Question

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?

Answer 1

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

$\Rightarrow$Answer(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 )

$\Rightarrow$Explanation:

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: P_sys = 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 : n_co2 =   ( 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

$\Rightarrow$Where:

1. P = Pressure = 455.0 Torr , in this case ..
2. V =  Volume = 0.565 L ( Liters )
3. n =  Number of moles ( i.e. here n_co2 =  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:

$\Rightarrow$T = P x V /   ( n x R )  

$\Rightarrow$T = [( 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:

$\Rightarrow$Part - ( A ):  Temperature of the gas ( CO₂ ) in ^oC : T = 361.03  ^oC  ( deg. C )