Problem 121 - Chemistry and Chemical Reactivity

Question

A General ChemistryNow CD-ROM or website Screen 4.8 limiting Reactants, explores the reaction of zinc and hydrochloric acid. $$\mathrm{Zn}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \longrightarrow \mathrm{ZnCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g})$$ Different quantities of zinc are added to three flasks, each containing exactly \(100 \mathrm{mL}\) of \(0.10 \mathrm{M} \mathrm{HCl} .\) Flask \(1: 7.00 \mathrm{g} \mathrm{Zn}\) Flask \(2: 3.27 \mathrm{g}\) Zn Flask \(3: 1.31 \mathrm{g}\) Zn The same amount of \(\mathrm{H}_{2}\) gas was generated in Flasks 1 and \(2,\) but a smaller amount was generated in Flask 3 The zinc was completely consumed in Flasks 2 and \(3,\) but some remained in Flask \(1 .\) Explain these observations.

Step-by-Step Solution

Answer

HCl limits reaction in Flask 1, while Zn limits in Flask 3; Flask 2 uses both fully.

Step 1: Calculate moles of HCl in each flask

First, convert the volume of HCl solution to liters: \(100 \text{ mL} = 0.100 \text{ L}\). Using the molarity, calculate the moles of HCl: \[\text{Moles of } \mathrm{HCl} = 0.10 \text{ M} \times 0.100 \text{ L} = 0.010 \text{ moles}\] All flasks have the same moles of HCl.

Step 2: Calculate moles of Zn in each flask

Next, convert the grams of Zn to moles using its molar mass (65.38 g/mol): - **Flask 1:** \[\text{Moles of Zn} = \frac{7.00 \text{ g}}{65.38 \text{ g/mol}} \approx 0.107 \text{ moles}\] - **Flask 2:** \[\text{Moles of Zn} = \frac{3.27 \text{ g}}{65.38 \text{ g/mol}} \approx 0.050 \text{ moles}\] - **Flask 3:** \[\text{Moles of Zn} = \frac{1.31 \text{ g}}{65.38 \text{ g/mol}} \approx 0.020 \text{ moles}\]

Step 3: Identify limiting reactant in each flask

Using the stoichiometry of the reaction, \(1 \text{ mole Zn} \) reacts with \(2 \text{ moles HCl}\). Each flask has 0.010 moles of HCl:- **Flask 1:** - Needs \(0.010\) moles Zn to completely react with \(0.010\) moles HCl. - Zn is in excess since \(0.107\text{ moles Zn} > 0.010\text{ moles Zn required}\).- **Flask 2:** - Also needs \(0.010\) moles Zn to completely react. - All Zn will be consumed with this amount of HCl (0.050 moles Zn).- **Flask 3:** - Needs only \(0.005\) moles Zn, and it has slightly more than this (0.020 moles). - But Zn is fully consumed as there is less HCl than required for residual additional Zn.

Step 4: Explain the generation of hydrogen gas

In each flask:- **Flask 1:** In excess of Zn, the reaction is limited by 0.010 moles of HCl forming 0.005 moles of \(\text{H}_2\) gas (due to the \(2:1\) HCl to \(\text{H}_2\) stoichiometry).- **Flask 2:** Entirely consumes Zn to react exactly with \(0.010\) moles HCl also forming 0.005 moles of \(\text{H}_2\) gas.- **Flask 3:** Limited by Zn and generates a smaller amount of \(\text{H}_2\) because all Zn reacts, and contributes to the smaller yield compared to Flasks 1 and 2.

Key Concepts

Stoichiometry

Stoichiometry is an essential concept in chemistry that involves the calculation of reactants and products in a chemical reaction. It is based on the balanced chemical equation that represents the reaction. In the scenario with zinc (Zn) and hydrochloric acid (HCl), the stoichiometry of the reaction is clear from the balanced equation:- For every 1 mole of Zn, 2 moles of HCl are required to produce 1 mole of hydrogen gas (\( \text{H}_2 \)) and zinc chloride (\( \text{ZnCl}_2 \)). To understand which reactant will be consumed first or left over, stoichiometry helps ascertain the exact amounts each reactant needs for a complete reaction. This can further identify the limiting and excess reactants, ultimately determining the maximum amount of products formed. To achieve this, we often rely on the mole ratios derived from the balanced equation.

• Mole ratios: These are crucial for determining how many moles of one substance are needed to react with or produce another substance.
• Calculating mass: By understanding stoichiometry, one can convert between mass of reactants and products using their molar masses.

Chemical Reaction

A chemical reaction represents a process where reactants transform into products. It involves breaking and forming chemical bonds, which accompanies changes in the physical and chemical properties of the substances involved. In our example of zinc reacting with hydrochloric acid, the reaction proceeds as follows:\[ \mathrm{Zn(s)} + 2 \mathrm{HCl(aq)} \rightarrow \mathrm{ZnCl}_2(\mathrm{aq}) + \mathrm{H}_2(\mathrm{g}) \]In this reaction:- Solid zinc (Zn) reacts with the aqueous hydrochloric acid (HCl).- The products formed are zinc chloride (\( \mathrm{ZnCl}_2 \)), which stays dissolved in water, and hydrogen gas (\( \mathrm{H}_2 \)).The reaction is driven by the breaking of bonds in HCl and the formation of new bonds in \( \mathrm{ZnCl}_2 \) and \( \mathrm{H}_2 \). Reactions like these often depend on specific conditions such as concentration and temperature, though this example focuses on limiting reactants and stoichiometry.

Mole Calculations

Mole calculations are an integral part of understanding chemical reactions and stoichiometry. A mole is a unit in chemistry that represents \( 6.022 \times 10^{23} \) entities, which could be atoms, molecules, or other particles. Calculating moles allows chemists to quantify the amount of substances involved precisely. For our zinc and hydrochloric acid reaction:1. **Conversion of mass to moles**: To find moles from grams, use the formula: \[ \text{Moles} = \frac{\text{mass in grams}}{\text{molar mass in g/mol}} \] For zinc with a molar mass of 65.38 g/mol:

• Flask 1: \( \frac{7.00 \, \text{g}}{65.38 \, \text{g/mol}} \approx 0.107 \, \text{moles Zn} \)
• Flask 2: \( \frac{3.27 \, \text{g}}{65.38 \, \text{g/mol}} \approx 0.050 \, \text{moles Zn} \)
• Flask 3: \( \frac{1.31 \, \text{g}}{65.38 \, \text{g/mol}} \approx 0.020 \, \text{moles Zn} \)

2. **Understanding the role of moles in reactions**: This calculation is crucial for determining which reactant is limiting the reaction since the stoichiometry shows the mole ratio.Mastering mole calculations enables effective prediction and regulation of chemical reactions, ensuring reactants can be measured precisely to control the product yield.