Sure, let's solve this problem step-by-step:
1. Write the balanced chemical equation for the reaction:
Zinc reacts with hydrochloric acid to produce zinc chloride and hydrogen gas. The balanced equation is:
[tex]\[
\text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2
\][/tex]
2. Determine the mole ratio:
From the balanced equation, we can see that 1 mole of zinc (Zn) produces 1 mole of hydrogen gas (H₂).
3. Given data:
We are given that zinc reacts with hydrochloric acid, and we have 0.40 moles of zinc.
4. Calculate the number of moles of hydrogen gas produced:
Since the mole ratio of zinc to hydrogen gas is 1:1, 0.40 moles of zinc will produce 0.40 moles of hydrogen gas.
5. Convert moles of hydrogen gas to volume at STP:
At Standard Temperature and Pressure (STP), 1 mole of any ideal gas occupies a volume of 22.4 liters.
Therefore, to find the volume of hydrogen gas produced:
[tex]\[
\text{Volume of } \text{H}_2 = \text{moles of } \text{H}_2 \times 22.4 \text{ liters/mole}
\][/tex]
[tex]\[
\text{Volume of } \text{H}_2 = 0.40 \text{ moles} \times 22.4 \text{ liters/mole}
\][/tex]
[tex]\[
\text{Volume of } \text{H}_2 = 8.96 \text{ liters}
\][/tex]
Hence, the volume of hydrogen gas produced is 8.96 liters at STP.
