Sure! Let's solve this problem step by step.
### Step 1: Write the balanced chemical equation
First, we need to start with the balanced chemical equation for the reaction between zinc (Zn) and hydrochloric acid (HCl):
[tex]\[ \text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2 \][/tex]
### Step 2: Identify the stoichiometric relationship
From the balanced chemical equation, we observe the stoichiometric relationship between Zn and HCl:
- 1 mole of Zn reacts with 2 moles of HCl.
### Step 3: Determine the moles of Zn required
We are given that we have 4.80 moles of HCl. Using the stoichiometric ratio from the balanced equation, we can find out how many moles of Zn are needed:
[tex]\[ \text{Moles of Zn} = \frac{\text{Moles of HCl}}{2} \][/tex]
[tex]\[ \text{Moles of Zn} = \frac{4.80 \text{ moles of HCl}}{2} = 2.40 \text{ moles of Zn} \][/tex]
### Step 4: Calculate the mass of Zn needed
Next, we need to find the mass of zinc (Zn) that corresponds to 2.40 moles. To do this, we use the molar mass of Zn:
- The molar mass of Zn is 65.38 grams per mole.
Using this, we can calculate the mass of Zn needed:
[tex]\[ \text{Mass of Zn} = \text{Moles of Zn} \times \text{Molar mass of Zn} \][/tex]
[tex]\[ \text{Mass of Zn} = 2.40 \text{ moles} \times 65.38 \text{ g/mole} \][/tex]
[tex]\[ \text{Mass of Zn} = 156.912 \text{ grams} \][/tex]
### Conclusion
Therefore, to completely react with 4.80 moles of hydrochloric acid (HCl), you will need:
- [tex]\(2.40\)[/tex] moles of zinc (Zn), which corresponds to [tex]\(156.912\)[/tex] grams of zinc (Zn).
This ensures that the reaction will go to completion, producing zinc chloride (ZnCl2) and hydrogen gas (H2) as specified.
