A sample of a gas in a piston/cyclinder apparatus occupies 41.8 mL at 1.37 atm and 21.5°C. If the volume of the sample is increased to 66.9 mL and the temperature changes to 44.6°C, what is the new pressure, in atm, of the sample? Enter your answer with three decimal places and no units.

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Alleei Alleei · Answer 1 · 2019-12-13T06:34:42+01:00

Answer : The new pressure of sample in atm is, 0.923

Explanation :

Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law.

The combined gas equation is,

[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]

where,

[tex]P_1[/tex] = initial pressure of gas = 1.37 atm

[tex]P_2[/tex] = final pressure of gas = ?

[tex]V_1[/tex] = initial volume of gas = 41.8 mL

[tex]V_2[/tex] = final volume of gas = 66.9 mL

[tex]T_1[/tex] = initial temperature of gas = [tex]21.5^oC=273+21.5=294.5K[/tex]

[tex]T_2[/tex] = final temperature of gas = [tex]44.6^oC=273+44.6=317.6K[/tex]

Now put all the given values in the above equation, we get:

[tex]\frac{1.37atm\times 41.8mL}{294.5K}=\frac{P_2\times 66.9mL}{317.6K}[/tex]

[tex]P_2=0.923atm[/tex]

Therefore, the new pressure of sample in atm is, 0.923