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A 0.286 g sample of carbon dioxide, CO 2 , has a volume of 565 mL...

A 0.286 g sample of carbon dioxide, CO 2 , has a volume of 565 mL and a pressure of 455 mmHg . What is the temperature, in kelvins and degrees Celsius, of the gas? Part A What is the temperature, in degrees Celsius, of the gas? Part B What is the temperature, in kelvins, of the gas?

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Answer #1

Following is the - complete Answer -&- Explanation: for the given: Question: in....typed format...

\RightarrowAnswer(s):

  1. part - ( A ) : Temperature of the gas ( CO2 ) in oC : T = 361.03  oC  ( deg. C )
  2. part - ( B ) : Temperature of the gas ( CO2 ) in Kelvin : T = 634.18 K ( Kelvin )

\RightarrowExplanation:

Following is the complete Explanation: for the above: Answer(s).

  • Given:
  1. ​​​​Mass of carbon di-oxide : CO2 = 0.286 g  ( grams )
  2. Volume of carbon di-oxide : CO2 = 565.0 mL = 0.565 L ( Liters )
  3. Pressure of the system: Psys = 455 mmHg = 455 Torr .
  4. We know: value of Ideal Gas Constant: R = 62.364 L. Torr / mol-1 . K-1  
  5. We know: molar mass of  CO2 = 44.01 g/mol  
  • ​​​​​​​Step - 1:

​​​​​​​Using the above stated: molar mass: of carbon di-oxide ; CO2, and the above stated mass of CO2, we will get the following :

\Rightarrow  Moles of CO2 : nco2 =   ( mass of CO2 ) / ( molar mass of CO2 ) = ( 0.286 g ) / ( 44.01 g/mol )

=  0.0065 mol ( moles, approx. )

  • Step - 2:

​​​​​​​We can use the Ideal Gas Law: to determine the value of temperature : of the gas: i.e. CO2  ....

\Rightarrow Ideal Gas Law:   P x V = n x R x T   -----------------------------Equation - 1

\RightarrowWhere:

  1. P = Pressure = 455.0 Torr , in this case ..
  2. V =  Volume = 0.565 L ( Liters )
  3. n =  Number of moles ( i.e. here nco2 =  0.0065 mol )
  4. R =   Ideal Gas constant =  62.364 L. Torr / mol-1 . K-1  
  5. T = Temperature of the system , in Kelvin ( unknown , in the given case )
  • ​​​​​​​Step - 3:

​​​​​​​We know:

\Rightarrow Ideal Gas Law:   P x V = n x R x T   -----------------------------Equation - 1

Plugging in values, in Equation - 1: we will get the following:

\RightarrowT = P x V /   ( n x R )  

\RightarrowT = [( 455.0 Torr ) x ( 0.565 L ) ] / [ ( 0.0065 mol ) x ( 62.364 L. Torr / ( mol. K ) ) ] = 634.18 K ( Kelvin )

\Rightarrow Therefore:  T = 634.18 K = ( 634.18 - 273.15 ) = 361.03  oC

Therefore: we will get the following: answer(s):

\Rightarrow Part - (B): Temperature of the gas ( CO2 ) in Kelvin : T = 634.18 K ( Kelvin )

AND:

\RightarrowPart - ( A ):  Temperature of the gas ( CO2 ) in oC : T = 361.03  oC  ( deg. C )

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