Zinc reacts with hydrochloric acid according to the reaction equation
Zn(s) + 2HCl(aq) ? ZnCl(aq) + H(g)
How many milliliters of 3.50 M HCl(aq) are required to react with 4.05 g of Zn(s)
The Correct Answer and Explanation is:
To solve the problem, we will use stoichiometry, which involves converting grams of zinc to moles, using the balanced chemical equation to find the required moles of HCl, and then calculating the volume of HCl solution needed using its molarity.
Balanced chemical equation:
$$
\text{Zn}(s) + 2\text{HCl}(aq) \rightarrow \text{ZnCl}_2(aq) + \text{H}_2(g)
$$
This equation tells us that 1 mole of Zn reacts with 2 moles of HCl.
Step 1: Convert grams of Zn to moles
The molar mass of Zn is approximately 65.38 g/mol.
$$
\text{Moles of Zn} = \frac{4.05\ \text{g}}{65.38\ \text{g/mol}} \approx 0.06195\ \text{mol}
$$
Step 2: Use the mole ratio to find moles of HCl required
From the balanced equation:
$$
1 \text{ mol Zn} : 2 \text{ mol HCl}
$$
$$
\text{Moles of HCl} = 0.06195\ \text{mol Zn} \times \frac{2\ \text{mol HCl}}{1\ \text{mol Zn}} = 0.1239\ \text{mol HCl}
$$
Step 3: Use molarity to find volume of HCl solution needed
Molarity (M) is defined as:
$$
\text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}}
$$
Rearranging to solve for volume:
$$
\text{Volume (L)} = \frac{\text{moles of HCl}}{\text{molarity}} = \frac{0.1239}{3.50} \approx 0.0354\ \text{L}
$$
Convert to milliliters:
$$
0.0354\ \text{L} \times 1000 = \boxed{35.4\ \text{mL}}
$$
Final Answer: $\boxed{35.4\ \text{mL}}$ of 3.50 M HCl(aq) is required.
Explanation (300 words)
This problem demonstrates a fundamental concept in chemistry known as stoichiometry, where we use the relationships in a balanced chemical equation to calculate quantities of reactants and products. We are asked how much hydrochloric acid (HCl) is needed to completely react with a known mass of zinc (Zn). The reaction given shows that one mole of zinc reacts with two moles of hydrochloric acid to produce zinc chloride and hydrogen gas.
First, we convert the given mass of zinc into moles using its molar mass, which is the number of grams per mole. The molar mass of zinc is approximately 65.38 grams per mole. Dividing the mass of zinc by its molar mass gives us the amount in moles. This step is essential because chemical reactions happen on a mole-to-mole basis, not a gram-to-gram basis.
Next, we use the mole ratio from the balanced equation to determine the number of moles of hydrochloric acid needed. Since two moles of HCl react with one mole of Zn, we multiply the number of moles of zinc by two.
Finally, we convert moles of HCl into volume using the given molarity of the HCl solution. Molarity is defined as moles of solute per liter of solution. Dividing the moles of HCl needed by the molarity tells us how many liters of the solution are required. Converting this to milliliters gives the final answer: 35.4 mL of 3.50 M HCl are needed to react with 4.05 g of zinc.
