A sample of gas occupies 100 ml at 27oC and 740 mm pressure. When its volume is changed to 80 ml at — States of Matter and Gaseous State Chemistry Question
Question
A sample of gas occupies 100 ml at 27oC and 740 mm pressure. When its volume is changed to 80 ml at 740 mm pressure, the temperature of the gas will be
💡 Solution & Explanation
# Gas Law Problem Solution **Given Information:** - Initial: $V_1 = 100$ ml, $T_1 = 27°C = 300$ K, $P_1 = 740$ mm - Final: $V_2 = 80$ ml, $T_2 = ?$, $P_2 = 740$ mm **Step 1: Identify the applicable law** Since pressure remains constant ($P_1 = P_2$), this is an **isobaric process**. Use Charles's Law: $$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$ **Step 2: Substitute values** $$\frac{100}{300} = \frac{80}{T_2}$$ **Step 3: Solve for $T_2$** $$T_2 = \frac{80 \times 300}{100} = \frac{24000}{100} = 240 \text{ K}$$ **Step 4: Convert to Celsius** $$T_2 = 240 - 273 = -33°C$$ **Answer:** The final temperature is **240 K or –33°C** (option C) The volume decreased proportionally, so temperature must also decrease proportionally at constant pressure, confirming our result.