The ratio of carbon-14 to carbon-12 in a chunk of charcoal from an archeological dig is deter-
mined to be one-half the ratio in a piece of
freshly cut wood. How old is the charcoal from
the dig site?

18 g

Explanation:

Step 1: Write the balanced equation

2 Al + 6 HCl ⇒ 2 AlCl₃ + 3 H₂

Step 2: Calculate the moles of Al

The molar mass of Al is 26.98 g/mol.

28.1 g × 1 mol/26.98 g = 1.04 mol

Step 3: Calculate the moles of HCl

46 mL of 1 M HCl react.

0.046 L × 1 mol/L = 0.046 mol

Step 4: Determine the limiting reactant

The theoretical molar ratio of Al to HCl is 2:6 = 0.33:1.

The real molar ratio of Al to HCl is 1.04:0.046 = 22.6:1

According to this, the limiting reactant is HCl.

Step 5: Calculate the mass of AlCl₃ generated from 0.046 moles of HCl

The molar ratio of HCl to AlCl₃ is 6:2. The molar mass of AlCl₃ is 133.34 g/mol.

0.046 mol HCl × 6 mol HCl/2 mol AlCl₃ × 133.34 g AlCl₃/1 mol AlCl₃ = 18 g AlCl₃