A gas of certain mass occupies volume of 1.2 L at 37°C and 3 atm. At what temperature will the volume and pressure of this gas become one-th

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A gas of certain mass occupies volume of 1.2 L at 37°C and 3 atm. At what temperature will the volume and pressure of this gas become one-third of their initial values?​

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Verity 3 years 2021-08-28T16:47:28+00:00 1 Answers 50 views 0

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    2021-08-28T16:48:53+00:00

    Answer: At a temperature of 34.44 K the volume and pressure of this gas become one-third of their initial values.

    Explanation:

    Given : V_{1} = 1.2 L,        T_{1} = 37^{o}C = (37 + 273) K = 310 K

    P_{1} = 3 atm,                  V_{2} = \frac{1.2}{3} = 0.4 L ,      P_{2} = \frac{3}{3} = 1 atm

    Formula used to calculate the final temperature is as follows.

    \frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}

    Substitute the values into above formula as follows.

    \frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}\\\frac{3 atm \times 1.2 L}{310 K} = \frac{1 atm \times 0.4 L}{T_{2}}\\T_{2} = \frac{1 atm \times 0.4 L \times 310 K}{3 atm \times 1.2 L}\\= \frac{124}{3.6} K\\= 34.44 K

    Thus, we can conclude that the final temperature is 34.44 K.

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