Answer:
69.7 mL ≅ 70 mL
Step-by-step explanation:
The chemical reaction between hydrobromic acid (HBr) and lithium metal (Li) produces lithium bromide (LiBr) and hydrogen (H₂) according to the following equation:
2HBr(aq) + 2Li(s) → 2LiBr(aq) + H₂(g)
Thus, 2 moles of HBr reacts with 2 moles of Li. So, the stoichiometric ratio is 1:1 (1 mol HBr reacts with 1 mol Li).
We convert the mass of Li to moles by using the molar mass (MM) of LiBr:
MM(LiBr) = 6.9 g/mol + 79.9 g/mol = 86.8 g/mol
moles of Li(s) = mass/MM(LiBr) = 19.4 g/86.8 g/mol = 0.223 moles Li(s)
Now, we can divide the moles of Li into the molarity of the HBr solution to obtain the volume in liters wee need to add:
V = moles Li(s)/M = (0.223 mol)/(3.2 mol/L) = 0.0697 L
0.0697 L x 1000 mL/1 L = 69.7 mL ≅ 70 mL
Therefore, 70 mL of 3.2 M HBr are needed to entirely dissolve the metal.