Answer: m= 1.02x10² g AlCl3 or 1091.3 g AlCl3
Explanation: solution attached.
Convert mass of Mg to moles
Do the mole ratio between Mg and AlCl3 based from the balanced equation.
Convert moles of AlCl3 to mass using its molar mass.
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The half life for C14 is 5730 years.
We assume that Carbon 14/ Carbon 12 ratio was steady for living organisms over time, the problem is actually telling us that
= 0.0725 = 
ˣ
Take the natural logarithm and In on both sides.
ln(0.725) = lnˣ
= - 0.3216 = xln ( = -0.6931x.
So x = (-.3216) / (-0.6931) = 0.464
or
t/t₁/₂ = 0.464
So t = 0.464 x t₁/₂ = 0.464 * 5730 yrs = 2660 years.
We assume that Carbon 14/ Carbon 12 ratio was steady for living organisms over time, the problem is actually telling us that
Take the natural logarithm and In on both sides.
ln(0.725) = ln
= - 0.3216 = xln (
So x = (-.3216) / (-0.6931) = 0.464
or
t/t₁/₂ = 0.464
So t = 0.464 x t₁/₂ = 0.464 * 5730 yrs = 2660 years.