Concept:This requires the use of the combined gas law, which deals with changes in all three variables: pressure, volume, and temperature.
Formula:$$ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} $$
Solution:- First, always convert temperatures to Kelvin by adding 273.
- Initial state: \( P_1 = 1 \text{ atm} \), \( V_1 = 1 \text{ dm}^3 \), \( T_1 = 25 + 273 = 298 \text{ K} \).
- Final state: \( P_2 = 2 \text{ atm} \), \( V_2 = ? \), \( T_2 = 50 + 273 = 323 \text{ K} \).
- Substitute into the formula: \( \frac{1 \times 1}{298} = \frac{2 \times V_2}{323} \).
- Rearrange to solve for \( V_2 \): \( V_2 = \frac{323}{298 \times 2} \).
- \( V_2 = \frac{323}{596} \approx 0.5419 \text{ dm}^3 \).
Why other options are incorrect:- Option B: This would be the answer if only temperature doubled in Kelvin and pressure was constant, which isn't the case here.
- Options C & D: These numbers are too large; since pressure doubled and temperature only increased slightly (in Kelvin), the volume must decrease significantly.
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