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1) How many moles of atoms are there in 3.1 × 10−12 g O? 

2) Assume a gasoline is isooctane, which has a density of 0.692 g/mL. What is the mass of 
3.4 gal of the gasoline (1 gal = 3.78 L)? 

3) The half-life of polonium-210 is 138.4 days. How many milligrams of polonium-210 remain 
after 179.92 days if you start with 7.3 mg of the isotope? 

4) The half-life of plutonium-239 is 24110 yrs. Of an original mass of 131 g, how much remains 
after 1.4466 × 105 yrs? 



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Posted Answers:

1. conversion factors and the unit-factor method 
3.1x10^-12g O x (1 mol O / 16.0g O) = 1.9x10^-13 mol ........... to two SF 

2. Assume gasoline is 2,2,4-trimethyl pentane is.... That's a poor assumption. There are better stand-in's for gasoline than this. The density and heat of combustion are both far too low to be a good analog of gasoline. Why not just give the average density of gasoline? 0.755 g/mL 
3.4 gal x (1L / 3.78 gal) x (0.692 kg/L) = 0.622 kg .... or .... 622 g 

3. Radioactive decay is a first-order process and can be described by this equation: 
A = Ao e^(-kt) ...... A = activities or amounts, t is the elapsed time, k is the decay constant which is related to the half life by k=ln2/t½ 
k = 0.693 / 138.4 day = 0.00501 day⁻¹ 
A = 7.3 mg x e^(-0.00501 day⁻¹ x 179.92 day) 
A = 3.0 mg ............. to two significant digits 

4. You now know how to do this one.