If the half life for the radioactive decay of zirconium 84 is 26 minutes and i start with a 175 gram sample, how much will be left over after 104 minutes? show work or explain your answer.

10.94 g.

Explanation:

kt = ln [A₀]/[A]

k is the rate constant = 0.02665 min⁻¹.

t is the time = 104.0 min.

[A₀] is the initial percentage of radioisotope = 175.0 g.

[A] is the remaining percentage of radioisotope = ??? g.

∵ kt = ln [Ao]/[A]

∴ (0.02665 min⁻¹)(104.0 min) = ln (175.0 g)/[A]

2.772 = ln (175.0 g)/[A]

15.99 = (175.0 g)/[A]

∴ [A] = (175.0 g)/(15.99) = 10.94 g.

in the given question, the partial pressure is calculated by using the ideal gas equation, that is, pv = nrt

here, p is pressure, v is volume = 25 l, n is number of moles = 0.0104 moles, r is gas constant = -0.0821 l.atm / mol.k

t is temperature = 273 k

p = nrt / v

p = (0.0104 mol × 0.0821 l.atm / mol.k × 273 k) / 25 l

= 0.0093 atm