Question

what volume (ml) of 2.50 m hcl(aq) is needed to react 2.00 g iron? (answer = 28.6 ml of 2.50 m hcl) fe(s) + 2 hcl(aq) → h2(g) + fecl2(aq)

Explanation:

Step1: Calculate the moles of Fe

The molar mass of Fe is \(M = 55.85\space g/mol\). Using the formula \(n=\frac{m}{M}\), where \(m = 2.00\space g\).

$$n_{Fe}=\frac{2.00\space g}{55.85\space g/mol}\approx0.0358\space mol$$

Step2: Determine the moles of HCl

From the balanced chemical equation \(Fe(s)+2HCl(aq)\to H_{2}(g)+FeCl_{2}(aq)\), the mole ratio of \(Fe\) to \(HCl\) is \(1:2\). So \(n_{HCl}=2n_{Fe}\).

$$n_{HCl}=2\times0.0358\space mol = 0.0716\space mol$$

Step3: Calculate the volume of HCl

Using the formula \(V=\frac{n}{C}\), where \(C = 2.50\space M\) (molarity of \(HCl\)) and \(n = n_{HCl}\).

$$V_{HCl}=\frac{0.0716\space mol}{2.50\space mol/L}=0.02864\space L$$

Convert liters to milliliters (\(1\space L = 1000\space mL\)):

$$V_{HCl}=0.02864\space L\times1000\space mL/L = 28.6\space mL$$

Answer:

\(28.6\space mL\)