a 2-L gas sample at 20°C. is cooled until it occupies a volume of 520ml.what is ...

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September 2022 1 0 Report

a 2-L gas sample at 20°C. is cooled until it occupies a volume of 520ml.what is the new temperature of gas ? express your answer in°C

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GreatRedSpot

SOLUTION:

Step 1: List the given values.

To convert the temperature from degree Celsius to kelvin, add 273 to the temperature expressed in degree Celsius.

$\begin{aligned} & V_1 = \text{2 L} \\ & T_1 = 20^{\circ}\text{C} = \text{293 K} \\ & V_2 = \text{520 mL = 0.52 L} \end{aligned}$

Step 2: Calculate the final temperature (in degree Celsius) by using Charles' law.

To convert the temperature from kelvin to degree Celsius, subtract 273 from the temperature expressed in kelvin

$\begin{aligned} T_2 & = \frac{T_1V_2}{V_1} \\ & = \frac{(\text{293 K})(\text{0.52 L})}{\text{2 L}} \\ & = \text{76.18 K} \\ & = -196.82^{\circ}\text{C} \\ & \approx \boxed{-197^{\circ}\text{C}} \end{aligned}$

Hence, the new temperature of a gas is -197°C.

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