Answer :
Answer:
[tex]\[0.438672 \text{ moles}\][/tex]
Explanation:
To determine how many moles of hydrogen gas [tex](\(\text{H}_2\)) will be liberated, we first need to calculate the moles of hydrochloric acid (\(\text{HCl}\)) that are reacting. We use the molarity (M) and volume (V) of the \(\text{HCl}\) solution.[/tex]
Step-by-Step Calculation
1. Calculate the moles of HCl:
[tex]\[\text{Moles of HCl} = \text{Molarity (M)} \times \text{Volume (L)}\][/tex]
Given:
[tex]\[ \text{Molarity} = 4.94\, \text{M} \] \[ \text{Volume} = 177.6\, \text{mL} = 0.1776\, \text{L} \][/tex]
Plugging in the values:
[tex]\[\text{Moles of HCl} = 4.94\, \text{M} \times 0.1776\, \text{L} = 0.877344\, \text{moles}\][/tex]
2. Determine the moles of [tex]\(\text{H}_2\)[/tex] produced:
The balanced chemical equation is:
Mg(s) + 2HCl(aq) [tex]\rightarrow[/tex] [tex]MgCl_2(aq)+\{H}_2(g)\][/tex]
From the equation, we see that 2 moles of HCl produce 1 mole of [tex]\(\text{H}_2\). Therefore, the moles of \(\text{H}_2\) produced can be calculated using the stoichiometry of the reaction:[/tex]
[tex]\[\text{Moles of } \text{H}_2 = \frac{\text{Moles of HCl}}{2}\][/tex]
Plugging in the moles of \(\text{HCl}\):
[tex]\[\text{Moles of } \text{H}_2 = \frac{0.877344}{2} = 0.438672\][/tex]
Answer
The number of moles of hydrogen gas [tex](\(\text{H}_2\)) liberated is:\[0.438672 \text{ moles}\][/tex]
The moles of hydrogen liberated is 0.438672 mol.
First, we need to calculate the moles of HCl. Using the formula:
Moles of HCl = Molarity (M) × Volume (L)
Convert 177.6 mL to liters:
177.6 mL × (1 L / 1000 mL) = 0.1776 L
Now, calculate the moles of HCl:
Moles of HCl = 4.94 M × 0.1776 L = 0.877344 moles
From the balanced equation, 2 moles of HCl produce 1 mole of H₂.
So, the moles of H₂ produced will be:
Moles of H₂ = 0.877344 moles HCl × (1 mole H₂ / 2 moles HCl) = 0.438672 moles H₂
