Ahalf-life is the time it takes an amount of substance to decay to one-half of its original amount. for example, the sample is one-half after the first half-life but one-quarter (i. e., one-half of one-half) after the second half-life. if the half life of uranium-235 is 700 million years, how long does it take for 10.0 grams to decay to 2.5 grams? express your answer in billions of years.

2.10 × 10⁹ yr  

Step-by-step explanation:  

The half-life of U-235 is the time it takes for half the U to decay.  

After one half-life, half (50 %) of the original amount will remain.  

After a second half-life, half of that amount (25 %) will remain, and so on.  

We can construct a table as follows:  

 No. of                           Fraction        Amount  

half-lives  t/(yr × 10⁶)   remaining  remaining/g  

      1                 700              ½                10.0  

      2              1400              ¼                 5.00  

      3              2100              ⅛                 2.50  

     4              2800              ¹/₁₆                 1.25  

We see that 2100 × 10⁶ yr is three half-lives, and the amount of U-235 remaining is 2.50 g.  

It takes 2.10× 10⁹ yr for the U-238 to decay to 2.50 g.

if the concentration of products is decreased, the equilibrium will shift toward the products). add an inert gas (one that is not involved in the reaction) to the constant-volume reaction mixture: this will increase the total pressure of the system, but will have no effect on the equilibrium condition.

explanation:

1. for the first question, we must find the mass of the anhydrous salt, mgso₄. the molar mass for mgso₄·7h₂o is 246.47 g/mol, while that of mgso₄ is 120.37 g/mol.7.834 g mgso₄·7h₂o * 1 mol mgso₄·7h₂o/246.47 g * 1 mol mgso₄/1 mol mgso₄·7h₂o * 20.37 g mgso₄/mol = 0.647 g mgso₄

2. mass of water = mass of sample - mass of anhydrous salemass of water = 7.834 - 0.647 = 7.19 gpercent water in hydrate = 7.19/7.834 * 100 = 91.74%