The volume of 250 mL of gas at 22°C is increased to 740 mL at constant pressure. What is the final temperature of the gas?Group of answer choices600 °C400 °C200 °C800 °C
Question
The volume of 250 mL of gas at 22°C is increased to 740 mL at constant pressure. What is the final temperature of the gas?Group of answer choices600 °C400 °C200 °C800 °C
Solution
To solve this problem, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin, provided the pressure is constant. The formula for Charles's Law is V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
Step 1: Convert all temperatures to Kelvin. The initial temperature is 22°C, which is 295.15 K (since Kelvin = Celsius + 273.15).
Step 2: Substitute the given values into the formula. We have V1 = 250 mL, T1 = 295.15 K, and V2 = 740 mL. We're solving for T2, the final temperature.
So, 250/295.15 = 740/T2.
Step 3: Solve for T2. Cross-multiplying gives us T2 = (740 * 295.15) / 250 = 876.22 K.
Step 4: Convert the final temperature back to Celsius. T2 = 876.22 - 273.15 = 603.07°C.
So, the final temperature of the gas is approximately 600°C.
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