed D(t)=ekt D(4.5)= ek(4.5) = .5 k= ln(.5)/4.5 Use new k value to solve for t with known amount decayed D(t)=.14 .16= e(ln(.5)/4.5)t ln(.16) = (ln(.5)/4.5)t t= .588 .588 billion years to decay 86% 2. Set up rate equation with units rate = 1.8*10-4 sec-1 [sucrose in mol/L] rate = 1.8*10-4 sec-1 [.160 mol/L] =2.88*10-4 mol/sec L 2.88*10-4 mol/sec L * (60 sec/ min) * (200 min) = .83 mol sucrose (.83 mol)( 342g/mol) = 283.86 grams sucrose
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