Sure! Let's solve this step-by-step using the principles of ideal gas law and conversion between units.
### Given values:
- Initial Pressure (P₁): 1.33 atm
- Initial Volume (V₁): 0.255 liters (255 milliliters converted to liters)
- Initial Temperature (T₁): 25°C (which needs to be converted to Kelvin, T = 25 + 273.15 = 298.15 K)
- Final Pressure (P₆): 796 torr (which needs to be converted to atm, 796/760 ≈ 1.0474 atm)
- Final Temperature (T₂): 25°C (also 298.15 K, because temperature remains the same)
### Step-by-Step Solution:
1. Convert all given units to the proper units used in gas law calculations (Pressure in atm, Volume in liters, Temperature in Kelvin).
- Initial Pressure (P₁): Already in atm (1.33 atm)
- Initial Volume (V₁): Already in liters (0.255 L)
- Initial Temperature (T₁): 25°C converted to Kelvin (298.15 K)
- Final Pressure (P₂): 796 torr converted to atm (796/760 ≈ 1.0474 atm)
- Final Temperature (T₂): 25°C converted to Kelvin (298.15 K)
2. Use the Ideal Gas Law relation for two sets of conditions:
[tex]\[
\frac{P₁ \cdot V₁}{T₁} = \frac{P₂ \cdot V₂}{T₂}
\][/tex]
3. Rearrange the equation to solve for V₂ (final volume):
[tex]\[
V₂ = \frac{P₁ \cdot V₁ \cdot T₂}{P₂ \cdot T₁}
\][/tex]
4. Substitute in the known values:
[tex]\[
V₂ = \frac{1.33 \cdot 0.255 \cdot 298.15}{1.0474 \cdot 298.15}
\][/tex]
(Since T₁ = T₂, the temperature values will cancel out in the division.)
5. Simplify the equation:
[tex]\[
V₂ = \frac{1.33 \cdot 0.255}{1.0474}
\][/tex]
6. Calculate the result:
[tex]\[
V₂ ≈ \frac{0.33915}{1.0474} \approx 0.3238 \text{ liters}
\][/tex]
### Conclusion:
The volume of dry hydrogen gas released would be approximately 0.324 liters. Therefore, the closest answer from the options provided:
0.325 L
This result matches the solution and confirms our step-by-step calculations.
