To solve this problem, let’s break it down into clear steps:
1. Calculate the moles of sulfuric acid (H₂SO₄):
The molarity (M) of H₂SO₄ is given as 1.50 M, and the volume of H₂SO₄ we have is 0.690 L.
Using the formula:
[tex]\[
\text{Moles of H₂SO₄} = \text{Molarity} \times \text{Volume}
\][/tex]
[tex]\[
\text{Moles of H₂SO₄} = 1.50 \times 0.690 = 1.035 \text{ moles}
\][/tex]
2. Determine the moles of carbon dioxide (CO₂) produced:
According to the balanced chemical equation provided:
[tex]\[
Na_2CO_3 + H_2SO_4 \rightarrow Na_2SO_4 + CO_2 + H_2O
\][/tex]
The reaction shows that 1 mole of H₂SO₄ produces 1 mole of CO₂.
Hence, the moles of CO₂ produced will be equal to the moles of H₂SO₄ reacted:
[tex]\[
\text{Moles of CO₂} = 1.035 \text{ moles}
\][/tex]
3. Calculate the volume of CO₂ gas produced using the Ideal Gas Law:
The Ideal Gas Law is:
[tex]\[
PV = nRT
\][/tex]
Where:
- [tex]\(P\)[/tex] is the pressure (in atm)
- [tex]\(V\)[/tex] is the volume (in L)
- [tex]\(n\)[/tex] is the number of moles
- [tex]\(R\)[/tex] is the ideal gas constant (0.0821 L·atm/(K·mol))
- [tex]\(T\)[/tex] is the temperature (in K)
Rearranging the Ideal Gas Law to solve for the volume ([tex]\(V\)[/tex]):
[tex]\[
V = \frac{nRT}{P}
\][/tex]
Substituting the given values:
- [tex]\(n = 1.035\)[/tex] moles
- [tex]\(R = 0.0821\)[/tex] L·atm/(K·mol)
- [tex]\(T = 298\)[/tex] K
- [tex]\(P = 0.98\)[/tex] atm
[tex]\[
V = \frac{1.035 \times 0.0821 \times 298}{0.98}
\][/tex]
[tex]\[
V \approx 25.838880612244896 \text{ L}
\][/tex]
4. Compare the calculated volume to the given options:
The possible answers are:
- 26 L
- 0.69 L
- 37 L
- 1.04 L
The calculated value, 25.838880612244896 L, is closest to 26 L.
Therefore, the volume of carbon dioxide gas produced from the complete reaction is 26 L.
