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How many liters of a 2.25 molar hydrobromic acid (HBr) solution would be needed to react completely with 100.0 grams of calcium metal?


Ca (s) + 2HBr (aq) CaBr2 (aq) + H2 (g)

Verified Answer :

MissPhiladelphia

We can solve by dimensional analysis. We are already given with the concentration of the acid, the amount of the metal, and the balanced chemical reaction, so:
100 g Ca (1 mol Ca / 40 g Ca) (2 mol HBr / 1 mol Ca) (1 L HBr / 2.25 mol HBr)
 = 2.22 L HBr
It would require 2.22 L of HBr to react completely 100 g of Ca.

Answer: 2.22 L

Explanation: To calculate the moles, we use the equation:

\(\text{Number of moles}=\frac{\text{Given mass}}{\textMolar mass}}\)    ....(1)

For calcium:

Mass of calcium given = 100 g

Molar mass of calcium = 40 g/mol

Putting values in above equation, we get:

\(\text{Moles of calcium}=\frac{100g}{40g/mol}=2.5mol\)

For the given reaction:

\(Ca(s)+2HBr(aq)\rightarrow CaBr_2(aq)+H_2(g)\)

By Stoichiometry of the reaction,

1 mole of calcium reacts 2 moles of hydrogen bromide

So, 2.5 moles of calcium will react with =\(\frac{2}{1}\times 2.5=5moles\) of hydrogen bromide.

Molarity is defined as the number of moles of solute dissolved per liter of solution.

Formula used :

\(Molarity=\frac{n}{V_s}\)

where,

n = moles of solute \(HBr\) = 5 moles

\(V_s\) = volume of solution in liter  = ?

\(2.25=\frac{5moles}{V_s}\)

\(V_s=2.22L\)

Therefore, the volume of solution in Liters is 2.22.

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